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1. Memorial University of Newfoundland Department of Mathematics and Statistics Applied Mathematics 2130 Technical Writing in Mathematics Course Outline and Manual 2009 Department of Mathematics and Statistics The revised Winter 2009 edition was prepared by Sergey Sadov in collaboration with Danny Dyer and Ivan Booth and with the technical assistance of Karen Williams and Melissa Roberts Changes in the Fall 2009 edition include Section 2 4 and Index added by Sergey Sadov and numerous small corrections Previous contributors to this Manual include the Instructors of Applied Mathematics 2130 from the Department of Mathematics and Statistics at Memorial University of Newfoundland 1994 2007 As well there are technical contributions from the systems personnel at the Depart ment of Computer Science and external contributions reproduced with permission from David Goss Ohio State University Steven Kleiman MIT Gavin Maltby University of Natal and Glenn Tesler MIT Printing and Binding by MUN Printing Services MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Contents 1 Introduction 1 1 1 The course and this Mamual 20 00 0000 00 eee ee es 1 112 Sub MISSIONS n ws da a a a lt des ral dt Co ind ade 2 1 37 Policies hoi a Reo ey in de Be Ree A ad le i 2 LSL Pivaluation tr BOR hoe a hk ets Ree Ge ace ln BS 2 1 3 2 Academic integrity and a
2. text within it 73 solving with Maple 89 equation usage of word 21 evaluation 2 of contents 2 of presentation 3 errors in ATEX source code 30 36 excuses 3 4 extensions of file names dvi 30 eps 97 log 30 pdf 30 tex 30 flow control 16 footers 25 35 font size 45 fonts use of 143 150 commands for 45 forge of results 4 formulas 146 in LaTeX see equation fractions 72 functions typesetting in TAT X 74 goal see purpose going off on tangents 8 Google 14 grade see marks headers running in LaTeX 35 headings 10 25 self explanatory 11 homothety 12 horizontal line 58 Ivs We 22 145 illustrations 146 indentation in ATRX 27 in programming 83 inequality usage of word 21 strict vs non strict 82 information sources of 5 informativeness 11 144 inline math 28 instructor see professor Internet citation of websites 19 credibility of information 5 improper use of 4 14 interview 2 Introduction 11 13 142 isometry 12 italic correction 46 jargon 145 Java programming language 17 Kile editor with integrated TX 30 127 Knuth Donald 40 laboratory assistant 4 Lamport Leslie 30 language of a technical paper 21 143 variety of 146 law see pattern late submissions 2 TAT X 40 TEX packages 24 layout commands 24 Lemma 150 letters Greek 65 calligraphic uppercase 66 ligatures 48
3. utilize and implement they offer no precision clarity or continuity and smack of pseudo intellectualism Beware of words like interface they are precise in some contexts yet imprecise and pretentious in others Jargon is vocabulary particular to a certain group and it consists of abbreviations and slang terms Jargon is not inherently bad Indeed it is useful in internal memos and reports However jargon alienates external readers and may even mislead them So beware Cliches are figurative expressions that have been overused and have taken on undesirable connotations Most are imprecise and unclear Avoid them or be laughed at In addition avoid numerals because they slow down the reading Write numbers out if they can be expressed in one or two words and are used as adjectives unless they are accompanied by units a percentage sign or a monetary sign For instance write The equation has two roots and One root is 2 Do not begin a sentence with a numeral or a symbol reformulate the sentence if necessary Be forthright write in an unhesitating straightforward and friendly style ridding your language of needless and bewildering formality Beware of awkward and inefficient passive constructions Often the passive voice is used simply to avoid the first person However the pronoun we is now generally considered acceptable in contexts where it means the author and reader together or the author with t
4. The library plots also makes available plotting multiple graphs on the same picture Each graph plot can be created separately then all of them are submitted at once to the display command When creating the individual plots use colon as a terminator otherwise Maple will spit out the long and nasty internal representation of a plot Example the following commands produce the plot identical to Figure 4 7 save for a label on the horizontal axis gt sinplot plot 5 3 sin x x 0 2 PI color green gt cosplot plot 5 2 cos x x 0 2 PI color red gt display sinplot cosplot While in this case the two curves can be conveniently plotted together using just the regular plot command as on p 101 it is easily conceivable that individual plots can be too many or too complicated so that computing them separately and then using the display command can be the only practical option The following example showing an equilateral triangle together with its inscribed and circumscribed circles Fig 4 10 would be too cumbersome to describe by a single plot command gt triangle plot 1 0 1 2 sqrt 3 2 1 2 sqrt 3 2 1 0 color red gt circumcircle plot cos t sin t t 0 2 Pi color blue gt incircle plot cos t 2 sin t 2 t 0 2 Pi color green gt display triangle circumcircle incircle scaling constrained axes none Page 104 Chapter 4 Programming and graphing 4 3 Drawing graphs Figure 4
5. The special variant Page 135 Appendix A Quick UNIX reference A 6 Working with directories and files cd ur makes the user s home directory the current directory Thus if Lisa types cd the current directory becomes users math study lisa no matter what it was before The command Is will list the names of all the files in the current directory If you give it a directory name it will list the names of all the files in that directory If you give it a file name it will list that name which can be useful if you just want to check if such a file exists For our sample directory tree if the current directory was users math study and you ran Is it would display lumsden Is bob lisa The command Is l u name will give you a detailed information about a file or files The command Is a displays unlike the bare Is those files and directories whose names begin with a dot like the name www which often denotes the directory in user s account accessible from the Internet Wildcards can be used to specify a pattern that we want a file name or a directory name to match The most useful wildcard character is the asterisk which matches any even empty combination of characters The command Is xtex will display all files with names ending in tex The command Is xtexx will in addition display all files with names containing tex at the beginning or in the middle like text1 doc latexnotes etc The
6. begin verbatim In the verbatim environment we can type anything we like So we do not need to look out for uses of amp etc nor will control sequences like newline have any effect end verbatim will produce the simulated input text In the verbatim environment we can type anything we like So we do not need to look out for uses of amp etc nor will control sequences like newline have any effect The only thing that cannot be typed in the verbatim environment is the sequence end verbatim You might notice that I still managed to simulate that control sequence above One can always get what you want in TeX perhaps with a little creativity If we want only to simulate a few typed words such as when I say to use newline to start a new line then the verb command is used This command has a slightly odd syntax pressed upon it by the use for which it was intended It cannot accept an argument because we may want to simulate typed text that is enclosed by braces What one does is to choose any character that is not in the text to be simulated and use a pair of these characters as argument delimiters I usually use the or characters as I rarely have any other uses for them Thus use to obtain a sign is typed as use verb to obtain a sign or use verb to obtain a sign Page 55 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends itemize enum
7. e 2 Sle a Rae A eR A ee ek Ee 141 Contents 3 Lanus Do ae Bk Tae e A y 143 4 Mathematics s o sr dice hae le ee ee a ne ees Pak ees 146 5 Example ros ara pea GUL Mews OE oie aa 148 Appendix Advanced mathematics 0 20 00004 150 B 2 Some Hints on Mathematical Style D Goss oo 152 Index 155 Page iv Chapter 1 Introduction 1 1 The course and this Manual The purpose of this course is to teach technical writing You will learn about typical require ments for research and technical papers and about some computer typesetting and graphical tools used to produce technical reports of professional quality You will be offered four projects laboratories to work on In those projects you will have to carry out a mathematical investigation of the given problem or situation to perform computer simulations to produce illustrations and to write a report A schedule for the four projects will be handed out on the first day of classes along with a description of the first laboratory Laboratories 2 to 4 will be made available as the course progresses All documents related to the course including the most recent version of this Manual will be available on the course web page http www math mun ca m2130 Three major topics that you will be mastering in this course and the corresponding chapters in this Manual are e Composition of technical mathematics intense papers Ch 2 e LATEX types
8. end thebibliography Don t forget to provide a numerical argument in thebibliography line It does not nec essarily be equal to the actual number of references it must just have the same decimal length like in our example 3 references and the number is 4 both are single digit numbers In the absence of the numerical argument TEX often gives a misleading information as to where the error is 3 2 6 Appendix and program source Use the section command for appendices Section 3 1 9 explains how to include the source code of your program in the report It is not always necessary A little note for those who needs to include a Maple code in the report in our experience the quickest way that does not compromise on typographical quality is simply to copy and paste the lines from Maple worksheet into the TFX file line by line Maple programs at least those in Math 2130 projects are usually rather compact Maple s numerical outputs can also be Page 36 Chapter 3 Typesetting with ATRX 3 2 Formatting your Math 2130 report in ATEX copied and pasted unless they contain exponents In the latter case please take a trouble to type the answer properly in the IATFX math mode for example 6 67 x 1071 If there are too many such numbers to type think about summarizing them in a table rather than just copying Maple s symbolic answers when copied into a text file are difficult to read Again if the answer is important so you ar
9. o umlaut or dieresis t oo o tie after accent o tilde or squiggle c o Q cedilla accent o macron or bar d o dot under accent o 6 dot accent b o o bar under accent Table 3 1 Control sequences for accents Thus we can produce by typing fo by typing v a and Pal Erd s by typing P a 1 Erd o s Take special care when accenting an i or a j for they should lose their dots when accented Use the control words i and j to produce dotless versions of these letters Thus the best way to type to type xigent is u e x uf ilgent Page 44 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends 3 3 4 Formatting Font commands We have seen a little of how to access various symbols using control sequences and we mentioned the em command to emphasize text but we did not see how to use them We look here at commands that change the appearance of the text Each of the control words here is a directive rather than a control sequence that accepts an argument This is because potential arguments consisting of text that wants to be emboldened or emphasized are very large and it would be a nuisance to have to enclose such an argument in argument enclosing braces To delimit the area of text over which one of these commands has effect its scope we make that text into what is called a group Groups are used extensively in ATEX to keep effects local
10. remove a directory pwd display the current directory man subject display the UNIX manual for the subject can be used to find out details about a command s syntax Ipq and Iprm request ID Ipq can be used to obtain a listing of the jobs in the printer queue waiting to be executed If by misfortune you have asked to print a document and suddenly wish to cancel the print job use Ipq to obtain the request ID number associated with your printing job and remove it from the printer queue with the command Iprm request ID A 6 Working with directories and files You change your current directory with the cd command cd takes one argument the pathname of the directory you want to change to For example the command lumsden cd users math study makes users math study the current directory In this case an absolute pathname was used which isn t a common practice for ordinary users Much more practically useful are relative pathnames You must of course know what your current directory is If not sure use the pwd command For instance if the current directory is users math study bob m2130 lab1 then typing pwd you get system s response Current directory is users math study bob m2130 lab1 Now typing cd will make users math study bob m2130 the current directory Note that if the user Bob types cd users math study lisa the system will reject this command as Bob is not authorized to access Lisa s home directory
11. 200 200 lineto 200 125 lineto stroke Second triangle filled 0 8 setgray newpath 200 0 moveto 275 0 lineto 275 100 lineto 200 0 lineto fill showpage Figure 4 1 A simple Postscript program and its effect You can immediately open the file triangles ps with Postscript viewer Ghostview gv triangles ps You can now insert the picture to a ATFX document A conversion to eps is required but if you want a quick try just replace the first line 4 PS Adobe 2 0 in the file by two other lines 4 PS Adobe 3 0 EPSF 3 0 ApBoundingBox 198 0 303 202 Save the file as triangles eps You can now type the line includegraphics triangles in a ATFX document and the picture will be inserted To put the triangles beside the Postscript program on Figure 4 1 we used a superimposition trick described in Section 4 4 4 Page 98 Chapter 4 Programming and graphing 4 3 Drawing graphs 4 3 2 Maple graphics Maple has versatile plotting capabilities They are realized by means of two basic commands plot plot3d and more functions provided by the plots package We will illustrate the usefulness of these commands with very basic examples To get a more elaborate description of plots and their options use Maple s Help and other available sources We begin with a graph of the function y sing on a specified interval 15 15 The formula does not make sense when x 0 but the limit of y as x 0 exists Setting y 1 when x 0
12. when the proof is in the paper and the statements can be rewritten to be directly quoted A well known result that is not in the literature should be proved if needed Rule 1 Proof A proof should give enough information to make the theorem believable and leave the reader with the confidence as well as the ability to fill in details should it be necessary Rule 1 e Other comments One should of course observe the usual conventions in terms of spelling punctu ation and the other basic elements of style Use complete sentences with subject verb and complement Rule 1 x A verb should not be replaced by a symbol It is bad to write if x 2 y 3 z 4 meaning if x 2 and y 3 then z is equal to 4 x It is also bad to write we prove Cq 2n 12 Q instead of we prove 2n that sq 2n belongs to Q or is rational T Use the present not the past form x As an example of bad writing we have We have proved that f x was equal to g x This is corrected to We have proved that f x is equal to g z Long computations that can easily be carried out by the reader should be avoided The ideas and results should be given with an invitation to the reader to do the calculation should it be desired Rule 1 The exception to this rule is when the long computation is an essential part of the argument In this case it should be g
13. 2 4 24 24 gt plot X MATT TATTOO TT NT TATTOO 2 1 0 al 2 Figure 4 5 Maple s graphs defined by an array of coordinate pairs Maple can plot parametric curves In the following example we equalize the x and y scales using the option scaling constrained Without this option the graph which is an ellipse Fig 4 6 would look like a circle gt plot 5 2 cos t 5 3 sin t t 0 2 Pi scaling constrained Attention A slight syntactic alteration of the command moving the bracket com pletely changes the picture instead of a parametric curve we obtain two curves on the same graph Fig 4 7 with t being the independent variable instead of being a parameter The option scaling constrained is unimportant in this example and omitted gt plot 5 2 cos t 5 3 sin t t 0 2 Pi Page 101 Chapter 4 Programming and graphing 4 3 Drawing graphs 5 5 Figure 4 6 An ellipse described parametrically x z Cos t y 3 sint crear AD 5 5 Figure 4 7 Curves y cost and y zint in the t y axes Page 102 Chapter 4 Programming and graphing 4 3 Drawing graphs Here is an example of a 3D graph Compare Maple s graph with Gnuplot s Fig 4 12 D gt F sin x 2 y72 x 2 y72 Eos sin x y x2 y gt plot3d F x 3 3 y 3 3 Figure 4 8 The default is not to show the axes However they can be added gt plot3d F x 3 3 y 3 3 axe
14. Appendix 19 36 audience see readership automatic numbering and referencing 37 60 backward spacing 27 balance of section sizes 13 14 banality see triviality bibliography 19 blank line in TFX 26 64 body of 2130 report 10 of ATFX document 24 of a mathematical paper 142 bounding box 97 98 128 braces 41 63 Calendar MUN 4 Chicago Manual of Style 19 citation see References clarity 7 9 144 collaboration 4 comments in TEX 25 compilers 80 127 complete sentences 153 Conclusion 13 conformance to standards 3 consistency 22 83 of notation 147 control symbols and words LATEX 42 converting ps file to eps 128 Corollary 150 correctness of program 4 17 cycloids 106 dash 50 63 data file 17 automatic generation 84 producing graphics from 98 101 109 data type int vs double 17 debugging 81 definitions 5 12 14 145 150 152 degree symbol in BTEX see circ delimiters scaleable in TEX 68 details see particulars disambiguation 14 discontinuity handling by Maple 101 displayed math 28 draft 9 efficiency of code 18 editing 9 editors with integrated T X30 electronic submission 2 37 113 123 ellipsis 73 emphasis in TAT X 43 MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Index encapsulated Postscript 97 environments in AT RX 25 52 floating 37 60 equation in ATEX 28
15. Contents 3 Typesetting with TX 24 3 1 Elements of ATEX e 24 Sul l Preamble G0 a Sauk bh be Oi we owe th be ae ph Lie e 24 312 Comments ri A ee ee ee eh a Se Re ee na 25 3 1 3 Environments 00 cr pe a oe ae 25 QL AS Space eV BG Sele ele EU a Se ee ee Pes 26 3 1 5 Math mode so s sosa he A Ee es 28 IKO DisS ee oA A OA aa ee te a band 29 3 1 7 Advanced math typesetting 2 2 0 0 00 eee eee 30 3 1 8 Processing and viewing MTRX files o 30 3 1 9 Including source code in IXATEX documents o o 31 3 1 10 Some commands defined in 2130 sty o 33 3 2 Formatting your Math 2130 report in ATEX o 34 3 2 1 Title page footers and headers e 34 3 2 2 Table of contents ee ee 35 3 2 3 Abstracth 08 aa ab eA ed ee E ae ee eo a ee aes 35 32 4 The body of report 2 5 82 ae A we ee eh eS 36 3 20 References tao dt nese ee ode E Re de Be a a eS 36 3 2 6 Appendix and program source 2 2 ee ee 36 3 2 7 Floating environments figures and tables 37 3 2 8 Automatic numbering cross references and citations 37 3 3 An introduction to T X and friends G Maltby 38 3 3 1 An Introduction to TEX 2 200 000 00 2 ee ee 38 3 3 2 A review of ATER seis age goa urg Ee eG ee ee G D 40 3 3 9 Special symbols eon ee a RG E eee a a a Al 94 gt Fo
16. RADA 8 gt Eigenvalues A 5 v33 Ls vas gt EValVec Eigenvectors A 4 4 EValVec megs 34 733 34733 5 v33 1 1 Note that the Eigenvectors command return the eigenvalues as well as the eigenvectors We can select the matrix comprised of the eigenvectors gt EVec EValVec 2 Page 93 Chapter 4 Programming and graphing 4 2 An introduction to Maple 4 4 EVec 34 V33 3 v33 1 1 Now if we want to separate the eigenvectors from one another and to make an array of them the following command will do it gt EVecArray seq Column EVec i i 1 2 4 4 EVecArray 3 V33 3 V33 1 1 Matrix multiplication and dot product of vectors are denoted by a single dot period gt B Matrix 2 0 31 1 2 111 2 0 3 mR ra i gt A B 8 8 2 20 16 10 An attempt to multiply matrices when dimensions don t match leads to an error message gt B A Error in MatrixMatrixMultiply first matrix column dimension 3 lt gt second matrix row dimension 2 4 2 6 Programming Maple can be used for programming It allows conditionals loops and user defined functions Compared to languages such as FORTRAN or C programming in Maple is more convenient there is no need to bother about input output operations and data types commands can be executed immediately and you have access to all of the built in commands and available packages The price to pay is efficiency Maple run
17. This name specifies the path you must travel through the tree to reach the file The full name of a file as understood by the system is the pathname from the root directory A full name begins with an initial slash with further slashes separating each directory name The actual name of the file by which it is known to its owner is the part of the pathname after the final slash For example the full pathname of the directory bob in the above example is users math study bob Note that UNIX is different from Microsoft Windows where the backslash is the sepa rator for pathnames and the top level directory is the drive name for example C Along with absolute pathnames just described there are relative pathnames They describe how you reach the required file or directory from the current directory Sometimes you may have to go up the reversed tree towards the root The directory one level higher the current directory is denoted double dot Thus the relative pathname from Bob s directory lab1 to his directory cs1510 is cs1510 In the same situation the pathname lab1 points at the directory we are in The standard way to refer to a directory from itself is by the relative pathname the dot directory means stay here Obviously in practice if a file is in the current directory you just call it by its name A 4 Shell While a graphical user interface is available for most modern programs it doesn
18. Thus log theta produces the perfect log 0 Table 3 13 shows various log like functions that are available and some examples of their use Notice how TEX does more than just set an operation like sup in roman type It also knew where a subscript to that operator should go 1 arccos cos csc NMexp ker limsup min Asinh Narcsin cosh deg gcd Mg 1n Pr sup arctan cot det hom lim log sec tan arg coth dim inf liminf max sin tanh Table 3 13 Log like functions Type To produce f x sin x log x72 f z sin x log a delta min delta_1 delta_2 min 91 62 chi X sup_ x in X chi x x X supzex x x lim_ n rightarrow infty S_n gamma limn x Sn Y Page 74 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Over and Underlining and bracing The underline command will place an unbroken line under its argument and the overline command will place an unbroken line over its argument These two commands can also be used in normal paragraphing mode but be careful TAT X will not break the line within an under or overlined phrase so do not go operating on large phrases You can place horizontal braces above or below an expression by making that expression the argument of overbrace or underbrace You can place a label on an overbrace resp underbrace by superscripting resp subscripting the group defined by the bracing command
19. and to to get quotes like this we type repeated and characters Note that modern convention is that punctuation comes after the closing quote character Page 49 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends Very rarely you have three quote characters together Merely typing those three quote characters one after the other is ambiguous how should they be grouped You tell ATEX how you want them grouped by inserting a very small space called a thin space and invoked with Ny NX Green ham or Eggs is the question gives the desired result Green ham or Eggs is the question Since we have a typesetter at our disposal we might as well use the correct dashes where we need them There are three types of dash the hyphen the en dash and the em dash A minus sign is not a dash Hyphens are typed as you would hope just by typing a at the point in the word that you want a hyphen Do not forget that IATFX takes care of hyphenation that is required to produce pretty linebreaks You only type a hyphen when you explicitly want one to appear as in a combination like inter college An en dash is the correct dash to use in indicating number ranges as in questions 1 3 To specify an en dash you type two consecutive dashes on the keyboard as in 1 3 An em dash is a punctuation dash used at the end of a sentence I tend to use them too mu
20. earlier in your document and PTFX will stop exactly there Everything that follows will be ignored This is a convenient method to find and fix errors in long documents 3 1 3 Environments The following construction very common in TFX is called an environment begin something end something Page 25 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX In this case we deal with a nonexistent something environment The whole document is an environment by itself Some common environments are displaymath equation tabular picture table figure center thebibliography itemize enumerate verbatim 3 1 4 Space TeX regards one return or enter one or more tabs and one or more blank spaces as equivalent to one space An exception to this rule is presented by the spaces within the verb command and the verbatim environment Paragraphs There are two ways to start a new paragraph 1 The usual simplest way is to leave a blank line in your text 2 Use the command par Line breaks You may force IATFX to start a new line within the current paragraph by means of the command double backslash The current line ends immediately at the same position as if the paragraph had ended The command is routinely used as a separator between lines in tables and arrays multi line formulas in math mode Another seemingly similar command is linebreak However it is rarely used
21. equivalently a particular substitution can be made into it A computer program can implement a method or an algorithm it is created or written by you to obtain produce results you run or execute it the results are presented or displayed in tables and graphs A value can be assigned to a variable or a variable can be assigned a value Also a value can be given in a closed form as a mathematical expression that does not involve an approxi mation e g v2 or arctan 1 3 or approximately as a decimal fraction e g 1 414 for V2 Page 21 Chapter 2 Technical writing 2 4 Suggestions about style An expression a sum an integral but not an equation can be evaluated calculated com puted also it can be transformed into an equivalent form expanded factored simplified reduced to a simpler form in a special particular case broken into two or more parts usually to reveal an essential structure But do not solve a sum A new concept or notation can be introduced defined or described in a manner of this sort let us say that X is an explanation in terms of known or previously defined terms follows 2 4 5 We versus I Whether you should write in the 1st person we or J or in the 3rd person is to a large extent a matter of choice and personal style It is more common to use J in the Introduction and Conclusion only if at all If you are bold enough to use Jin the main part of your paper do so
22. line break 26 51 line spacing 24 listing printout of program 20 lists in ATEX 29 logic of exposition 14 logic of program 16 Page 156 Index Maltby Gavin 27 30 Maple computer algebra system 87 LTRXing output 36 reserved names 88 programming 94 graphics 99 math mode in LATEX 28 61 Mathematical details 14 matrix typesetting of 76 margins 24 marks 2 5 18 method 14 methodology 14 MIT s writing requirements 139 modal verbs 23 notation 14 in mathematics vs in programming lan guage 15 numbered equations 28 referring to 37 numbers writing out 145 open ended project 18 packages in ATEX 41 paragraph in ATEX 26 paragraph mode in TEX 27 61 parameters large and small 15 particulars 10 14 partition of an integer 12 13 16 pattern 18 penalty for lateness 2 4 for plagiarism 5 for spelling errors 20 percent sign 25 41 plagiarism 4 plan of a paper 7 8 point 1pt typographical 27 preamble of TAT X document 24 40 precision of language 7 14 144 prime in ATEX 72 professor instructor 2 4 6 8 14 17 Program details 14 15 programming style 16 83 programs compilers C C FORTRAN Java 127 dvips 126 dvipdf 30 126 Gnuplot 107 gv GhostView 98 126 kile 127 latex 30 lgrind 31 pdflatex 126 xdvi 30 126 xfig 112 pronouns 144 proof of a theorem 147 14
23. no record remains of the ultimate parameters Hence the instructor may not be in position to tell how exactly your graph was generated based on the Maple worksheet you would submit electronically Of course if you fully document any manipulations then these restriction will not apply Page 106 Chapter 4 Programming and graphing 4 3 Drawing graphs 4 3 3 Gnuplot Gnuplot used to be thought of as a UNIX command line utility and it still is but now it is also available for Windows with a handy clickable menu It is a freely distributed software Gnuplot can display graphs on a computer screen and save them as files of various graphics types The kind of output display device is described by the parameter terminal of Gnuplot s set command The program is controlled by user s commands typed in the command line several com mands can be put together into a file to form a re usable script Gnuplot can handle two dimensional and three dimensional data and graphs It automat ically changes line styles when several curves are plotted It automatically produces a legend for each curve and permits the user to include such things as arrows and mathematical text anywhere on the graph Gnuplot is somewhat clumsy to use even with the simplest of data because of much typing necessary In exchange it provides a lot of flexibility in regard to line styles labeling and such perhaps significantly more than Maple It is also a very straightf
24. p q to allow for vertical lines given by 0 1 or 0 1 depending on the direction Another complication in the syntax of a line segment which is given by line p q len is that len refers not to the length on the line but to its projection in the x direction unless of course it is vertical when len means the vertical length Even worse each line segment must be put somewhere with a put command of the form put a b line p q len You can see that the simple process of drawing a straight line is quite complicated 4 4 3 Enhanced Pictures However help is at hand with enhanced picture styles Since you will have started almost every document for this course with documentclass article usepackage 2130 it makes sense to learn a few new commands available in the picture environment The join command The most useful command is Xjoin x1 y1 x2 y2 This draws a straight line from x1 y1 to x2 y2 Already you can see an advantage over the standard line command The restrictions on slope no longer apply Even better by using join x1 y1 x2 y2 x3 y3 we get a straight line from x1 y1 to x2 y2 followed by a straight line from x2 y2 to x3 y3 By doing this successively with the points sufficiently close together we can draw curves So you must first calculate the appropriate data set for the curve see Sect 4 1 3 The computed data set can be either pasted into the tex file or
25. precision It identifies the subject precisely and instills interest in it by giving details that did not fit into the title or abstract such as how the subject arose and where it is headed how it relates to other subjects and why it is important A strong introduction touches on all the significant points and no more A strong introduction gives enough background material for understanding the paper as a whole and no more Put background material pertinent to a particular section in that section weaving it unobtrusively into the text A strong introduction discusses the relevant literature citing a good survey or two Finally a strong introduction discusses the organization of the paper it summarizes the contents again but in more detail than in the abstract and it says what can be found in each section It gives a road map which indicates the route to be followed and the prominent features along the way This road map is placed at the end of the introduction to ease the transition into the next section The body discusses the various aspects of the subject individually In writing the body your hardest job is developing a strategy for parcelling out the information Every paper requires its own strategy which must be worked out by trial and error There are however a few guidelines First present the material in small digestible portions Second beware of jumping haphazardly from one detail to another and of illogically making some
26. 2 black 2 For comparison here is an equivalent more explicit Maple code for the same plot a 0 3 fx a xt sin t fy a l cos t pO plot 0 5 fx fy t Pi 9 Pi scaling constrained color red pi plot L fx 2 fy t Pi 5 Pi scaling constrained color blue p2 plot 2 fx 4 fy t Pi 3 Pi scaling constrained color black plots display p0 p1 p2 VVVV NM How to insert a Maple graph in a WTpX document First you have to save your graph as an Encapsulated Postscript file The simplest method is to right click on the graph you want to import and to save image as EPS file Alternatively especially if you have many pictures in your file a convenient way to save all of them at once is to click on menu File ExportAs and choose file type LaTeX If say the name of the Maple worksheet is cycloids mw then the name of the Maple created IATFX file is cycloids tex and the first plot will be saved as cycloidsplot1 eps the second plot if exists as cycloidsplot2 eps and so on As advised on page 87 ignore the TFX file that Maple creates but pick the companion eps files Once you have extracted an eps file or files from a Maple worksheet import them in your master IATFX file by means of the includegraphics command As a final remark we ask you not to include graphics modified via the pop up menu that appears when you right click on a picture While this menu provides convenient manipulations
27. 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX it is easy to lose a sign when typing a long formula a math environment is provided for such occasions you can use begin math and end math as the math shift instructions Of course you could just decide to use and take your chances Let us have a look at some mathematics LaTeX is normally in paragraphing mode where it expects to find the usual paragraph material Including a mathematical expression like 2x 3y 4 1 in the paragraph text is easy TeX has been taught to recognize the basic elements of an expression and typeset them appropriately choosing spacing positioning fonts and so on Typing the above expression without entering math mode produces the incorrect result 2x 3y 4 1 will produce the following paragraph I4TRX is normally in paragraphing mode where it expects to find the usual paragraph material Including a mathematical expression like 2x 3y 4 1 in the paragraph text is easy T X has been taught to recognize the basic elements of an expression and typeset them appropriately choosing spacing positioning fonts and so on Typing the above expression without entering math mode produces the incorrect result 2x 3y 4 1 Notice that TFX sets space around the binary relation and space around the binary operators and on the left hand side of the equation ignoring the spacing we typed in the input
28. It causes IXT X to stretch the current line to page width to compensate for the text that has been forced out to the next line ATRX may find the required stretch intolerable and deny the requested line break Vertical space LT X does a reasonable job of inserting space and turning up new pages Still there are times when the user would like to assert his her own influence The regular preferred method to add vertical space between paragraphs or figures is by using one of the three commands smallskip adds a little extra space to the regular space between lines medskip adds about twice that much bigskip adds yet about twice that much as medskip Page 26 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX The command vspace 1ex instructs ATEX to push the next line down by the height of a letter x in the current font size These commands ought to be given after a blank line in particular they should not be given within a paragraph otherwise the layout of your page may turn out to be rather odd The command vskip lex has the same effect in most cases however its use in MIX documents is now deprecated There are several allowed measures of length including inches in centimeters cm and millimeters mm and finally points pt which are the preferred unit to a typesetter There are 72 points to an inch Besides these absolute units the units relative to the current font size are often used ex see
29. It was also able to recognize that the 1 on the right hand side of the equation was a unary minus negating the 1 rather than being used to indicate subtraction and so did not put space around it It also italicized the variables x y and z However it did not italicize the number 1 In typing a mathematical expression we must remember to keep the following in mind 1 All letters that are not part of an argument to some control sequence will be italicized Arguments to control sequences will be set according to the definition of the command used So typing x gt 0 for x gt 1 will produce flee Of ora gt 1 instead of the expression fee for al that we intended Numerals and punctuation marks are set in normal roman type but IATRX will take care of the spacing around punctuation symbols as in f x y geq 0 which produces f x y 20 Page 62 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX 2 Even a single letter can constitute a formula as in the constant a To type this you enter a in your source file If you do not go in to math mode to type the symbol you will get things like the constant a 3 Some symbols have a different meaning when typed in math mode Not only do ordinary letters become variables but symbols such as and are now interpreted as mathematical symbols Thus in math mode is no longer considered a hyphen but as a minus sign 4 ATEX ignores all
30. This statement is remarkable because the two processes appear to be so different differentiation gives us the slope of a curve integration the area under the curve Here is a precise statement of the theorem Theorem 5 1 First Fundamental Theorem of Calculus Let f be a function defined and continuous on the closed interval a b and let c be in a b Then for each x in the open interval a b we have Ej tOa ta Proof Take a positive number h such that x h lt b Then f Te f f t dt ga By hypothesis f is continuous Hence there is some z in x x h for which this last integral is equal to h f z by the Mean Value Theorem for integrals 2 p 154 which is not hard to derive from the Intermediate Value Theorem The setup is shown in Figure 5 1 the Mean Value Theorem says that the area under the graph of f is equal to the area of the rectangle Therefore A n 7 f t dt f t de f z Now x lt z lt x h Hence as h approaches 0 the difference quotient on the left approaches f x A similar argument holds for negative h Thus the derivative of the integral exists and is equal to f x The proof is now complete The First Fundamental Theorem says that given a continuous function f there exists a function F namely F x f f t dt whose derivative is equal to f Page 148 Appendix B 1 Writing a Phase II Math Paper 5 Example ln t a c zzar h b gt Figure B 1 G
31. Type To produce overlinefat bi a bi a bi a bi overline overline atbi a bi at bi a bi And some examples of horizontal bracing A n overbrace A times A times ldots times A mbox n terms forall x underbrace exists y y succ x _ mbox scope of foral1 will produce n terms OT AAA A AxAx xA and Va dy y gt x __ gt scope of V Stacking symbols I4TRX allows you to set one symbol above another through the stackrel command This command accepts two arguments and sets the first centrally above the second Type To produce X stackrel f rightarrow Y X E Y 1 x stackrel triangle x 2 1 f x t41 Operators Sums Integrals etc Each of the operation symbols in table 3 11 can occur with limits They are specified as sub and superscripts to the operator and ATFX will position them appropriately In an in text formula they will appear in more or less the usual scripting positions but in a displayed formula they will be set below and above the symbol which will also be a little larger The following should give you an idea of how to use them Page 75 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Type To produce sum_ i 1 7 N a_i Di int_a b f Ee oint_ cal C 4 x dx fo f x de prod_ alpha Nin A X_ alpha Haca Xa lim_ N rightarrow infty sum_ i 1 N f x_i Delta x_i limy gt o DA f ai Axi We will have
32. University of Newfoundland September 4 2009 Chapter 4 Programming and graphing 4 1 Programming A more fundamental time saving suggestion concerns testing and debugging Do not bother to create a friendly user interface or to add various features to your program until you achieve basic functionality Suppose your program is to compute the area of a polygon given the coordinates of its vertices Eventually you want the program to prompt the user to enter the number of vertices N and their coordinates one by one like this Please enter the number of vertices N 3 Vertex 1 x 1 1 y 0 4 Vertex 2 x 3 4 y 4 56 Vertex 3 x 3 12 y 9 4 However do not begin programming by creating the input interface Instead put a temporary initialization block with fixed hardcoded data at the beginning of the program use simple data to enable an easy check by hand calculation N 3 x 1 y 1 x 2 y 2 x 3 y 3 3 D O NMO O This set of data corresponds to a right triangle with two sides running along the coordinate axes Then as the mathematical part of your program matures you should change the data test the program on a triangle that is acute or obtuse shift it then test the program on a quadrilateral etc As you will be catching mistakes in the program you will have to run it more than once on each sample data set while modifying the data infrequently Eventually you will spend much less time on data input
33. Y forall o infty h hbar emptyset 3 exists Box 2 imath V nabla 2 neg A triangle 9 jmath y surd b flat A triangle Nell T top 4 natural amp clubsuit go wp 1 bot sharp diamondsuit R Re MI Nbackslash Y heartsuit S Mm Z Nangle O partial amp spadesuit U mho Table 3 8 Miscellaneous symbols Arrow symbols TeX has a multitude of arrow symbols which it will set the correct space around Note that vertical arrows can all be used as delimiters see section 3 4 3 The available symbols are listed in table 3 9 lt leftarrow lt longleftarrow T uparrow lt Leftarrow lt Longleftarrow Ph Uparrow rightarrow Nlongrightarrow l downarrow gt Rightarrow gt Longrightarrow Y ADownarrow gt leftrightarrow lt NMlongleftrightarrow updownarrow Leftrightarrow lt gt Longleftrightarrow Updownarrow gt mapsto Mlongmapsto nearrow hookleftarrow gt hookrightarrow NX searrow leftharpoonup rightharpoonup Y swarrow leftharpoondown gt rightharpoondown N nwarrow rightleftharpoons leadsto Table 3 9 Arrow symbols Expression delimiters A pair of delimiters often enclose an expression as in E d Sad oks ifa lt 1 a21 Q22 a ifa gt 1 LT X will scale delimiters to the correct size determined by what they enclose for you if you ask it to There are times when you do not want a delimiter to b
34. above and em see below The command vspace has no effect at the top of a page or at the bottom Why would you want space when you are about to move to a new page If you insist you must use vspace to force IATFX to make space In the line break command inside a paragraph of text as well as inside tables arrays in math mode and parboxes one can create space by affixing an argument to the command for example tex leaves lex of additional space after the current line To make IATRX to skip more space between paragraphs as is done throughout this Manual you may add the following command in the preamble of your document setlength parskip smallskipamount Finally the commands pagebreak and newpage end the current page and start putting text on the new one Horizontal space The command hspace 10pt skips 10 points approx 3 5 mm of horizontal space The command hskip 10pt has the same effect in most cases but its use is discouraged At the beginning of a line hspacef will have no effect so you must use the command hspace instead It is recommended that you use the units em the width of a letter m in the current font size for horizontal space By default paragraphs in MIX begin with indentation except those immediately after the headings made with commands like section To suppress indentation you can use the command noindent Math space Spacing commands like
35. accordingly For example the following line in a C program will print a ATEX command that puts a small solid circle in a specified position printf put Zf circle 0 1 x y An equivalent FORTRAN code is PRINT put x y circle O 1 Page 86 Chapter 4 Programming and graphing 4 2 An introduction to Maple 4 2 An introduction to Maple Maple is a computer algebra system CAS created around 1980 by a team of researchers based at the University of Waterloo Currently it is commercial software supported by Maplesoft Inc and it is available to MUN students through the LabNET wide licence It may be necessary for you to set up your account so that you can use Maple see Section 5 3 4 Maple s most vigorous competitor is CAS Mathematica a product of Wolfram Research Inc USA Another software that has many similar capabilities but focuses on matrix computations at the expense of sophisticated symbolic manipulations is Matlab Users familiar with one of these systems will have little difficulty with another as soon as they understand the basic syntax and work out a few examples In Math 2130 we focus on Maple Maple s functionality and interface have evolved over about 30 years As of now there exist three types of user interface in Maple Two of them are graphical user interfaces standard modern and classic worksheet and the third is non graphical text based interface which can be used in a comman
36. allow transmission of information through noisy and defective channels Asa very general rule the definitions should go before the results that they are used in Rule 1 The quantifiers should always be clear Rule 1 Some examples to avoid x We have f x g x x X What does the parenthesis mean That f x g x for all x X or for some x X x What does fiu x y O gtu xz y mean Very often it means that t u y are fixed and zx is allowed to vary Quantifier problems are especially troublesome with big O notation The word constant is terribly ambiguous It is important to make explicit exactly which variables the constant depends on Theorem Proposition Lemma Corollary Give clear and unambiguous statements of results These are what other people are reading your paper for so you should ensure that these at least can be understood by the reader Rule 1 Page 152 Appendix B 2 Some Hints on Mathematical Style x The statement of the Theorem Proposition Lemma Corollary should not include comments except for an occasional brief remark in paren thesis or examples If you use or quote an important result of another person you should give a reference You should avoid giving the impression that such a result is obvious a generally accepted fact due to you and so on A reference to a book should always give the page Try to avoid using by the proof of
37. alternatively it can be kept in its own file say curve tex and the command input curve can be used to import the data into your master TEX file Page 115 Chapter 4 Programming and graphing 4 4 The ATEX picture environment Dotted lines dottedline dotchar dotgap x1 y1 x2 y2 xn yn This draws a dotted line joining x1 y1 to x2 y2 and so on to xn yn The dotgap is given in the units equal to the unitlength defined and needs not be an integer The optional dotchar may be omitted to give the default of a small dot but any character may be used You can use this with the appropriate dotgap as a method for putting markers on curves Dashed lines dashline stretch dashlen dotgap for dash x1 y1 x2 y2 xn yn This draws a dashed line joining x1 y1 to x2 y2 and so on to xn yn The dashlen is the length of the dash Each dash is in fact a dotted line and the optional dotgap for dash is the gap between each dot that is used to construct the dash Both are in current unitlengths The optional stretch is an integer between 100 and 00 You should experiment with these to find the appropriate relationship among the parameters to suit your purpose Here are some examples created by begin center setlength unitlength 1em begin picture 20 7 dottedline 7 0 6 20 6 dottedline bullet 7 0 5 20 5 join 0 4 20 4 dashline 8 0 2 0 3 20 3 dashline 8 0 2 20 2 th
38. and the headers of sections and subsections For instance the title Mathematical details can be changed into Geometry of tangent circles if that s the mathematical subject dealt with It can be further divided if appropriate into subsections like Tangency condition in terms of coordinates Relation between the radii of four tangent circles etc The table of contents that exhibits such Page 10 Chapter 2 Technical writing 2 3 Organization of report subject specific and self explanatory headers allows the reader to grasp the developments in the paper at a glance In short reports the table of contents may not be needed at all You may still be asked to include it as a typesetting exercise Check with your instructor 2 3 4 Abstract From a reader s perspective the abstract serves the purpose of classification where does the paper belong Should I take a closer look The abstract should be short yet informative Refer to the real world problem or the mathematical question that gives rise to the project Define the area of mathematics involved Briefly characterize an algorithm and or a program Squeeze in the essence of results or mention a particularly striking result perhaps schematically in an easy to grasp form Avoid extensive details In practice abstracts are often restricted to a prescribed numbers words Try to limit yours to 100 words Learn word saving tricks Cross out epithets excessive verbiage and the obvious Th
39. arguments to the Nincludegraphics command and as with all optional arguments in ATFX they are included within square brack ets Any valid T X unit of length can be used Counter clockwise direction of rotation is deemed positive and the angle is measured in degrees Other possible optional arguments for includegraphics are totalheight width and origin The difference between height and totalheight is that the former specifies the elevation of the graphics above the baseline while the latter equals to height plus depth the part below baseline The argument origin specifies what point to use for a rotation origin origin c rotates about the centre Page 97 Chapter 4 Programming and graphing 4 3 Drawing graphs Postscript programming Postscript ps eps files are usually created by specialized graphing or more universal pro grams like Gnuplot XFig or Maple However Postscript by itself is a human readable language and one can write a program in Postscript describing a picture Also you can generate a Postscript file automatically by your own FORTRAN or C program As an example the following short program in raw Postscript Fig 4 1 describes two Pythagorean triangles shown on the right Type the program in a text editor and save the file as say triangles ps The unit length in Postscript is point which is 1 72 of an inch PS Adobe 2 0 First triangle contour newpath 200 125 moveto 300 125 lineto
40. belongs to a group The owner can open or close access to his her files independently for self group and others or for all at once and for three purposes to read to write and to execute The command is chmode Consider a few examples The following prohibits writing to file project1 tex to all even to its owner A possible purpose is to protect the important work after it is finished from accidental deletion lumsden chmode a w projecti tex To prohibit group members and others i e everbody but the file owner from any kind of access to the file project1 tex lumsden chmode go wrx projecti tex To grant everybody a permission to read all existing pdf files in current directory lumsden chmode a r pdf Programs that you routinely work with editors compilers etc properly set the access privileges to the files that they create or modify If by any chance a program says Access denied you may need to explore the status of the file concerned A possible reason is that the file is currently being used by another program which temporarily closed an access to it Page 138 Appendix B Two papers on mathematical writing B 1 Writing a Math Phase Two Paper STEVEN L KLEIMAN with the collaboration of GLENN P TESLER Word smithing is a much greater percentage of what I am supposed to be doing in life than I would ever have thought Donald Knuth 6 p 54 Abstract In this paper we discuss the kind of wr
41. best tackled by one or other of the TFX environments Some environments are used to display a portion of text i e to set it off from the surrounding Page 52 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends text by indenting it The center environment note the American spelling allows us to centre portions of text while the flushright environment sets small portions of text flush against the right margin But the true power of ATEX begins to show itself when we look at environments such as those that provide facilities for itemized or enumerated lists complex tabular arrangements and for taking care of figure and table positioning and captioning What we learn here will also be applicable in typesetting some complicated mathematical arrangements in the next section All the environments are begun by a begin name command and ended by an end name where name is the environment name These commands also serve as begin group and end group markers see Sect 3 3 4 so that all commands are local to the present environment they cannot affect text outside the environment We can also have environment embedded within environment within environment and so on limited only by memory available on the computer We must however be careful to check that each of these nested environments is indeed contained within the one just outside of it quote environment This environment can be used to display a part of a se
42. consistently do not hide behind we in inconvenient places That said modern professional scientific writing overwhelmingly prefers we Think about it this way as a reader goes through your paper he she feels your company and gentle support We I the author you the reader You should use J when expressing personal opinions e g I found the results obtained in this laboratory truly surprising There are other situations where the subject J sounds more appropriate than we Consider this example I have encountered difficulty implementing this algorithm Substituting we in place of J would imply that your innocent reader shares your responsibility for the trouble Do not switch lightly between we and I If the subject is indeed necessary its use should be confined to a particular section better the Introduction or Conclusion and there J not we should be used throughout While working on the project you perform concrete actions like searching a database writing a program etc If you feel uncomfortable to write we when describing such actions use sentences stated in the 3rd person For example A program has been written instead of I have written a program However papers written in the 3rd person from the beginning to end usually leave an impression of an indirect cumbersome style 2 4 6 Verb forms tense mood modal verbs Use present tense predominantly when discussing mathematical th
43. details specific and others generic Third if possible follow a sequential path through the subject If such a path simply does not exist then break the subject down into logical units and present them in the order most conducive to understanding If the units are independent then order them according to their importance to the primary audience Page 142 Appendix B 1 Writing a Phase II Math Paper 3 Language There are three main reasons for dividing the body into sections 1 the division indicates the strategy of your presentation 2 it allows readers to quickly and easily find the information that interests them and 3 it gives readers restful white space allowing them to stop and reflect on what was said Make the introduction and the several sections of the body roughly equal in length When you title a section strive for precision and clarity then readers will have an easier time finding particular information In a short paper do not use subsections they make the flow too choppy Each main point should be accented via stylistic repetition illustration or language Stylis tic repetition is the selective repetition of something important for example you should talk about the important points once in the abstract a second time in the introduction and a third time in the body When appropriate repeat an important point in a figure or diagram Finally accent an important point with a linguistic device italics boldface
44. hspace and vspace only work in paragraph mode outside math The horizontal spacing commands in math mode are MX quad qquad which can be found in Maltby That s how much they measure and and and quad and qquad l The remaining distance is a tiny step backward Vertical spacing in math mode is best handled with L Page 27 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX Centering To center a block of text use the center environment begin center end center Note the American spelling of center XIX is very unforgiving if you make a spelling error in a command 3 1 5 Math mode Inline math and displayed math TeX can typeset in a paragraph mode or in math mode which in its turn can be of two kinds inline math or displayed math To begin and end the inline math mode use the dollar signs This places the mathematical formula as the next word in the line of text like here x y a y xz y However if you wish to display the formula use begin displaymath end displaymath A shorter delimiter for displayed math both to begin and to end is double dollar sign The displayed formula is automatically centered on its own line This can be artificially changed but rarely needed A displayed formula is still considered to be a part of a paragraph unless there is a blank line separating it from the paragrap
45. it is used in the proof of a theorem a proposition or another lemma Thus a lemma never has a corollary although a lemma may be used on occasion in deriving a corollary Normally a lemma is stated and proved before it is used The terms definition and remark are also often abused A formal definition should simply introduce some terminology or notation there should be no accompanying discussion of the new terms or symbols A formal remark should be a brief comment made in passing the main discussion should be logically independent of the content of the remark Often it is better to weave definitions and remarks into the general discussion rather than setting them apart formally Typographically the statements of theorems propositions corollaries and lemmas are tra ditionally set in italics and the headings themselves are set in boldface or in caps and small caps Theorem or THEOREM and so forth The texts of definitions and remarks are set as ordinary Page 150 Appendix B 1 Writing a Phase II Math Paper Advanced mathematics text so are the texts of proofs examples and the like These headings are traditionally set in italics boldface or small caps There is also a tradition of treating definitions typographically like theorems but this tradition is less common today and less desirable All these formal statements and texts are usually set off from the rest of the discussion by putting some extra white space b
46. more to say about the use of in section 3 4 4 Let us have a look at each of those expressions when displayed N b Fe Do Pr Aroa IS acA Arrays The array environment is provided for typesetting arrays and array like material It accepts two arguments one optional and one mandatory The optional argument specifies the vertical alignment of the array use t b or c to align the top bottom or centre of the array with the centreline of the line it occurs on the default being c The second argument is as for the tabular environment a series of 1 r and c s that specify the number of columns and the justification of these columns The body of the array environment uses the same syntax as the tabular environment to specify the individual entries of the array For instance the input A left begin array rrr 12 amp 3 amp 4 2 amp 1 amp O 3 amp T7T amp 9 end array right will produce the output 12 3 4 2 1 0 3 7 9 Note that we had to choose and supply the enclosing brackets ourselves they are not placed for us so that we can use the array environment for array like material also we get to choose what type of brackets we want this way As in the tabular environment the scope of a command given inside a matrix entry is restricted to that entry We can use ellipsis within arrays as in the following example A aii q12 Cin a21 a22 02n det A Am1 Am2 ide Amn Page 76 Chapter 3 Types
47. name Since it is common to delimit the end of a control word by a space ATEX will ignore any space that follows a control word since you want that space treated as end of control word space rather than interword space This has one important consequence The character in the input file immediately after a control symbol will be seen by ATX but any space following a control word will be discarded and never processed This does not affect one much if you adopt the convention of always typing a space after a control sequence name There is a rare circumstance in which this necessitates a little extra work and thought which we illustrate by example If we type a control word like LaTeX in the running text then we must be cautious because the string of spaces that come after it will be discarded by the LaTeX system which produces the output If we type a control word like 4TfXin the running text then we must be cautious because the string of spaces that come after it will be discarded by the TX system Accents IXT X provides accents for just about all occasions They are accessed through a variety of control symbols and single letter control worlds which accept a single argument the letter to be accented These control sequences are detailed in table 3 1 o grave accent ufo 0 breve accent o acute accent v o h ek or check o circumflex or hat H o 6 long Hungarian umlaut
48. numerator and the de nominator in that order Before we look at examples of its use let us just note that many simple in text fractions are often better written in the form num den as with 3 8 which can be typed as 3 8 This is also often the better form for a fraction that occurs within some expression Page 72 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Type To produce frac x i x 2 in x aT 2 frac 1 x 2 1 22 1 7 frac 1 x 2 x 2 y 2 x72 y ay ate 2 y frac 1 1 frac x 2 7 2 1 frac 1 1 x 2 142 2 Roots The sqrt command accepts two arguments The first and optional argument specifies what order of root you desire if it is anything other than the square root The second and mandatory argument specifies the expression that the root sign should enclose ee To produce sqrt at b Jat sqrt 5 atb 277 sqrt n frac i x 1 x 2 a ae frac sqrt xt1 sqrt 3 x73 1 es ee Ellipsis Simply typing three periods in a row will not give the correct spacing of the periods if it is an ellipsis that is desired So TEX provides the commands ldots and cdots Centered ellipsis should be used between symbols like x x and Here are some examples Type To produce a_1 cdots a_n arten x_1 times x_2 times cdots times x_n 1 X 2 X X Tn v_1 v_2 cdots v_n 0 v v Un O f x_
49. of all match the information in your text and illustrations Secondly place the illustrations closely after never before their references in the text 4 Mathematics Mathematical writing has some special problems because it tends to involve many abstract symbols and formal arguments Here are some principles to keep in mind Formulas are difficult to read because readers have to stop and work through the meaning of each term Do not merely list a sequence of formulas with no discernible goal but give a running commentary Define all the terms as they are introduced state any assumptions about their validity and give examples to provide a feeling for them Similarly motivate and explain formal statements Do not simply call a statement important interesting or remarkable but show why it is so Display an important formula by centering it on a line by itself and give a reference number in the margin if it is especially important or if you need to refer to it Also display any formula that is more than a quarter of a line long or that would be broken badly between lines Punctuate the display with commas a period or whatever as you would if you had not displayed it Be clear about the status of every assertion indicate whether it is a conjecture the previous theorem or the next theorem If it is not a standard result and you omit its proof then give Page 146 Appendix B 1 Writing a Phase II Math Paper 4 Ma
50. or default font for your document to be 10 11 or 12 point Roman If no options are specified the default is 10 point Roman The table shows for instance that if I issue a large in this document for which I chose the 12pt document class option the result will be a 14 point Roman typeface We mentioned that to restrict the scope of a type changing command we will set the text to be affected off in a group Let us look at an example of this When we want to em emphasize some text we use the tt em command and use grouping to restrict the scope We can change font large sizes in much the same way We can also obtain it italicized bf emboldened sc Capitals and sf sans serif styles When we want to emphasize some text we use the em command and use grouping to restrict the scope We can change font S1Zes in much the same way We can also obtain italicized emboldened CAPITALS and sans serif styles Notice how clever grouping allows us to do all that without once having to use rm or normalsize One more thing slipped into that example an italic correction This is a very small amount of additional space that we asked to be inserted to allow for the change from sloping emphasized text to upright text because the interword space has been made to look less sub stantial from the terminal sloping character One has to keep an eye open for circumstances where this is necessary See the effect of omitting an italic co
51. or quotations marks a one sentence paragraph a short sentence at the end of a long paragraph or a repetition of parallel phrases or sentence structures In particular set a technical term in italics or boldface or enclose it in quotation marks if it is only moderately technical once at the time it is being defined Do not use underlining when italics or boldface is available Use headings such as Table 1 1 Figure 1 2 and Theorem 5 2 and refer to them as Table 1 1 Figure 1 2 and Theorem 5 2 note that the references are capitalized and set in roman The list of references contains bibliographical information about each source cited The style of the list is different in technical and nontechnical writing so is the style of citation In fact there are several different styles used in technical writing but they are relatively minor variations of each other The style used in this paper is commonly used in mathematics The citation is treated somewhat like a parenthetical remark within a sentence Footnotes are not used neither are the abbreviations loc cit op cit and ibid The reference key usually a numeral is enclosed in square brackets When citing particular material such as pages sections or equations do so at the point of citation within the brackets place the page numbers section numbers or equation numbers preceded by a comma after the reference key If the citation comes at the end of a sentence
52. programmers Differentiate between strict and non strict inequalities i gt 0 vs i gt 0 Check whether it is possible that your loop will skip immediately say the loop condition is while i gt j and the initial value of i is equal to the initial value of j If this is possible in the program was it meant e Quite often special arrangements are to be made on the first and or last pass of a loop For example in a loop that produces n pairs of coordinates separated by commas the comma should be printed only n 1 times see example on p 86 e Array indexing In FORTRAN and Maple if the array has N elements the index runs from 1 to N while in C and Java it runs from 0 to N 1 Also when you update the array and the new values depend on the old values watch the order of the update closely Consider for example the cyclic permutation x 1 x 2 gt gt x n gt x 1 CORRECT WRONG tmp x n tmp x n FOR i 1 n 1 FOR i 2 n x n i 1 x n 1 x i x i 1 END DO END DO x 1 tmp x 1 tmp In the wrong code the old value of x 1 will propagate through the array while the old values of x 2 x 3 x n will be lost e When you use output to files in C or FORTRAN make sure to close the file otherwise a part of the output may be lost Close the file outside the outermost loop otherwise a multiple closure will cause the program to crash e A confusion between the assignment operator and the equality condi
53. returned to the student while the final one will be retained by the instructor The typical weights of the reports are 15 marks 25 marks 30 marks and 30 marks respec tively However your instructor s first day handout takes priority in regard to the method of evaluation The following two paragraphs apply to Labs 1 to 3 Late submissions are subject to penalty A submission within a week past the due date will result in a deduction of 5 marks Thus a second lab worth 22 out of 25 marks will receive a final grade of 17 out of 25 if it is just one day late Further delays result in a deduction of 5 marks per week of lateness Within a week or two following the submission date you will be asked to meet with your instructor to go over your paper At the meeting the instructor will suggest possible improvements in the paper while you must be prepared to explain mathematical details the workings of a computer program sources of information collaboration etc The results of such interviews can affect your grade on the project The evaluation criteria for the projects address quality of contents and presentation But before anything else the instructor will check whether you have completed the assigned task In a laboratory that asks to write a computer program that does so and so neither an amusing narration and fancy graphics nor five pages of mathematical definitions and theorems will help if your program doesn t work or doesn t solve the
54. size of the Conclusion should not exceed 1 2 of a page in many cases one or two paragraphs will suffice Avoid trivial non informative phrases like Upon completion of this laboratory certain conclusions can be drawn An Introduction or Conclusion longer than one of the central sections is a sign that the material should be re balanced Page 13 Chapter 2 Technical writing 2 3 Organization of report 2 3 6 Technical details Other commonly used titles are Method or Methodology Feel free to devise a subject specific explanatory title If the original problem has several parts subdivide this section accordingly A subdivision may be needed simply for a better balance of section sizes or it can be demanded by the logic of exposition if say different aspects of the method employ different techniques This section should describe all the fine or heavy details of the problem or model and the details of the mathematical method or algorithm used to solve it as well as the structure and particulars of your computer code The requirements in brief are Attention to details and particulars Relevance to the topic The subsection Mathematical details or whatever your subject specific title generally includes notation used definitions mathematical formulation set up of a model relevant theoretical facts and the mathematical essence of the algorithm used to solve the problem Do not attempt to reach far and w
55. source file strongly objectionable say incorrect command syntax then return to editing 6 Run a previewer to preview your compiled document on the screen 7 Go back to editing your document until glaring errors have been taken care of 8 Make a printout of your compiled document and check for those errors that you failed to notice on the screen Performing these steps may be effected through typing at the system prompt bare bones tech nique or through choosing menu options in a TpXshell program The latter will probably provide some conveniences to make your life easier 3 3 2 A review of PTX The TFX typesetting system was designed by the eminent Stanford computer scientist Donald Knuth on commission from the American Mathematical Society It was designed with enormous care to be ultimately powerful and maximally flexible The enormous success of Knuth s design is apparent from the vast number of diverse applications TFX has found In reading the following you must keep one thing clearly in mind there is only T X language and all the other packages whose names end in the suffix T X simply harness its power via a whole lot of complicated macro definitions TX proper is a collection of around 300 so called primitive typesetting commands These work at the very lowest level affording enormous power But to make this raw power manage able some macros must be defined to tame raw TEX somewhat In the few years after the initia
56. spaces and carriage returns when in math mode without exception So typing something like the constant a will produce the constanta You should have typed the constant a IATFX is responsible for all spacing when in math mode and as in paragraphing mode you have to specially ask to have spacing changed Even if ATX does ignore all spaces when in math mode you should as always in TEX still employ spaces to keep your source file readable The above means that at least for most material a typist need not understand the math ematics in order to typeset it correctly And even if one does understand the mathematics BTFX is there to make sure that you adhere to accepted typesetting conventions whether you were aware of their existence or not So one could type either f x y 2 x y y 5xy 3 or f x y 2 xty y 5xy 3 and you would still get the correct result f x y 22 y y 5xy 3 There are some places where this can go wrong For instance if we wish to speak of the x y plane then one has to know that it is an en dash that is supposed to be placed between the x and the y not a minus sign as x y would produce But typing x y will produce x y since both dashes are interpreted as minus signs To avoid speaking of the x y plane or the x y plane we should type it as the x y plane We are fortunate that ATRX can recognise and cope with by far the majority of our mathematical type
57. submitting it for compilation No special interface is necessary here you just use your favourite text editor perhaps customising it to enhance TpXnical typing Thus T X user interfaces are usually small and simple often even missing One frequently uses T X at command line level just running the editor compiler etc as you need them Sometimes a T Xshell program is present which runs these for you when you choose various menu options Whatever the interface there are just a few basic steps to preparing a document 1 Choose a document style to base your document on e g letter article 2 Glance through the material you have to type and decide what definitions might be made to save you a lot of time Also decide on the overall structure of the prospective document e g will the largest sectional unit be a chapter or a part If you are going to compose as you type then pause a moment to think ahead and plan the structure of your document The importance of this step cannot be overstressed for it makes clear in your mind what you want from TX 3 Prepare your input file specifying only the content and the logical structure parts sec tions theorems thereof and forgetting about formatting details 4 Submit your input or source file to the TFX compiler for compilation of a dvi file Page 39 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends 5 If the compiler finds anything in your
58. tell IAT X that it is typesetting math as opposed to some other random string of symbols that it does not understand either We will come to mathematical typesetting in good time We need to dwell on a TRXnicality for a moment How does ATEX know where the name of a control sequence ends Will it accept both pm3 and pm 3 in order to set 3 and will emWalrus and em Walrus both be acceptable in order to get Walrus The answer is easy when you remember that a control word consists only of alphabetic characters and a control symbol consists of exactly one nonalphabetic character So to determine which control sequence you typed ATEX does the following 1 when a character is encountered ATEX knows that either a control symbol or a control word will follow 2 If the is followed by a nonalphabetic character then ATFX knows that it is a control symbol that you have typed It then recognises which one it was typesets it and goes on to read the character which follows the symbol you typed Page 43 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends 3 If the is followed by an alphabetic character then BTEX knows that it is a control word that you have typed But it has to work out where the name of the control word ends and where the ensuing text takes over again Since only alphabetic characters are allowed TATRX reads everything up to just before that first nonalphabetic character as the control sequence
59. the height of the operator as in N hi i 1 Table 3 11 describes what variable size symbols are available showing both the small in text and the large displayed form of each In section 3 4 4 we will learn how to place limits on these operators X y sum N A bigcap O bigodot II Il prod U U bigcup Q amp bigotimes TH Il coprod U _ bigsqcup B bigoplus S if int V V bigvee ly l biguplus f oint A A bigwedge Table 3 11 Variable sized symbols Accents The accenting commands that we learned for paragraphing mode do not apply in math mode Consult table 3 12 to see how to accent a symbol in math mode all the examples there accent the symbol u but they work with any letter Remember that i and j should lose their dots when accented so imath and jmath should be used Page 69 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX There also exist commands that give a wide hat or a wide tilde to their argument widehat and widetilde hat u acute u bar u dot u check u grave u u vec u ddot u breve u tilde u Table 3 12 Math accents 3 4 4 Some common mathematical structures In this section we shall begin to learn how to manipulate all the symbols listed in section 3 4 3 Indeed by the end of this section we will be able to typeset some quite large expressions In the section following this we will learn how use variou
60. the operator followed by the same little space and finally the second argument Table 3 6 shows the binary operators that are available via ATEX control words recall that the binary operators and can be typed from the keyboard Here are some examples of their use Type To produce a b a b a b otimes c a b c a vee b wedge c aV b Ac X A cap B X A cup X B X AN B X A U X B Page 66 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX pm M cap diamond 9 Noplus F mp U NXcup A Nbigtriangleup Nominus x times W uplus Y bigtriangledown amp otimes div sqcap lt triangleleft O Noslash ast sqcup gt triangleright odot x star V vee AN wedge Nbigcirc dagger Vo setminus Il amalg o Xcirc t ddagger cdot 2 wr bullet Table 3 6 Binary Operation Symbols Binary relations TEX has been taught to recognize the use of binary relations too Table 3 7 shows those available via TFX control words There are a few that you can obtain directly from the keyboard lt gt and To negate a symbol you can precede the control word that gives the symbol by a not Some symbols come with ready made negations which should be used instead of the not ing method because the slope of the negating line is just slightly changed to look more pleasing Thus notin should be used instead of not in an
61. the values that are denoted xmin xmax numpoints in the good code occur somewhere else in the program and you wish to change all or some of the values it is easy to do you just need to change the values assigned to the symbolic names in one place only In simple cases like in the example above the points are generated independently of each other as soon as a point has been computed it can be printed immediately In more complicated cases when dependency of some sort is present you may have to create an array and to complete computation of all the points before you can print them out Another suggestion use scaling parameters and translation parameters The good code above is good in particular because it is easy to implement this suggestion Modify the output operator as follows PRINT xscale x xorigin yscale y yorigin Page 84 Chapter 4 Programming and graphing 4 1 Programming This stretches or shrinks the distances by a factor xscale in the x direction and by a factor yscale in the y direction In addition the point where x y xorigin yorigin will be printed as 0 0 that is it will become the origin of the coordinate system on the plotting device The trivial default values can be initialized xscale 1 yscale 1 xorigin 0 yorigin 0 If you are not satisfied with size or position of your graph it will be very easy to change Formatting coordinates You must format the coordinates i
62. two ways 1 As stand alone structure units in a separate paragraph with the title word Definition in a distinguished font style This format should be used when you introduce a major concept or when a definition is lengthy Do not hesitate to make definitions lengthy and detailed even boring precision and disambiguation are the priorities Think of a legal code 2 Inline definitions as a part of the flow can be used if the definition is very short simple or natural or if the concept is supposed to be generally familiar to the reader Example To describe the shape of a rectangle with side lengths a and b we introduce the parameter u b a called the aspect ratio Page 14 Chapter 2 Technical writing 2 3 Organization of report The definitions the notation and the method should be described in such detail that a motivated reader could reproduce your work on his her own and obtain identical results How about yourself a few months later Keep adding details and clarifying your writing until you are able to answer in the affirmative We refer to Appendix B 1 Section 4 for further tips on mathematical writing Let us just make one more suggestion regarding the mathematical method in general and contents of your Mathematical details section in particular Think about simple particular cases where the situation is either obvious or the answer can be obtained easily Do this before you write a program and before you explore t
63. will be not quite in that case you should admit it and explain Example In this paper a method for counting all partitions of a given positive integer N is described A FORTRAN program has been written and the number of partitions has been computed for all N lt 30 It is apparent that the number of partitions P N exhibits a rather rapid growth as N increases We observed and proved that P N gt N for N gt 9 and that P N lt 2 for all N but we did not come up with a definite conclusion about the precise law describing the growth The program presented here uses direct enumeration of partitions A Wikipedia article 2 suggests another supposedly more economical method for counting par titions based on recurrence relations We have also attempted to implement that method but have not been able to complete the programming in a timely manner It is too late in the conclusion to bring in new material not found earlier in the paper Instead you may discuss possible extensions of the work done or point out some connections between your subject and other applications or techniques which you might have come across in the course of the work but which have not been been worked out in detail in the paper body The Introduction and Conclusion may contain other material that the author considers relevant for example a personal remark or opinion which cannot be conveniently expressed in the central more formal part of the paper The
64. would try to excuse themselves for spelling and grammar errors saying that this is not a course in English others with poor knowledge of programming would complain that creating a correctly working program carries so much weight Such excuses and complaints will be rightfully dismissed by the instructor Also it is very normal in this course to learn chunks of mathematics on the fly Thus if a project asks you to simulate a dynamics described by differential equations and you have not taken Math 3260 just look up a few relevant facts 1 3 2 Academic integrity and academic misconduct Academic integrity means honesty and courtesy in your course work and research The opposite is academic misconduct In our experience situations occur in this course on a regular basis where students are at risk of violating academic integrity in the following ways e forging research results e plagiarizing Page 3 Chapter 1 Introduction 1 3 Policies A Forging research results A graph downloaded from the Internet and presented as the output of a student s own program is an example of a forged research result But forging does not necessarily involve someone else s results it can also occur as entirely one s own activity If a student s program does not solve an equation as expected and the student decides to correct the program s output by hand hoping to fool the instructor that s a forge Sometimes the borderline between an involunta
65. writing 2 1 Technical versus non technical writing Most things about writing that you learn in English courses apply equally to technical writing This chapter does not pretend to teach you the rules of grammar basic principles of composition and style in general We rather focus on the elements of writing specific to this course Yet some common spelling errors etc will be mentioned see Sect 2 4 1 Writing requires you to organize your flow of thought into a coherent sequence of units carrying sense The smallest such unit is a sentence Then comes a paragraph A short story may contain no further structural units while more sizeable pieces of fiction are often organized into Parts and Chapters Scholarly writing as compared to fiction is characterized by a more sophisticated hierarchy of logical units Some of them such as Sections Subsections References determine the plan of the paper Others such as Definitions Remarks Tables help the readers to pause and digest one relatively small piece of information at a time Good graphics can be truly informative and replace a hundred words Particular to mathematical writing are such units as Theorems and their Proofs Common in technical reports are fragments of computer code or whole program listings In Section 2 3 we make recommendations concerning the global structure of your Math 2130 reports Some useful advice can be found in Appendix B 1 Section 2 The use of language in te
66. 0 Technical details 14 tense 22 153 terminology 14 21 tests for a program 15 TREX 38 Theorem typesetting of 78 147 150 ties in TEX 50 title page of 2130 report 10 34 title of paper 10 142 titles of sections 10 14 triviality banality 13 14 units of length in ATEX 27 unnecessary words 20 23 usage of mathematical terminology 21 147 usefulness of paper 3 user defined commands in TAT X 25 user interface of your program 16 vagueness 9 validation of data 16 variables 15 self explanatory names of 17 84 verb noun collocations 21 We vs I 22 145 Weisstein Eric 19 which vs that 144 white space 147 Wikipedia 13 14 19 word saving tricks 11 20 145 WRITE in FORTRAN 17 writing advisor 5 Writing Centre 5 6 9 writing strategies bottom up approach 9 free flow approach 9 top down approach 8 Page 158 Index 70 25 amp 29 58 28 61 28 27 77 27 77 Xx 27 77 27 77 26 58 L 27 29 78 GN 61 L F 63 58 12pt subsidiary style 24 41 2130 sty package 24 24 33 115 addtotableofcontents 35 amssymb 25 67 array environment 29 76 article document class 24 41 begin 25 begin document 24 bf 45 bibitem 36 bigskip 26 caption 37 60 center environment 28 cdots 73 circ 67 circle 117 cite 37 cos 74 description environment 56 displaymath environment 28 displaystyle 25 28
67. 1 ldots x_n 0 f 1 n 0 Text within an expression One can use the mbox command to insert normal text into an expression This command forces AT X temporarily out of math mode so that its argument will be treated as normal Page 73 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX text Its use is simple but we must be wary on one count remember that TX ignores all space characters when in math mode so to surround words in an expression that were placed by an mbox command by space you must include the space in the mbox argument Type To produce f _i x leq O mbox for x Nin I fila lt 0 forx el Gamma n n 1 mbox when n is an integer n n 1 when n is an integer In section 3 4 4 we will learn of some special spacing commands that can be used in math mode These are often very useful in positioning text within an expression enhancing readabil ity and logical layout Log like functions There are a number of function names and operation symbols that should be set in normal roman type in an expression such as in f 0 sin 6 log 0 1 sinh 6 1 and lim sinh _ h gt 0 h We know that simply typing log theta would produce the incorrect result log and that using mbox log theta would leave us having to insert a little extra space between the log and the 0 log9 So MTFX provides a collection of log like functions defined as control sequences
68. 10 Equilateral triangle with inscribed and circumscribed circles Our last example demonstrates a combination of Maple elements just described and those described in Section 4 2 We construct three similar parametric curves called cycloids each given by the parametric equations x C 0 3t sint y C 0 6 1 cost 4 1 The parameter C equals 0 5 1 and 2 for the three curves respectively To make the x span of the curves approximately equal we choose the t range the bigger the smaller C is Specifically we set t 1 9r for C 0 5 t 7 5a for C 1 and t 7 37 for C 2 The pattern is tmin 7 and tmax 1 4 C r Instead of creating plots of the three curves individually we take advantage of the clear pattern and create a procedure The first argument is the value C in Eq 4 1 and the second argument is the color to strike the curve with gt cycloidC proc C col local t tmax fx fy fx 0 3 t sin t fy 0 6 1 cos t tmax 1 4 C Pi return plot C fx C fy t Pi tmax color col end proc We then assign the colors gt cycloid_colors red blue black In the final plotting command we use the array manipulation methods from Section 4 2 4 gt display seq cycloidC 2 n 2 cycloid_colors n n 1 3 Page 105 Chapter 4 Programming and graphing 4 3 Drawing graphs Figure 4 11 Cycloids given by Eq 4 1 with C 0 5 red C 1 blue and C
69. 29 div 42 KTpX commands keywords packages and environments documentclass 24 ds user defined command 25 em unit of length 27 end 25 end document pagerefp edoc enumerate environment 56 eqnarray environment 28 77 eqnarray environment 29 77 equation environment 28 evensidemargin 24 ex unit of length 27 exp 74 fi 25 figure environment 37 60 float package 60 footers 25 frac 43 72 geq 62 graphicx 25 headers 25 hskip 27 hspace 27 hspace 27 iffalse 25 includegraphics 97 106 111 infty 42 int 75 it 45 itemize environment 56 join 115 large 45 LaTeX 42 left 68 lgrind package 31 lim 75 Mine 115 Page 159 Index linebreak 26 ldots 73 log 74 mathbb 67 medskip 26 multicolumn 59 newcommand 25 newline 51 newpage 27 newtheorem 78 noindent 27 nonumber 29 normalsize 45 oddsidemargin 24 overline 43 75 pagebreak 27 pageref 37 par 26 parskip 27 picture environment 114 pm 42 prod 75 put 115 qquad 27 77 quad 27 77 quote environment 35 53 ref 37 right68 rm 45 scaledpicture environment 114 scriptstyle 28 section 27 36 section 35 36 setlength 27 sin 74 smallskip 26 sqrt 43 73 subsection 36 sum 75 table environment 37 60 tableofcontents 35 60 tabular environment 58 textheight 24 textstyle 28 textwidth 24 thebibliography environment 36 topmargin 24 tt 45
70. 3 Some TEX input and the corresponding output declaration of begin document and that of end document Definitions that are to apply to the entire document can be made before the declaration of the document beginning The specification of document class must precede all other material In future examples we will not explicitly display the commands that select document class and delimit the start and end of the document But if you wish to try any of the examples do not forget to include those commands The article document class will do for most of our examples Of course the preceding example looks not at all like an article because it is so short and because we specified no title or author information Most of what you need to know to type regular text is contained in the example above When you consider that by far the majority of any document consists of straight text it is obvious that ATRX makes this fabulously straightforward TeX will do all the routine work of formatting and we simply get on with the business of composing IXAT X does more than simply choose pleasing line breaks and provide natural spacing when setting a paragraph Remember we said that TeX has inherited the knowledge of generations of professional printers well part of that knowledge includes being on the look out for ligatures Page 47 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends These are combinations of letters within words
71. 3D data in the format similar to 2D each line in the file represents the coor dinates x y z of a single point on the surface There is an option to remove hidden lines so that foreground and background can be differentiated Figure 4 14 was produced from the file glass dat author Gershon Elber 1990 which is a part of the repository of samples provided with Gnuplot distributions It can be downloaded separately from http www challenge nm org ctg graphics glass dat Page 109 Chapter 4 Programming and graphing 4 3 Drawing graphs filet dat al file2 dat Al Figure 4 13 Graphs of y x 3x and y tr produced from data files The glass is a surface of revolution which can be mathematically described by an equation of the form r f z in the cylindrical coordinates in R3 with r y 22 y2 The function f z in this case is not given by a formula but it is rather a result of an artwork Rendering three dimensional surfaces is no simple business If you venture to try we recom mend that all slices level curves have the same number of points per slice or level curve The reason for this is that given a set of say x slices Gnuplot attempts to work out the missing y slice data in order to perform the hidden line removal Gnuplot will not necessarily fail if this advice is not followed but its behaviour is then somewhat unpredictable The data file glass dat contains 16x16 256
72. 4674407 107 Let s see how to do slightly more interesting operations Symbolic names can be used gt y1 x 3 2 9 2 x 2 2 x 6 y2 x74 x 3 15 x 2 9 x 54 2 x7 3 2 x 2 8 x 8 1 9 1 lt x 2x 6 y 2 2 x x9 15x 9x 54 2x3 2x 8x 8 y2 Expressions can be symbolically factored gt yif factor y1 x 1 x 8x 12 Alb goes y 2 Or expanded gt expand y1f yi x A 2x 6 2 2 A remark on symbolic names Some names in our examples x y1 y2 y1f denote user defined variables these names are arbitrary you can change them any way you like Other names are keywords known to Maple like factor expand These names are protected an attempt to assign a value to them will prompt an error message Maple knows a few special constants which are also protected The most famous one is PI m 3 14159 not so many students are familiar with Euler s constant gamma y 0 57721 You may be surprised that the symbols e and E are not protected the natural logarithm base e 2 71828 can be accessed in Maple as exp 1 in symbolic calculations or as exp 1 0 numerically The availability of the symbol e is convenient for astronomers who use e to denote eccentricities of planetary orbits The fact that gamma is reserved is unfortunate for geometers who like to denote the angles of a triangle as a p y We continue a tour of basic Maple commands The si
73. 489743 Higher accuracy is available through an optional argument of the evalf command gt evalf XX 20 5505102572168219018 5 4494897427831780982 Page 89 Chapter 4 Programming and graphing 4 2 An introduction to Maple Maple knows complex numbers too Note that symbol I in Maple is the imaginary number v 1 usually denoted as i gt solve x 2 x 1 0 x 1 1 1 1 1V3 2 1v3 SS 2 1V3 Maple s exact answers to equations of degrees 3 and 4 can be impractical For roots of polynomials of degree 5 and higher no general formulas exist and unless the equation can be factored Maple will return gibberish In all such cases evalf can be used to get an approximation of the roots The command fsolve returns approximations of real roots only gt evalf solve x 3 x 1 0 x 6823278040 0 3411639019 1 161541400 I 0 3411639019 1 161541400 I gt fsolve x 3 x 1 0 x 6823278038 Maple can solve not only algebraic equations but many others too Beware however of its simplistic approach Every math student knows that the equation cosx 0 has infinitely many solutions but not Maple gt solve cos x 0 1 ah Nor can Maple find all approximate solutions in a given interval containing many roots gt fsolve cos x 0 x 100 200 48 69468613 4 2 3 Calculus Maple can do calculus both symbolically and numerically Recall the expression y1 from our example on page 88 we can use Maple for differentia
74. 688 2 380 1 566 2 360 1 446 2 340 1 329 2 320 1 214 2 300 1 101 2 280 0 990 2 260 0 882 2 240 0 775 2 220 0 671 2 200 0 569 2 180 0 470 2 160 0 372 2 140 0 277 2 120 0 183 2 100 0 092 2 080 0 003 2 060 0 084 2 040 0 169 2 020 0 252 This is a typical example of a file that you can generate by your own program as described in Section 4 1 3 Page 120 Chapter 4 Programming and graphing 4 4 The ATEX picture environment Finally here is the set of commands for the diagram that follows begin scaledpicture 50 13 12 0 1 join 0 0 12 5 0 5 10 0 0 join 12 5 0 2 5 5 join 4 8 8 0 swput 0 0 B seput 12 5 0 E sput 8 0 C Input 5 10 G angleput 153 1 2 5 5 D angleput 153 1 4 8 A angleput 55 1 6 5 3 F put 2 5 5 rtangle 243 5 put 10 25 0 join 05 25 05 25 join 05 25 05 25 put 3 25 6 5 rotate 63 join 05 25 05 25 join 05 25 05 25 put 6 5 3 arc 5 5 15 arc 5 5 18 arc 5 5 15 arc 5 5 18 put 0 0 arc 6 0 64 arc 75 0 64 put 8 0 arc 6 0 64 arc 75 0 64 put 5 10 arc 0 6 34 arc 0 6 27 arc 0 75 34 arc 0 75 27 end scaledpicture B C E Two commands here rotate and rtangle are defined in the 2130 sty file using a bit of Postscript programming and by means of a command speci
75. 7 153 proposition mathematical statement 150 punctuation 144 purpose of Math 2130 course 1 of your paper 8 Python programming language 17 quadratic formula 14 21 readership 8 11 12 14 142 redundancy 9 152 references 19 143 formatting in LaTeX 36 to preceding assertions 147 relevance 14 Remark structure unit in paper 150 research value of paper 18 what it is not 5 results 8 forge of 4 presentation of 17 reproducibility of 15 scaling constrained 101 scope 8 set up of a model 14 shape geometrical 12 simple particular cases 15 Page 157 Index size of report 10 of Abstract 11 of Introduction 12 of Conclusion 13 source code of programs 31 space horizontal 27 space vertical 26 space in math mode 27 77 special characters in ATEX 25 41 special mathematical symbols 65 specifics see particulars spelling 20 stacking symbols 75 Stewart James 19 strong words 21 strong vigorous writing 142 145 structure of 2130 report 9 units in a technical paper 7 141 style file 24 stylistic repetition 143 subdivision of a section 14 submission requirements 2 subroutine 16 subscripts and superscripts 28 70 superimposition of graphs 98 122 symbol not to begin sentence with 145 153 syntax of programming language 15 syntax errors in programming 81 Table of contents 10 35 adding entry to 35 taste 1
76. BoundingBox specification immediately after so the second line in your updated file must be similar to this BoundingBox 20 118 575 673 d Finally save the file as fig1 eps 4 Do not use command pdflatex or the corresponding icon in Kile if your XIX file contains references to eps graphics Compile your tex file into a dvi file and then convert dvi into pdf if you wish You can successfully use pdflatex if the only type of graphics in your document is that provided by the ATRX s picture environment or its extensions as described in Sect 4 4 5 The command 1grind Sect 3 1 9 may not work on your home computer although you may have successfully installed a ATEX distribution Page 129 Appendix A Quick UNIX reference UNIX is a common name for a family of operating systems most popular of which in this epoch is Linux This document is by no means a UNIX tutorial Sophisticated UNIX users may find some of the material here grossly simplified Only a small subset of the shell commands available is given and very few options are mentioned A l Files A file is a collection of data with a unique name Names are case sensitive lowercase and uppercase letter are considered distinct All permanent storage on UNIX consists of files In this course you will encounter several different types of files that are recognized by their extensions The extension is the ending of the file name following the last dot Some extensions are expec
77. Fig you build a diagram by mouse manipulations and immediately see the result Thus as we see the creation of XFig diagrams is not relied on a digital algorithm although the resulting file is a digital description of the figure As such XFig should not be used in the cases where you must generate definite unambiguously reproducible graphics It can be used for auxiliary artwork like illustrations or schemes To start XFig just enter the command xfig The XFig window has several icons along the left several menu options along the top including Help rulers along the top and right as well as a few setting boxes on the bottom Playing with the icons on the left and the bottom is perhaps the best way to discover what you can do The scull and bones button allows you to delete previously created objects Once you get going a few of the setting boxes on the bottom are worth noting such as the Point Posn Depth and Fill Style Notice that the functionality of each of the 3 mouse buttons varies from option to option and is displayed in the upper right corner of the window For example the following diagram contains 4 objects that were each drawn with a different depth setting Once you ve got a diagram ready for inclusion in a ATEX document first use the File menu option and save the figure in a file with a fig extension such as diagram fig Then use the Export menu option to export the figure using the Encapsulated Postscrip
78. On the other hand you must explain the internals the workings of the code and primarily the part pertaining to mathematical operations It is the latter that we want you to emphasize in this section You are writing a research report not a user manual a technical text too but of a different kind If your program validates initial data reports an error on input of a negative distance say good but do not get overexcited about the user interface It is better to make an effort to explain the overall logic of the program flow control loops if else operators and the organization of data unless it is very obvious Example 1 Suppose your program counts the number of partitions P N for N from 1 to 30 Your description of the program can begin as follows Each run of the outermost loop of the program corresponds to computation of P N for a particular value of N DO N 1 MAXN Computation of P N END DO The upper bound MAXN of the loop is set to 30 by default but it can be changed through user s input Example 2 A line like this DISTANCE TIME SPEED is self explanatory and doesn t need comments A loop like this DO I TMIN 1 TMAX DISTANCE DISTANCE DT SPEED 1 END DO can be commented on at the author s discretion for example In this loop the distance traveled over time interval from TMIN 1 to TMAX is com puted The array SPEED is initialized at the beginning of the program according to fo
79. Student name amp bfseries Number amp bfseries Test 1 amp bfseries Test 2 amp bfseries Comment hline F Basset amp 865432 amp 78 amp 85 amp Pleasing hline H Hosepipe amp 829134 amp 5 amp 10 amp Improving hline I N Middle amp 853931 amp 48 amp 47 amp Can make it hline end tabular which will give Student name Number Test 1 Test 2 Comment F Basset 865432 78 85 Pleasing H Hosepipe 829134 5 10 Improving I N Middle 853931 48 47 Can make it That way of laying out the source file makes it clear where the lines will go As we by now well know the returns that we pressed after the s in typing this table might as well have been spaces as far as IATFX is concerned Thus it is common to have the hline commands following the s on the input lines We will do this in future examples The multicolumn column can be used to overrule the overall format of the table for a few columns The syntax of this command is multicolumn n H pos Hitem where n is the number of columns of the original format that item is to span and pos specifies the justification of the new argument begin tabular 1lclclcl hline multicolumn 4 c LaTeX size changing commands hline Style option 10pt default ttfamily 11pt ttfamily 12pt hline tt footnotesize amp 8pt amp Opt amp 10pt hline tt small amp Opt am
80. There is one in the library Commons area and one in the Chemistry Physics CP2003 4 This money is not locked into a particular lab and can be used on all LABNeT printers A noted peculiarity is that once started a printing job will apparently be finished even if it results in a negative account balance but the card reader will be showing zero balance until you cover the debt Page 125 Chapter 5 Local system particulars 5 3 Software 5 3 Software 5 3 1 Processing PTpX files in the command line You process the file mylab1 tex with the command latex mylab1 Note that there is no need for the extension tex If there are errors IATFX will stop at the first one and leave you hanging at a question mark on the screen At this point you may answer x to stop processing and to fix the reported error Or if you answer r for run ATEX will finish processing to the best of its ability writing all errors to mylab log which you can then review in one window while correcting mylab tex in another To view mylab dvi use a UNIX program called xdvi xdvi mylab1 Again there is no need for the extension dvi As of now it is not possible to print your dvi document from the viewer s window For printing you need to convert it to either to a Postscript file dvips mylab1 dvi mylab1 ps or to a PDF file dvipdf mylab1 dvi mylab1 pdf To open a Postscript picture invoke the GhostView viewer by typing gv or ghostview on the command l
81. aced at the bottom of a text page but no earlier than the present page p the object should be set on a page of floats that consists only of tables and figures A combination of these indicates decreasing order of preference The default is tbp You may also force IFEX to place the figure or table in a desired spot by using capital H To do this you must include the float package by using usepackage float in your preamble IAT X will also number a figure or table for you supply a caption and compile a list of tables and a list of figures Just include listoffigures and listoftables next to your tableofcontents command at the beginning of the document To caption a table of figure include caption caption text just before the end table or end figure command Here is a sample source file begin table htbp begin tabular 1rll end tabular caption Mark analysis end table To leave space for a figure that will inserted by some other means at a later date we can use the vspace command begin figure htbp vspace 9 5cm caption An artists impression end figure Page 60 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX 3 4 Mathematical typesetting with BT X Original text by Gavin Maltby 1992 adapted by Math 2130 Instructors 1995 1998 The last section taught us a good deal of what we need to know in order to prepare quite complicated non mathematical documents There
82. ain TeX document file you have to be sure to include the 1grind package usepackage lgrind At the point in the document where you want to include the source code give the command lgrindfile sample tex Figure 3 1 A presents an example of how the file would show in your document An alternative method of including source code which does not require any intermediate processing would be to declare a few commands near the start of your ATEX document newcommand beginverb begin verbatim newcommand inputfile 1 input 1 newcommand verbatimfile 1 expandafter beginverb inputfile 1 and later on make use of the verbatimfile command small verbatimfile sample c end verbatim Don t forget to close the brace after end verbatim otherwise the rest of your document will be printed in a small font size The program listing printed with this method is displayed on Figure 3 1 B Page 31 Chapter 3 Typesetting with ATRX 3 1 Elements of WIpX A This is a short C program to compute the sum of the integers from 1 to 1000 and print the result Z include lt stdio h gt define N 1000 int Sum int maxnum int main printf The sum of the integers from 1 to d is Z d n N Sum N return 0 int Sum int maxnum int i total 0 for i 1 i lt maxnum i total i return total This is a short C program to compute the sum of the in
83. al When the special command is used the result may not always be dispalyed correctly In this case the dvi picture may have some unrotated elements but when a dvi file is converted to pdf the correct rotation is put in place Some other picture commands in 2130 sty closecurve a b c d e f produces a triangle on the vertices a b c d and e f curve a b c d e f produces two segments joining a b to c d to e f rotate deg object rotates the object through deg degrees This needs Postscript rtangle deg size is used in diagrams to produce a right angle marker Needs Postscript Page 121 Chapter 4 Programming and graphing 4 4 The ATEX picture environment 4 4 4 Superimposition The picture environment can be used to manipulate position of graphics and text by hand if needed While this should not be considered as a good practice in general Do not fight TAT X It knows better sometimes knowing how to fine tune your document may help As an example consider the layout of Figure 4 1 on page 98 On the left we have the text of a program made within the verbatim environment and on the right there is an eps picture of the two triangles inserted by means of the incudegraphics command The question is how it is possible to make TFX to put the graphics in such a non standard place The key trick is the picture environment with a tiny height which however enables precise positioning of any objects graphics
84. an be obtained from just a single key press They are lt gt and Note that these must be typed within math mode to be interpreted as math symbols Of course all of a z A Z the numerals 0 1 2 9 and the punctuation characters and are available directly from the keyboard Alphabetic letters will be assumed to be variables that are to be italicized unless told otherwise see Sect 3 4 4 The numerals receive no special attention appearing precisely as in normal paragraphing mode The punctuation symbols are still set in standard roman type when read in math mode but a little space is left after them so that expressions like x i 1 2 10 look like they should Note that this means that normal sentence punctuation should not migrate into an expression Greek letters Tables 3 4 and 3 5 show the control sequences that produce the letters of the Greek alphabet We see that a lowercase Greek letter is simply is accessed by typing the control word of the same name as the symbol using all lowercase letters To obtain an uppercase Greek letter simply capitalise the first letter of its name Just as mistake produces mistake because the letters are interpreted as variables so too will tau epsilon chi produce the incorrectly spaced Tex if you try to type greek words like this T X can be taught to set Greek but this is not the way 7ex incidentally is the Greek word for art and it is from the initia
85. ance is just to say The roots are x 5 and z3 1 Of course the style and level of details that you should or should not provide depend on who your readers are In any case saying that to use the Quadratic Formula is necessary here is unprofessional 2 4 4 Common words in mathematical writing Learn to use basic mathematical terminology precisely and avoid common misuses For example watch the following as you write e An equation must have two parts sides connected by the sign A thing like sin x cos is not an equation it can be described as an expression or more precisely as a trigonometric polynomial Also don t call x y gt 2 xy an equation it is an inequality e At the beginning of a mathematical argument you often make an assumption while at the end you arrive at a conclusion Expressions like Assume suppose that something is or equivalently Let something be are very standard Steps of your argument or formulas that you display or refer to should be verbally connected using words like imply follow yield etc to make the flow of the argument smooth and its logic transparent e Here are some common frequently used safe verb noun collocations An equation can be solved or solved for x In contrast a polynomial like x 5a 6 without any right hand sign cannot be solved there is no equation to solve but it may have roots Also a polynomial can be evaluated at a particular point
86. ancy In the end rewrite the introduction anew No matter what approach the chance of writing a good paper from scratch in one attempt is small Editing will be necessary Read what you have written Note what sounds ugly awkward cumbersome Strive for clarity Move material around to achieve the best logical order Replace vague phrases and words with clear cut ones Check your writing against this Manual cross read the papers with a friend consult with the Writing Centre 2 3 Organization of report 2 3 1 General requirements A typical report in this course contains or may contain the following components in this order O O O Title page Table of contents Abstract Body of report Introduction Technical Details Mathematical details Program details Results and Analysis Conclusion Acknowledgements References Appendix Page 9 Chapter 2 Technical writing 2 3 Organization of report The items marked with solid bullets are mandatory the presence of others depends on the circumstances We ll comment on each of them one by one The body of your report from Introduction to Conclusion excluding in text graphs and illustrations should not exceed six printed pages This means that you must clarify your ideas and arguments and write them in a very precise and concise way 2 3 2 Title page The title page should give the following information e The title and number of the lab e The course name and n
87. are still a number of useful topics that we have not covered such as cross referencing but we will defer discussion of those until a later section In the present chapter we will learn how ATFX typesets mathematics It should come as no surprise that ATEX does most of the work for us 3 4 1 Introduction In text only documents we saw that our task was to describe the logical components of each sentence paragraph section table etc When we tell ATEX to go into mathematical mode we have to describe the logical parts of a formula matrix operator special symbol etc TEX has been taught to recognize a binary operation a binary relation a variable an operator that expects limits and so on We just need to supply the parts that make up each of these and T X will take care of the rest It will leave appropriate space around operators italicize variables set an operator name in roman type leave the correct space after colons place sub and superscripts in the correct positions based on what it is you are working with choose the correct typesizes the list of things it has been taught is enormous When you want to revert to setting normal text again you tell ATEX to leave math mode and go back into the mode it was in paragraphing mode IXATFX cannot be expected to perform these mode shifts itself for it is not always clear just when it is mathematics that has been typed For example should an isolated letter a in the input file
88. at how to arrange symbols all over the show e g the subscripting above we must learn how to access the multitude of symbols that are used in mathematical texts Page 64 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX 3 4 3 Using mathematical symbols IXT X puts all the esoteric symbols of mathematics at our fingertips They are all referenced by name with the naming system being perfectly logical and systematic None of the control words that access these symbols accepts an argument but we will soon see that some of them prepare IXTEX for something that might follow For instance when you ask for the symbol IATpX is warned that any sub or superscripts that follow should be positioned appropriately as limits to a summation In keeping with the TEX spirit none of this requires any additional work on your part We will also see that some of the symbols behave differently depending on where they are used For instance when I ask for gt _ a within the running text the limits are places differently to when I ask for that expression to be displayed n 20 i 1 Again I typed nothing different here just asked for display math mode It is important to note that almost all of the special math symbols are unavailable in ordinary paragraphing mode If you need to use one there then use an in line math expression Symbols available from the keyboard A small percentage of the available symbols c
89. at plagiarism is and details the range of consequences that result from an act of plagiarism This section is not intended to frighten you and to discourage sharing ideas with fellow students or using available information resources The Calendar points out that the properly acknowledged use of sources is an accepted and important part of scholarship Just know the limits They are sometimes subtle The next two sections should help you develop a better understanding of situations routinely occurring in practice 1 3 3 Collaborative work During the course students are encouraged to work together Feel free to trade ideas about how to approach a given project how to write programs how to use Maple and FATRX etc Page 4 Chapter 1 Introduction 1 4 MUN Writing Centre All help received should be acknowledged see Section 2 3 8 and all sources consulted must be referenced However when the time comes to prepare a report each student will see this activity as entirely his or hers Each student is completely responsible for the intellectual content of his or her report and later may be asked to explain any material contained in the report All reports must be written by students on their own They cannot be based on any report previously submitted for this course say by a sister a friend or a tutor or a report being submitted concurrently by a classmate Also if a student is repeating the course reports are not permitted to b
90. ate is deter mined by points each point being a pair of coordinates x y Continuous mathematical curves consisting of infinitely many points are most commonly approximated by polygonal lines con sisting of segments whose endpoints are to be computed by the program When writing a program you have to make a decision as to what the bounds for x and y should be if the mathematical curve is infinite and by how many points you want to define the curve To get a rough estimate of a reasonable number let us take 5 in as a largest dimension of a picture and note that human eye even sharp can hardly resolve distances less than 1 200 of an inch Thus 5 x 200 1000 data points across a sheet is perhaps enough in most cases The smoother a curve the smaller number of points will suffice often 50 or even 10 A good idea is to have variables in your program for the x and y limits and for the number of points rather than to use specific numbers throughout the code Compare the two fragments of FORTRAN code GOOD BAD xmin 5 xmax 5 numpoints 20 xstep xmax xmin numpoints DO i 0 numpoints DO i 0 20 x xminti xstep x 5 140 5 y SIN x PRINT x y PRINT x SIN x END DO END DO The bad code does not look bad at all it is concise easy to understands and correct But it has two drawbacks 1 the code conceals the meaning of the numbers what are those 20 and 5 and 0 5 2 if
91. be meeting many more of these type of control sequences Incidentally underlining was the traditional way in which writers working only with type writers were able to provide emphasis Nowadays underlining is poor form because it so easy to italize With TEX use em something pretty long or emph a word or two to produce something pretty long or a word or two Another enormously powerful class of control sequences is those that accept arguments They tell IATFX to take the parts of text you supply and do something with them like make a fraction by setting the first argument over the second and drawing a line of the appropriate length between them These are part of what makes TFX so powerful and here are some examples e overline words causes words to be overlined e frac atb c d sets the given two argument as a fraction doing most of the dirty work a b for us c d e sqrt 5 a b typesets the fifth root of a b like this Va b The 5 is in square brackets instead of braces because it is an optional argument and could be ommited all together giving the default of square root Mandatory arguments are given enclosed by braces and optional arguments enclosed by square brackets Each command knows how many arguments to expect so you do not have to provide any indication of that We have actually jumped the gun a little The above examples include examples of mathe matical typesetting and we have not yet seen how to
92. be regarded as a word as in the definite article or a mathematical variable as in the variable a There are no reliable rules for ATEX to make such decisions by so the begin math and end math mode switching is left entirely to you The symbol is specially reserved See Sect 3 3 3 by ATEX as the math shift symbol When TeX starts setting a document it is in paragraphing mode ready to set lines of the input file into paragraphs It remains in this mode until it encounters a symbol which shifts TeX into mathematical mode It now knows to be on the look out for the components of a mathematical expression rather than for words and paragraphs It reads everything up to the next sign in this mathematical mode and then shifts back to paragraphing mode i e the mode it was in before we took it in to math mode You must be careful to balance your begin math and end math symbols It is often a good idea to type two symbols and then move back between them and type the mathematical expression If the math shift symbols in a document are not matched then ATEX will become confused because it will be trying to set non mathematical material as mathematics For those who find having the same symbol for both math begin and math end confusing or dangerous there are two control symbols that perform the same operations the control symbol C is a begin math instruction and the control symbol is an end math instruction Since Page 61 Chapter
93. cademic misconduct 3 A Forging research results 2 2 2 ee 4 Bz Plagiarism a Ne SA Be hh 4 1 33 Collaborative work 1 a 4 1 3 4 Use of online materials 2 e e a 5 1 4 MUN Writing Centre aio uk RON ee eB po ee po OR e a iy 5 2 Technical writing 7 2 1 Technical versus non technical writing ee 7 2 2 EII process ca a A eo A a Be a nh at 8 2 3 Organization of report ooo 9 2 3 1 General requirements 9 22822 Lite Pate a a el Aa oo eh Pa aa ee PRON ey 10 23 3 Table f contents ai amp oe AS A A eB Be a oe A 10 2 3 4 NDSUEACh A fees Sacer ai talento She I ey he ee Pee Bhd De et 11 2 3 5 Introduction and Conclusion 2 e a a ee 11 2 3 6 Technical details e 14 23 7 Results and Analysis cx hee oS BU ee Ee eS 17 2 3 8 Acknowledgements and References 0 0 00 eee 18 23 9 Appendix see A eee Se a is rara 19 2 4 Suggestions about style aooaa ee 20 24 1 A note OMSpellde ieas A ee lee Ge Gus Gtk ew he hin ee es 20 2 4 2 Squeeze water out Eliminate unnecessary words 20 2 4 3 A note on strong words 0 2 00000 eee ee ee 21 2 4 4 Common words in mathematical writing 21 24 5 WE Versus iia eS Sod wig Ee SUS Bae BL Aa EO OS BALE PS 22 2 4 6 Verb forms tense mood modal verbs 2044 22 MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009
94. center begin picture 24 5 put 2 3 circle 0 put 3 3 circle 1 put 5 3 circle 2 put 8 3 circle 3 put 12 3 circle 4 put 17 3 circle 5 end picture end center Page 117 Chapter 4 Programming and graphing 4 4 The ATEX picture environment setlength unitlength 0 1em begin center begin picture 140 50 put 0 30 circle 0 put 10 30 circle 1 put 20 30 circle 2 put 30 30 circle 3 put 40 30 circle 4 put 50 30 circle 5 put 60 30 circle 6 put 70 30 circle 7 put 80 30 circle 8 put 90 30 circle 9 put 110 30 circle 10 put 135 30 circle 12 end picture end center 0000000 O O 0 0000 a In the scaledpicture environment drawing circles is made easy and consistently correct with the command arc This command has three parameters and is used thus put a b arc p q deg Here the centre of the arc is at a b the point where the arc begins is p q with this being taken relative to the centre of the arc and the arc is drawn deg degrees in the positive counter clockwise sense from the starting point For example put 0 1 arc 2 0 360 will draw a circle of radius 2 centered at 0 1 Labels Labels can be placed on a diagram using the command put x y label A label is usually a letter or a number typed in math mode like A to produce a slanted A on the picture for n
95. ch To specify an em dash you type three consecutive dashes on the keyboard as in a sentence I tend to Theorems 1 3 concern the semi completeness of our new construct in the case that it satisfies the first axiom yields Theorems 1 3 concern the semi completeness of our new construct in the case that it satisfies the first axiom Ties When you always remember to use ties you know that you are becoming T Xnically inclined Ties are used to prevent IATFX from breaking lines at certain places ATFX will always choose line breaks that result in the most aesthetically pleasing paragraph as judged by its stringent rules But because ATEX does not actually understand the material it is setting so beautifully it can make some poor choices A tie is the character It behaves as a normal interword space in all respects except that the line breaking algorithm will never break a line at that point Thus Dr Seuss should be typed as Dr Seuss for this makes sure that TEX will never leave the Dr at the end of one line and put the Seuss at the beginning of the next Page 50 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends One should try to get in to the habit of typing ties first time not after waiting to see if I4TpX will make a poor choice This will allow you to make all sorts of changes to your text without ever having to go back and insert a tie at a point that has migrated to th
96. chnical writing is strongly biased towards precision and clarity as opposed to figurative metaphoric language common in non technical narration Technical writers should as a rule keep a neutral tone and abstain from emotional bursts There are also specific problems whether to use I or We or write in the third person what tense to use etc Questions of this kind are discussed in Sect 2 4 and B 1 3 Writing mathematics properly is a special art which does not come easily Section 4 in Appendix B 1 should help you get started MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Chapter 2 Technical writing 2 2 Writing process 2 2 Writing process Before setting out to write a report one must have something to report This means in our case results a solution to the assigned problem Obtaining the results usually takes up most of the time students spend on their Math 2130 assignments Remember however properly presenting your work in writing is not a simple task either With the results obtained and the pertinent information collected do you need anything else before starting to write Perhaps There are questions to answer and decisions to make e What is the main purpose of your paper Is it to illustrate a certain mathematical theory with examples you have produced by hand and with the help of a computer Or is it to report your algorithm of solution of the a
97. class or style file that determines what a theorem will appear like so do not go changing this if you are preparing for submission for publication because the journal staff want to substitute their production style for your document class choice and not be over ridden by other commands Page 79 Chapter 4 Computer assisted research programming and graphing 4 1 Programming 4 1 1 Development process A program development cycle is the incremental process of building up your code testing and debugging It involves four steps e Write and modify source code of your program in a text editor e Create an executable file from the program source file with a compiler e Run your program e Observe the effect and decide if further changes in the code are needed A computer cannot directly run a program source file which is a human readable text file The source file must be translated into an executable binary file which the computer understands A compiler is a program that does this translation For each programming language there is its own compiler sometimes more than one See information about the compilers available on local machines in Section 5 3 3 Often during the development cycle you have to repeat certain commands over and over again for example gcc project2 c a out To minimize typing you can use a history keystroke Esc K or see Sect A 4 MMIX Department of Mathematics and Statistics Memorial
98. clauses or use two sentences Keep your sentences simple and to the point It may help to keep most of them short but you need some longer ones to keep your writing from sounding choppy and to provide variety and emphasis A pronoun normally refers to the previous noun Unfortunately it is common to abuse pronouns particularly it this and which Make sure the reference is immediately clear especially when you refer broadly to a preceding phrase topic or idea It is also common to use a plural pronoun such as their to refer back to a singular but indefinite antecedent such as a reader This usage is still considered unacceptable in formal writing reformulate your sentence if necessary The pronouns that and which are not always interchangeable Either may be used to introduce a restrictive clause but use that ordinarily Only which may be used to introduce a descriptive clause and the clause must be set off with commas Strunk and White in their classic guide to style 8 p 47 recommend which hunting Punctuation is used to eliminate ambiguities in language and to smooth the flow of the text A simple misuse of punctuation can weaken your authority Learn how to punctuate properly and use a handbook like The Chicago Manual of Style In optional cases use the punctuation if it promotes clarity at all but strive for consistency through out the paper Here are a few rules Us
99. command cd Ls 2 issued from Bob s directory m2130 lab1 will change directory to Bob s math2130 lab2 because only one directory name matches the pattern x2 The cp command creates a new copy of a file For example if the current directory contains one file lab1 tex and you ran cp lab1 tex newlab tex then Is would display lumsden cp labl tex newlab tex lumsden Is labi tex newlab tex Page 136 Appendix A Quick UNIX reference A 7 Redirection of output and the contents of newlab tex would be identical to lab1 tex If a file named newlab tex had already existed that file would have been overwritten The command cp with wildcards in its arguments is very convenient when you copy your files from the working directory to the submission directory see Sect 5 1 The command cp u u m2130 al will copy all files from the current directory to its subdirectory named m2130 al This may not be exactly the desired outcome for instance log aux dvi and a out files need not be included So a better command is ls tex y eps f which will copy all possibly single TEX source file s any encapsulated Postscript figures and any Fortran programs The mv command is similar to the copy command However the original name of the file will be lost after the command is finished You can also use mv to move a file from one directory to another The mv command has similar behaviour to cp if its last argument is a di
100. contentsline toc section Appendix A Program source code 3 2 3 Abstract Abstract The quote environment provides a nice format for an abstract Type the word Abstract in boldface and the rest in a regular font style Abstract should not be included in the TOC Page 35 Chapter 3 Typesetting with ATRX 3 2 Formatting your Math 2130 report in ATEX 3 2 4 The body of report Use the section command for section headers like Introduction Technical Details etc Use the subsection command for parts of the main sections Having third tier headers subsubsections can hardly be justified in a typical Math 2130 report Acknowledgements and Appendix should not be numbered as regular sections Use the section command for example section Acknowledgments The so formatted sections are not automatically referenced in the TOC You should include a reference to Appendix or Appendices but probably not to Acknowledgements 3 2 5 References The list of references is printed using thebibliography environment For example begin thebibliography 4 bibitem hagin Frank G Hagin A first course in differntial equations Prentice Hall Inc New Jersey 1975 bibitem m2130 Math 2130 Course Manual MUN 2008 bibitem fourier bio Jean Baptiste Joseph Fourier biography verbthttp www history mcs st andrews ac uk history Mathematicians Wverb Fourier html Accessed December 2 2008
101. coordinate triples x y z There are 16 data blocks each describing the level curve z z of the glass that is the circle with radius f z for 16 different not equally spaced values z in the range from z 0 911 to 216 1 101 Each block in its turn consists of 16 points equally distributed along the level circle with angular separation 360 16 Here are the commands used to obtain figure 4 14 and a brief explanation unset key Do not show legend set hidden Do not show hidden lines set xtics 0 5 0 5 0 5 Set ticks on x axis starting from 0 5 set ytics 0 5 0 5 0 5 with step 0 5 ending at 0 5 set xyplane 0 Adjust the position of the base xy plane set border 4095 Draw a box around the plot splot glass dat using 2 1 3 with lines 2 1 3 means interchange x and y data Page 110 Chapter 4 Programming and graphing 4 3 Drawing graphs Figure 4 14 Plot produced from file glass dat with hidden lines removed The order in which the columns in the data file are used was changed with the using 2 1 3 option in an effort to get a solid line to represent the forefront portion of the glass Otherwise the dashed line appears on the front somehow This is a harmless move in this case thanks to the rotational symmetry of the glass Generating Postscript with Gnuplot Once in the course of a Gnuplot session you have a complete graph exactly as you want it then simply issue the commands g
102. d pstex files besides the main tex file Page 113 Chapter 4 Programming and graphing 4 4 The ATEX picture environment 4 4 The PTX picture environment and enhancements 4 4 1 Introduction The most straightforward way to draw diagrams in a 4TfXed document is to use the picture environment begin picture xlen ylen leftcornerx leftcornery end picture Here xlen and ylen are the ranges from zero of the x and y coordinates The optional parameters leftcornerx and leftcornery change the bottom left hand corner from the origin to the new coordinates They may be omitted if the bottom left hand corner is the origin The picture environment essentially allows you to do only one thing to put put xcoor ycoor object An object can be a IATRX s graphics element line circle or a text formula paragraph parbox table etc It can also be the includegraphics command referring to an eps file to be imported The dimensions of the picture in the environment s header and the coordinates in put com mands are given just as numbers without specyfying the unit of length The default unitlength is 1 point 1 72in 0 35mm It is rather too small for practical purposes and for conve nience it can be reset by a command like setlength unitlength 1cm printed just before the beginning of the picture environment IAT X has very limited and poor graphical faclities of its own Its line command cannot even c
103. d and perhaps rewritten from the reader s point of view Rule 1 A good way to begin is to use a standard classic of mathematical exposition e g Bourbaki Algebra works by Serre or Milnor as a basic model e Some further sources to look at P Halmos How to write mathematics Enseign Math 16 1970 123 152 W Strunk Jr amp E B White The Elements of Style Macmillan Paperbacks Edition 1962 D Knuth et al Mathematical Writing MAA Notes 14 1989 Some conventions on citations and pronouns may be found in S Zucker Variation of a mixed Hodge structure II Inventiones Math 80 1985 p 545 e Finally I quote from a letter Serre wrote commenting on my original version It strikes me that mathematical writing is similar to using a language To be understood you have to follow some grammatical rules However in our case nobody has taken the trouble of writing down the grammar we get it as a baby does from parents by imitation of others Some mathematicians have a good ear some not and some prefer the slangy expressions such as iff That s life Page 154 Index abbreviating ATEX commands 25 abbreviations abuse of 145 153 academic integrity 3 academic misconduct 3 academic offences 4 accents in ATEX 44 Abstract 11 35 142 acknowledging help 5 18 Acknowledgements 18 algorithm 15 implementation of 15 Alice and Bob 12 alignment in math mode 77 ampersand amp 29
104. d ne should be used instead of not If negating a symbol produces a slash whose horizontal positioning is not to your liking then use the math spacing characters described in section 3 4 4 to adjust it lt Meg gt geq equiv H models lt prec gt succ sim perp lt preceq gt succeq simeq mid amp ll gt gg lt Nasymp parallel C subset D supset approx X bowtie C subseteq 2 supseteq cong X Join E sqsubset 4 sqsupset A neq smile E sqsubseteq 1 sqsupseteq doteq frown Vin gt ni x propto E vdash dashv Table 3 7 Binary relations Miscellaneous symbols Table 3 8 shows a number of general purpose symbols Remember that these are only available in math mode Note that imath and jmath should be used when you need to accent an i or a j in math mode see Sect 3 4 3 you cannot use Ni or j that were available in paragraphing mode To get a prime symbol you can use prime or you can just type when in math mode as in f x x which produces f x z7x The symbols N Z Q R C H commonly used to denote number domains natural inte ger rational real complex and quaternion respectively are obtained by the commands like mathbb N You need to includepackage amssymb in the preamble of your document Page 67 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX N Naleph prime
105. d line mode Of the two graphical interfaces the classic worksheet is the one which is easier to transform to a printed document Our presentation will be based on the classic worksheet The examples below were tested on Maple version 11 in November 2008 Maple graphics is dealt with in Sect 4 3 2 Maple can in principle save a worksheet in ATEX format However this feature doesn t seem to be implemented carefully We suggest that you paste fragments of your Maple code into your reports by hand cf Sect 3 2 6 4 2 1 Basic Arithmetic and Algebra To start Maple open a terminal window and at the prompt simply type xmaple Maple also has a classic worksheet option which can be accessed by typing xmaple cw at the prompt Maple has a very useful help area where you can find instructions on the many operations it can perform In the classic worksheet the Help command is located in the top right hand corner In the standard Maple it is located under Tools Also in all interfaces of Maple help can be accessed by typing help Maple can be used as a calulator Hit Enter to execute the command The keystroke Shift Enter makes carriage return without an immediate execution Our first examples are gt 4 3 7 gt 2 5 672 10 Page 87 Chapter 4 Programming and graphing 4 2 An introduction to Maple 36 Note the difference between exact and floating point operations gt 2764 18446744073709551616 gt 2 0764 1 84
106. d your program in a half a year period of time Use indentation to improve readability of loops especially long ones and if else clauses GOOD BAD for i 1 i lt n i for i 1 i lt n i if a il gt 0 if alil gt 0 sum sumta i sum sumta il else else sum sum ali sum sum a i Use meaningful names of variables and functions but don t make them too long A variable name like AreaOfTriang1le is hardly better than just Area If practical use very short names that match the notation you use in the description of the mathematical method Strive for consistency in your programming style as in everything else Good programmers tend to use modular approach subroutines in FORTRAN functions in C classes in C and Java to make the structure of a program more transparent and to confine those few cumbersome mathematical lines of code Modularity also makes debugging easier However in programs with simple linear structure or in short programs modularity can be a burden rather than a benefit Appropriate generalization is another feature of a solid style Make your program flexible make it easy to play with parameters An example of a coordinate generating code on the next page will help you to grasp the idea Page 83 Chapter 4 Programming and graphing 4 1 Programming 4 1 3 Generating graphics data with your own program We will discuss two dimensional graphs only Essentially every graph you gener
107. e Hints on Mathematical Style B 2 Some Hints on Mathematical Style DAVID Goss Many years ago just after my degree I had the good fortune to be given some hints on mathematical writing by J P Serre Through the years I have found myself trying to repeat this very sound advice to other mathematicians who are also starting out Recently I have been involved in the publishing of a proceedings volume as well as being an editor of the Journal of Number Theory Many of the papers coming my way are from young authors so I have written down these hints in order to speed the process along This is a second and most probably final version of these hints I have added comments from a number of mathematicians who read a first version These hints are presented as a source of ideas on mathematical style Feel free to use them in any way that you deem useful e Two basic rules are 1 Have mercy on the reader and 2 Have mercy on the editor publisher We will illustrate these as we move along e General Flow of the Paper Definition All basic definitions should be given if they are not a standard part of the literature It is perhaps best to err on the side of making life easier on the reader by including a bit too much as opposed to too little Rule 1 Some redundancy should be built into the paper so that one or two misprints can not destroy the understandability The analogy is with error correcting codes which
108. e end of a line from the middle of a line as a result of those changes Figure 3 4 shows some more examples of places where you should remember to place ties Lemmas 3 and 4 Chapter 10 Donald E Knuth Appendix C width 2 Figure 1 function f Theorem 2 1 72 0x3 Lemmas 3 and 4 equals 5 Figure 3 4 Some places where ties are useful Over ruling some of T X s choices We have seen that ties can be used to stop linebreaks occurring between words But how can we stop ATEX from hyphenating a particular word More generally how can we stop it from splitting any given group of characters across two lines The answer is to make that group of characters appears as one solid box through use of an mbox command For instance if we wanted to be sure that the word em currentitem is not split across lines then we should type it as mbox em currentitem If for some reason we wish to break a line in the middle of nowhere preventing ATFX from justifying that line to the prevailing right margin then we use the newline command One can also use the abbreviated form We start with a short line newline And now we continue with the normal text remembering that where we press Return in the input file probably will not correspond to a line break in the final document More short lines are easy too will produce the line breaks we want We start with a short line And now we continue with the normal text rememb
109. e not just filling up a space it is worth to neatly re type in a proper mathematical format Important results can hardly be too many A copy of your Maple worksheet submitted electronically is a definitive document and will be used by the instructor should any discrepancy between your reported input and Maple s output be revealed 3 2 7 Floating environments figures and tables LT X has its own ideas as to where it is best to place your figures and tables made by means of the corresponding environments In the processed document it usually does not put them where they ought to be according to their position in the source tex file Many students and not only often find this frustrating However ATEX s behaviour is in most cases backed by well established rules and conventions of typography In general try not to fight ATX very hard If it puts your figure on top of the next page rather than dropping it just on spot think whether you can agree with that decision Only if the displacement of the figure leads to a mess in the logic of your presentation or if a large unfilled area remains on the page you should insist The way to make TEX to put the picture exactly here is to use the figure environment with argument H begin figure H The option H is not provided by standard TEX you must usepackage float in order to be able to use it All this equally applies to the table environment 3 2 8 Automatic numbering cross refe
110. e on the same topics as those submitted previously If a student is not able to explain and or defend the contents of a report the grade on that report may be adjusted If there is evidence that written material in the report has been shared the students concerned may receive a grade of 0 on that report In the case of a last report the student s may be given an incomplete grade and be required to return to campus for a follow up interview Finally if there is a repetition of this sort of activity a grade of zero in the course will be given 1 3 4 Use of online materials The Internet as a source of information can be great if used diligently Proper acknowledgements must be made to all resources cited Another thing to keep in mind is that for the purposes of this course research does not mean googling whatever hopefully relevant stuff is out there and copying it to your paper Not all information on the Internet is credible and correct Also the meaning of being correct is not absolute A definition acceptable for a Ph D level research monograph may be inappropriate in your paper even if it refers to the same concept On the other hand a definition suitable for a common language dictionary may lack significant technical details and also be inappropriate for your purposes even if it comes from a reliable source Do not yet discard printed books in particular textbooks used in courses They are gener ally more reliable and de
111. e periods only to end sentences A complete sentence within parentheses should begin with a capital letter and end with a punctuation mark unless the sentence is part of another Page 144 Appendix B 1 Writing a Phase II Math Paper 3 Language and would end with a period Avoid abbreviations that require periods for example use that is instead of i e Always use commas to separate three or more items in a list and to set off contrasted elements they often begin with but or not Most of the time use a comma after an introductory phrase Use colons to introduce lists definitions and explanations but not in continuing statements if a statement is stopped at the colon then the words should form a complete sentence Use a semicolon to join two sentences to indicate that they are closely linked in content however if you insert a conjunction not an adverb then use a comma Use a dash as a comma of extra strength but use it sparingly Place closing quotation marks after commas and periods it is a matter of appearance not logic To inform you must use language familiar to your readers Define unfamiliar words and familiar words used in unfamiliar ways If the definition is short then include it in the same sentence preceding it by or or setting it off by commas or parentheses If the definition is complex or technical then expand it in a sentence or two Do not use words like capabil ity
112. e scaled so it is left up to you to ask for scaling To ask that a delimiter be scaleable you precede it by left or right according as it is the left or right member of the pair Scaled delimiters must be balanced correctly It sometimes occurs as in the right hand example above that only one member of a delimiting pair is to be visible For this purpose use the commands left and right which will produce no visible delimiter but can be used to correctly balance the delimiters in an expression For examples of the use of delimiters see section 3 4 4 where we learn about arrays Page 68 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Table 3 10 shows the symbols that ATEX will recognize as delimiters i e symbols that may follow a left or a right Note that you have to use left and right in order to get scaled braces a uparrow downarrow M o updownarrow 1floor rfloor Ph Uparrow lceil Mrceil Y Downarrow Nlangle rangle f Updownarrow 1 Y backslash MI Table 3 10 Delimiters Operators like f and y These behave differently when used in display math mode as compared with in text math mode When used in text they will appear in their small form and any limits provided will be set so as to reduce the overall height of the operator as in soe fi When used in display math mode TAT X will choose to use the larger form and will not try to reduce
113. e unless there are exceptional circumstances and they successfully petition their departmental coordinators and the CWR In the Department of Mathematics there is no cooperative subject and nearly every student writes a paper to satisfy Phase Two About three quarters of the papers begin as term papers for a single course 18 310 Principles of Applied Mathematics Every paper must have some technical mathematics in it When the student and the supervisor feel the paper is ready the student picks up a cover sheet in the Undergraduate Mathematics Office Room 2 108 The student fills out the top and gives it to the supervisor who must vouch for the paper s technical accuracy and may comment on the quality of the writing The student then submits the paper to the undergraduate office The paper must be submitted by the start of IAP if the student intends to graduate the following June After a paper is submitted it is read for organization and language by the departmental coordinator who determines whether the paper is acceptable as is or needs to be improved If the paper requires further work the department s Writing TA contacts the student and sets up an appointment to discuss the areas requiring further work The student submits further revisions of the paper to the TA and when the revisions are perfected the paper is resubmitted to the coordinator On occasion the coordinator works directly with the student The goal is to help students bot
114. eason to incorporate a section long language tutorial When it comes to small details give priority to those that require special care Why does the value of J change from 0 to N 1 and not from 1 to N Why is the variable numpoints defined as double while it naturally represents a positive integer quantity Conceivably you want to allow it to assume very large values beyond the range of the type int Issues like these can be addressed For the reader s convenience include only short critical fragments of the actual code in the body of the report The complete listing can be included as an Appendix In any case the program code must be submitted electronically as a part of the assignment bundle The above is not dogma For example it can be important to explain to the reader how exactly your FORTRAN program produces the data file with coordinates in which case the details of the WRITE operator should be discussed although it is not a computational issue 2 3 7 Results and Analysis As in the case with the Technical details section this one can be subdivided if the research has several parts In different projects the meaning of solution or results is different There have been few labs in this course where the answer can be stated in a really short form like projects asking to decipher a coded message In most labs results come from a series of runs of a program that a student creates Each single outcome can be jus
115. efore and after them Assign sequential reference numbers to these headings irrespective of their different natures and use a hierarchical scheme whose first component is the section number Thus Corollary 3 6 refers to the sixth prominent statement in Section 3 and indicates that the statement is a corollary If the statement is the second corollary of the third proposition in the paper then it may be more logical to name the statement Corollary 2 but doing so may make the statement considerably more difficult to locate References E M Alley The Craft of Scientific Writing Prentice Hall 1987 T M Apostol Calculus Volume I Second Edition Blaisdell 1967 bo 3 Committee on the Writing Requirement Guide to the MIT Writing Requirement Under graduate Education Office Room 20C 105 MIT 1989 4 H Flanders Manual for Monthly Authors Amer Math Monthly 78 1971 1 10 5 L Gillman Writing Mathematics Well Math Assoc Amer 1987 6 D E Knuth T Larrabee P M Roberts Mathematical writing MAA Notes Series 14 Math Association of America 1989 7 J R Munkres Manual of style for mathematical writing Undergraduate Mathematics Office Room 2 108 MIT 1986 8 W Strunk Jr and E B White The Elements of Style Macmillan Paperbacks Edition 1962 9 G B Thomas and R L Finney Calculus and Analytic Geometry Fifth edition Addison Wesley 1982 Page 151 Appendix B 2 Som
116. ents due If you mistakenly submit incorrect file s or you make changes to your file s after you have submitted them you may submit again before the due time Your most recent submission must exactly match the submitted hard copy of the report Be aware that the size of your total submission is limited by 10 MB and the size of each single file being submitted should not exceed 2MB Why are the electronic submissions required They are archived year over year and can be automatically checked to detect any occurrences of textual overlap An instructor can use electronic submissions to verify whether your reported results are actually obtained through your program If such a verification is impossible due to insufficient information provided the instructor has a right to doubt the integrity of your research see Sect 1 3 2 5 2 Laboratory computers on campus 5 2 1 Where There are two computer laboratories available to mathematics and statistics majors HH 3030 3056 and EN 2036 As well students may use computers in various General Access Labs around campus For example students may access their accounts through one of the computers located in Chemistry Physics General Access Lab C 2004 or at the Commons located in the QEII Library They also may access computers in C 2003 and CS 1019 when there are no classes taking place in these labs Please note that those machines are maintained by the Department of Computing and Communication S
117. eometric setup of the proof of the First Fundamental Theorem Such a function F is called an integral or a primitive or an antiderivative of f Integrals are not unique if F is an integral of f then obviously so is F C for any constant C On the other hand there is no further ambiguity any two integrals F and G of f differ by a constant because their difference F G has vanishing derivative F G x F x G x f x f x 0 for every z and hence F G is constant by a simple consequence of the Mean Value Theorem for derivatives see 2 Theorem 4 7 c p 187 When we combine the First Fundamental Theorem with the fact that an integral is unique up to an additive constant we obtain the following theorem Theorem 5 2 Second Fundamental Theorem of Calculus Let f be a function defined and continuous on the open interval I and let F be an integral of f on I Then for each c and x in I f E E 5 1 Proof Set G x f7 f t dt By the First Fundamental Theorem G is an integral of f Now any two integrals differ by a constant Hence G x F x C for some constant C Taking x c yields F c C because G c 0 Thus G x F x F c and Equation 5 1 follows The proof is now complete The Second Fundamental Theorem is a powerful statement It says that we can compute the value of a definite integral merely by subtracting two values of any integral of the integrand In practice integra
118. eories and other abstract facts they last indefinitely Naturally in talking about background and history of the problem you would use the past tense You may choose to use either past or present to describe how you have created a computer program and produced the results of numerical simulation The story may be the past for you when you submit the report but it will be current for the reader as he she reads it Variation of tense can be employed just for a particular purpose Do not constantly swing between one tense and another especially within a paragraph or even a section Write in the indicative mood for the most part use conditional only when it is unavoid able Theorems are true not would be true Page 22 Chapter 2 Technical writing 2 4 Suggestions about style Watch other modal verbs besides would In many of students papers the verbs can and must are unnecessarily frequent Example 1 Saying that Equation 1 can be shown to yield formula 2 leaves the reader wonder whether you omit significant steps If the answer is yes you ought to show how the for mer yields the latter Otherwise if the connection between 1 and 2 is transparent enough simply say Equation 1 yields formula 2 Example 2 Here must is used unnecessarily Therefore Equation 3 must hold when t 0 It really means that Equation 3 holds when t 0 Say thus shorter and better Page 23 Chapter 3 Typeset
119. erate description environments IXT X provides three predefined list making environment and a primitive list environment for designing new list environments of your own We shall just describe the predefined ones here There is delightfully little to learn in order to be able to create lists The only new command is item which indicates the beginning of a new list item and the end of the last one if this is not the first item This command accepts an optional argument which means you would enclose it in square brackets that can be used to provide an item label If no optional argument is given then IATFX will provide the item label for you in an itemize list it will bullet the items in an enumerate list it will number the items and in a list of descriptions the default is to have no label which would look a bit odd so you are expected to use the optional argument there Remember that item is used to separate list items it does not accept the list item as an argument begin itemize item an item is begun with verb item item if we do not specify labels then LaTeX will bullet the items for us item I indent lines after the first in the input file but that is just to keep things readable As always LaTeX ignores additional spaces item a blank line between items is ignored for LaTeX is responsible for spacing items item LaTeX is in paragraph setting mode when it reads the text of an item and so will
120. ere is absolutely no room for duplication elaboration and emotions Example This is a bad abstract Abstract In this paper we discuss how to create a program that is useful for modeling global warming Unlike in the real world however where water vapor and carbon dioxide both play an important role our program makes simplifying assumption that there is only one gas responsible for the greenhouse effect whose concentration is proportional to re radiation of heat Finally results of simulations are presented Cut out deadwood and unnecessary elaboration preserve the useful particulars add some specifics on the method and results and a much better version is obtained Abstract We discuss a computer simulation of global warming based on a simple mathe matical model in which one gas is responsible for the greenhouse effect and its concentration is proportional to re radiation of heat The program iterates over time steps one per sea son Instability of temperature is observed if the intensity of gas emission exceeds a certain critical value 2 3 5 Introduction and Conclusion If after glancing at the Abstract the readers feel the paper is not out of touch with their interests they browse through the Introduction and Conclusion The central part of the paper with all the technicalities is the last place the readers will go The Introduction as the name suggests should introduce the reader to the problem being investigated Mo
121. ering that where we press Return in the input file probably will not correspond to a line break in the final document More short lines are easy too A warning is in order newline must only end part of a line that is already set It cannot be used to add additional space between paragraphs nor to leave space for a picture Page 51 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends you want to paste in This is not to be awkward but is just part of ATFX holding up its end of the deal by making you have to specially request additional vertical space This prevents unwanted extra space from entering your document Later we shall see how to impose our own choice of page size paragraph indentation etc For now we will continue to accept those declared for us in the document class 3 3 5 Document structure Sectioning commands As part of our task of describing the logical structure of the document we must indicate to TeX where to start sectional units To do this we make use of the sectioning commands chapter section subsection subsubsection Each sectioning command accepts a single argument the section heading that is to be used TFX will provide the section numbering and numbering of subsections within sections etc so there is no need to include any number in the argument TAT X will also take care of whatever spacing is required to set the new logical unit off from the others perhaps through a li
122. es too should be numbered for easy reference Most papers have an abstract an intro duction a number of sections of discussion and a list of references On occasion papers have appendices which give special detailed information or provide necessary general background to secondary audiences In mathematics few papers have a section of conclusions and recommen dations Such a section would discuss the results from an overall perspective bring together the loose ends and possibly make recommendations for future research In mathematical papers these issues are almost always incorporated into the introduction Normally short papers have no formal table of contents Sectioning involves more than merely dividing up the material you have to decide about what to put where about what to leave out and about what to emphasize If you make the wrong decisions you will lose your readers There is no simple formula for deciding because the decisions depend heavily on the subject and the audience However you must structure Ithe Mathematical Association of America Page 141 Appendix B 1 Writing a Phase II Math Paper 2 Organization your paper in a way that is easy for your readers to follow and you must emphasize the key results The title is very important If it is inexact or unclear it will not attract all the intended readers A strong title identifies the general area of the subject and its most distinctive features A strong t
123. etting system ATEX Ch 3 e Computer programming and computer generated graphics Ch 4 An attempt has been made in this Manual to isolate the discussion in Chapters 2 4 from particulars of the computing environment Chapter 5 provides details about computer facilities on campus available to Math 2130 students and about software pertaining to this course MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Chapter 1 Introduction 1 2 Submissions 1 2 Submissions Students are required to submit a neatly stapled printed copy of the report and also to submit all reports electronically Section 5 1 explains the purpose and procedure of electronic submission The electronic submission must contain a master WT X file and all files that the master file refers to in most cases these will be eps graphics files In addition the electronic submission must include computer code s written to produce the reported results Two sections in this Manual specifically deal with report format Section 2 3 contains recommendations about a logical structure and size of the reports Section 3 2 describes the standard report layout and ATEX commands used to produce it 1 3 Policies 1 3 1 Evaluation Grades in the course are based on four projects each requiring a written report submitted in printed form and electronically There is no final examination The first three reports will be
124. etting with ATRX 3 4 Mathematical typesetting with ATRX It has been produced by det A left begin array cccc a_ 11 a_ 12 cdots a_ 1n a_ 21 a_ 22 cdots a_ 2n vdots amp vdots amp ddots amp vdots a_ mi amp a_ m2 amp cdots amp a_ mn end array right The array environment is often used to typeset material that is not strictly speaking an array f x left beginfarray 11 x amp mbox for x lt i x 2 mbox for x geq 1 end array right which will yield Changes to spacing Sometimes TFX needs a little help in spacing an expression or perhaps you think that the default spacing needs adjusting For these purposes we have the following spacing commands 3 thin space medium space negative thin space NG thick space quad a quad of space qquad two quads of space The spacing commands quad and qquad can be used in paragraphing mode too Here are some examples of these spacing commands used to make subtle modifications to some expressions Type To produce sqrt 2 A x v2x int_a b f x dx S f x de Gamma_ 2 T gt lint_a b int_c d f x y dx dy S f a y de dy x sin x x sinx sqrt sin x V sing 3 4 5 Alignment Recall that the equation environment can be used to display and automatically number a single line equation see Sect 3 4 2 The eqnarray environment is used for display
125. files are created by ATEX to be printed on various devices such as the screen or a laser printer These files names will end in dvi This stands for device independent e pdf files The extension pdf stands for Portable Data Format developed by Adobe Inc Files in this format are produced by many word and data processors including TFX Acrobat Reader is the most popular viewer for these files e ps and eps files The extension ps denotes Postscript another page description format developed by Adobe Inc In fact Postscript is pretty much a programming language Postscript graphics files can even be created by hand but usually their creation is helped by a software Encapsulated postscript eps format is almost identical The only difference is that an eps file must contain the Bounding Box information see Sect 4 3 1 This tiny difference is important when you have to incorporate a Postscript graphics into your TATFX document e mw and mws These are the extensions assigned to Maple worksheets Depending on context the term file name can refer either to the full name or to the part preceding the dot after which the extension follows So we would often say the IAI X file project3 here the full file name project3 tex is implicit Each file must have a unique name which distinguishes it from all other files If a file is named sensibly the name will give a clue as to the contents One important point is to distinguish be
126. finitive sources of information unlike many Internet sites they have gone through a strict review process and multiple proofreadings 1 4 MUN Writing Centre Look up the Writing Centre webpage http www mun ca writingcentre about and consider dropping in there some day Students who experience problems with their writing may find their marks dramatically different depending on whether or not they show their work to a knowledgeable writing advisor before final submission Page 5 Chapter 1 Introduction 1 4 MUN Writing Centre If you consider yourself to be a good writer the mark improvement through the use of the Writing Centre may not be a big issue But it s a misconception that only weaker students should seek help there Not quite so In fact the better you write the more efficient the help can be you and your advisor can concentrate on how to make your paper really enjoyable and perfection has no end Remember however that people in the Writing Centre are not supposed to understand the technical content of your paper and they may not be familiar with specific requirements traditions and habits of mathematical exposition Those who help you ought to get due credit but the remaining deficiencies are yours No one but you is ultimately responsible for everything in your paper including style spelling and punctuation And your instructor will have the last say in evaluating your writing Page 6 Chapter 2 Technical
127. g The commands used to generate each plot are given but we are not attempting to explain the options involved Look up a reference and play around with them to see for instance what effect the absence of the command unset key will produce or what will a different numerical value of spacing samples isosamples etc do Page 107 Chapter 4 Programming and graphing 4 3 Drawing graphs 1 i gt 7 0 8 a ES A a H J 0 6 f os x E 0 4 j 02 4 i fo 0 L 4 o2t y a a fd oat A A S Vif 0 6 A y i 0 8 1 Figure 4 12 Graphs of functions produced by Gnuplot on its own A B set key spacing 2 unset key set parametric plot 0 2 pi sin x cos x set trange 1 7 set samples 10000 plot log t cos 100 t log t sin 100 t C D unset key set ztics 0 5 0 5 1 5 unset tics unset border unset key set xrange 1 1 set isosamples 50 20 set view 18 45 1 3 set yrange 1 1 set xrange 3 3 set yrange 3 3 splot x 2 y 2 x 2 y 2 1 5 splot sin x 2 ty 2 x 2 y 2 cos 100t Notes B represents a parametric curve logarithmic spiral Int sin 100t D displays the same function as Figure 4 8 on p 103 Page 108 Chapter 4 Programming and graphing 4 3 Drawing graphs Two dimensional data plots We will now use Gnuplot to plot data from a file supplied by the user For two dimensional plots the content
128. g algorithm I have to this point not once chosen a page break in this document Punctuation Typists have a convention whereby a single space is left after a mid sentence comma and two spaces are left after a sentence ending period How do we enforce this if TFX treats a string of spaces just like a single one The answer unsurprisingly is that we do not To have a comma followed by the appropriate space we simply type a comma follows by at least one space To end a sentence we type a period with at least one following space No space will be inserted if we type a comma or period followed straight away by something other than a space because there are times when we will not require any space i e we do what comes naturally will produce To have a comma followed by the appropriate space we simply type a comma follows by at least one space To end a sentence we type a period with at least one following space No space will be inserted if we type a comma or period followed straight away by something other than a space because there are times when we will not require any space i e we do what comes naturally IATRX will produce suitable space after commas periods semi colons and colons excla mation marks question marks etc if they are followed by a space In stretching a line to justify to the right margin it also knows that space after a punctuation character should be Page 48 Chapter 3 Typesetting with ATRX 3 3 An intr
129. gram for counting partitions of integers Definition A partition of a positive integer N is a set of positive integers arranged in non increasing order ny gt n2 gt gt nz such that ny no nk N Page 12 Chapter 2 Technical writing 2 3 Organization of report You can help the reader to understand the definition without breaking away from the formal style by adding a comment or remark explaining important particular cases For example A partition with the least value k 1 consists of one element n N A partition with maximum number of elements k N is ni ng ny 1 The project may later deal with special classes of partitions say those with non equal members It is not necessary and hardly appropriate to put all definitions in the Introduction The last section Conclusion or Concluding Remarks contains a brief summary of the findings of your report By reading only the summary a reader should be able to ascertain the most important facts resulting from your work Do not overload the conclusion with details of the results It is tempting to create the Conclusion from the Introduction by a simple copy and paste method However such an approach misses the point Observe the difference If your intro duction sets up a goal or makes a promise as we suggest it should the conclusion serves as a checklist has the goal been reached is the promise fulfilled Sometimes the answer
130. h before or after In particular the text following the displayed math without blank line in between will not be indented A modification of the displaymath environment is the equation environment which dis plays a single numbered equation like this 24 2 4 1 LIT X automatically numbers equations enclosed in the equation environment consecutively starting from 1 It does not number inline equations and equations within the displaymath environment but it does number equations within the eqnarray environment described below There is a difference in style of math formulas depending whether they are printed in the inline or displayed math mode In the displayed mode for instance fractions numerators and denominators are printed in the regular font size while in the inline mode they are printed in a reduced font size There is a way to force ATRX to type math in a prescribed mode this is done by the commands displaystyle and textstyle There is also a similar command scriptstyle to print in small size like subscripts or superscripts Page 28 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX 3 1 6 Lists Text paragraph mode Use the enumerate environment or the itemize environment begin enumerate begin itemize item item item item item item end enumerate end itemize to generate a numbered bulletted list of items respectively Math m
131. h improve their papers and become better writers The paper must be approved by registration day of the student s last semester The present paper is a primer on mathematical writing especially the writing of short papers Indeed this paper itself is intended to be a model of format and style Mathematical writing is primarily a craft which anyone can learn The aim is to inform efficiently The basic principles are discussed and illustrated here Some of these principles are simple matters of common sense others are conventions that have evolved from experience None need be Page 140 Appendix B 1 Writing a Phase II Math Paper 2 Organization followed slavishly but none should be breached thoughtlessly When they are breached the breach may stand out like a sore thumb just as unconventional spelling does However the writing itself should fade into the background leaving the information to be conveyed out front Following these principles will not cramp anyone s style there is plenty of room for individual variation The various principles are discussed more fully in a number of works including the following works on which this primer is based Alley s down to earth book 1 Flander s article 4Jand Gillman s manual 5 for authors of articles for MAA journals the notes 6 to Knuth s Stanford course on mathematical writing and Munkres brief manual of style 7 Section 2 of this paper discusses the normal way a sh
132. he real data for which you cannot predict the results While creating your program you will have convenient simple tests For example if you have to write a program to compute the area of a triangle with sides 14 23 12 497 and 9 72 test your program on the Pythagorean triangle with sides 3 4 5 first also test it in the case where a triangle degenerates to a segment say for the sides 1 2 and 3 Also think what happens when a certain parameter or a ratio of parameters becomes extremely large or extremely small Quite often intuition will suggest an answer and you ll be in a better position to make sense of the computed results Example 1 Suppose as a part of the assignment you have to construct a common tangent to two given circles A circle collapses to a point when its radius tends to zero Consequently a common tangent to the two given circles becomes a line passing through the two given points when both radii shrink to zero This limiting case provides a convenient test for your calculations and your computer program Example 2 Suppose the assignment asks you to find the number of grid points whose both coordinates are integers inside the circle of radius R centered at the origin Think what happens as R oo Every grid point corresponds to the unit square of which it is the center so the number of the grid points is approximately equal to the area of the circle that is 7R The fraction of the area contributed by inco
133. he reader looking on Still we should not be used as a formal equivalent of I and I should be used rarely if at all For instance do not write By solving the equation it is found that the roots are real Instead write Solving the equation we find the roots are real or Solving the equation yields real roots Beware of dangling participles It is wrong to write Solving the equation the roots are real because the roots cannot solve the equation Concise writing is vigorous Conciseness comes from eliminating needless repetition fat phrases and empty words thus reducing sentences to their simplest forms Conciseness comes from eliminating pretentious diction thus being clear and forthright Concise writing is simple and efficient thus beautiful The flow of a paper is disturbed by weak transitions between sentences and paragraphs To smooth the flow start a sentence where the preceding one left off Use connective words Page 145 Appendix B 1 Writing a Phase II Math Paper 4 Mathematics and phrases Avoid gaps in the logic and give ample details Do not take needless jumps when deriving equations Use parallel wording when discussing parallel concepts Do not raise questions implicitly and leave them unanswered Many papers stagnate because they lack variety The sentences begin the same way run the same length and are of the same type The paragraphs have the same length and st
134. heading PS Adobe 2 0 by hand or have your program to print it automatically newpath 1 1 moveto O O lineto 1 1 lineto stroke Page 85 Chapter 4 Programming and graphing 4 1 Programming e Maple you must cut and paste this array to Maple s plot command 1 1 0 0 11 11 e Gnuplot feed the file to Gnuplot s plot command use option with lines 1 1 00 1 1 Since the list opening and list closing are to be printed only once this can be done outside of the coordinate generating loop On the other hand the separator between the pairs must be printed after each pair save the last one So it must be done within the loop the last pass of the loop must be a little different We present short FORTRAN and C codes that produce the data in Maple s style For simplicity of presentation we sacrificed any flexibility in violation of a good programming style we promote FORTRAN C OPEN UNIT 1 FILE line1 dat FILE f fopen line1 dat w WRITE 1 List opening fprintf f List opening DO i 0 2 for int i 0 i lt 2 i x i 1 y x 2 x i 1 WRITE 1 x y y pow x 2 IF i lt 2 THEN fprintf f f x y WRITE 1 separator if i lt 2 END IF fprintf f separator END DO WRITE 1 List closing fprintf f List closing CLOSE 1 fclose f If instead of connecting the points by lines you need to render them differently your program can be written
135. hnically dense as the subsequent sections In many cases it is not a place to put precise definitions but rather a place to motivate and anticipate them by describing the major concepts in a less formal way Example 1 The notion of two graphs having identical shape may be important What exactly does it mean for two graphs to have an identical shape There are geometric defi nitions and analytic definitions They will be discussed in Section 2 Example 2 When we say that one geometric figure is an expansion of another there is an intu itive understanding of the two being alike and differing only in size For the purposes of this project a precise geometric definition is required It refers in turn to the notion of isometry or distance preserving transformation of a plane and to the notion of homothety which is stretching or squeezing in the same proportion along all directions going from a fixed center Then the introduction proceeds informally In a later section the technical definitions say in a coordinate form are given In some cases a precise technical definition properly belongs in the introduction Suppose the assignment asks you to write a program that counts in how many ways a given positive integer N can be broken into a sum of positive integers It is rather pointless in this case to keep an informal tone Get straight to the point The purpose of this laboratory is to design a method and to write a computer pro
136. hould you have difficulty logging into a computer please advise the person who is working in the lab 5 2 2 Your computer account Everyone has been assigned a computer account which provides access to the desktop worksta tions which comprise MUN LABNeT Each student is provided with his her home directory Page 124 Chapter 5 Local system particulars 5 2 Laboratory computers on campus on the student disk where your personal files reside You are not able to read or write files in someone else s home directory and no one else can read or write to yours Each workstation has a name Newfoundland communities are used in HH 3030 3056 the workstations in EN 2036 are named after Transformers characters The machines in HH 3030 3056 will boot to either Linux or Microsoft Windows They boot to Windows by default To work with IATFX and program compilers you must click on Linux To log in type your user name and hit Enter then type your password and hit Enter in the appropriate field in the middle window Assuming no typing errors the screen will clear and you will see a desktop with a few icons to the left and a toolbar along the bottom The home directory where all your files reside does not depend on the particular worksta tion you are using nor on the operating system you are booted to Thus if one day you log onto lumsden in HH 3030 3056 under Windows and the next day to bumblebee in EN 2036 under Linux your files will be the
137. icklines dashline 30 8 0 1 20 1 end picture end center Grids Grids can be created in many ways using grid xlen ylen Axlen Aylen init x init y This creates a grid measuring xlenxylen with each xlen interval being Axlen and each ylen interval being Aylen The inputs of init x and init y give the coordinates of the bottom left hand corner of the grid Page 116 Chapter 4 Programming and graphing 4 4 The TFX picture environment The next diagram is generated within picture environment by the command grid 12 6 4 3 5 2 Picture dimensions are 12 6 and unitlength is set equal to lem 5 9 13 17 8 8 5 5 2 2 5 9 13 17 Circles The standard AT FX picture environment allows you to draw circles using the command put x y circle diam The parameter diam is the diameter of the circle measured in unitlength centered on x y and is an integer in the range 0 lt diam lt 5 However there is also a restriction on the maximum diameter of circle that can be drawn in absolute units it cannot exceed 15 points about 0 5 cm In the enhanced picture enviroment these restrictions no longer apply although large circles will turn out to be rectangles with rounded corners There is a variation circle diam which gives a solid disk instead of a hollow circle If you try to make a solid circle that is too large BTEX will not fill it in setlength unitlength 1lem begin
138. ide apply judgement Suppose for instance that the problem is to find the distance between two skew lines in space A student googles for distance finds a Wiki article on metric spaces and blindly copies a definition to her paper Big math the prof must be pleased Wrong Irrelevant Plus the level is inappropriate for the target audience which is not the prof Another student faced with the equation z 5x 6 0 engages in a lengthy step by step calculation using the quadratic formula Five lines down he finds the roots to be 2 and 3 It isn t such a serious crime but it wastes space on a triviality In such simple cases the answer ought to be given next to the equation In more involved cases a detailed solution of a quadratic equation would make sense Your reader may not immediately see that the roots of the equation x 2tx t 1 0 are z t 1 and 22 t 1 Neither speculating about things you don t understand nor reiterating banalities is good Focus on a content that s not over your head and that really matters Any symbol that appears in your calculations arguments or later in tables and graphs should be defined Definitions and terminology should be accommodated to the concrete situation In an anecdotal case a student writing a paper on graphs of polynomial functions started with a definition of a graph from Graph Theory Let us elaborate on definitions a bit further They can be stated in
139. iles They are used as in the following example usepackage options package where package is the modifying style file and options is a list of style files modifying the style file For example here is a possible preamble documentclass article usepackage amsmath usepackage 2130 3 3 3 Special symbols In the coming sections we will see that the the ten characters ha 2 7 NAF are reserved for special use Page 41 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends But what if we need one of these special symbols to appear in our document The answer for seven of the symbols is to precede them by a character so forming another control symbol remember that followed by a space was also a control symbol It is not 100 straightforward to typeset the characters amp _ but given the enormous convenience of the use they are normally reserved for this is a small price to pay produces It is not 100 straightforward to typeset the characters amp _ but given the enormous convenience of the use they are normally reserved for this is a small price to pay So what are control symbols and words In typing a document we can think of ourselves as being in one of two distinct modes We are either typing literal text which will just be set into neat paragraphs for us or we are typing text that will be interpreted by ATEX as an instruction to insert a special symbol or t
140. ine gv mylab1 ps PDF files are viewed with familiar Acrobat Reader acroread mylab1 pdf Both GhostView and Acrobat allow you to print the document you are viewing TATpXfiles that do not contain eps graphics can be conveniently processed in one step by the pdflatex command pdflatex mylab1 Remember to run the ATEX compiler whether latex or pdflatex two times if your file contains either of the following the table of contents the bibliography section automatically numbered equations or figures Page 126 Chapter 5 Local system particulars 5 3 Software 5 3 2 Kile integrated PT EX environment Kile launched by the command kile is a UNIX text editor specifically designed to assist with preparation of ATEX documents Besides the many functions common to text editors including spell checking and text highlighting Kile allows you to compile TEX documents and view them without switching to a shell window The icon depicting a little blue wheel invokes latex command The icon where the wheel overlaps with a red curve invokes pdflatex There are buttons that launch dvi ps and pdf viewers and buttons that convert dvi to ps or pdf 5 3 3 Compilers There are compilers available on the Linux machines for the FORTRAN C C and Java languages Some students may use other languages of their choice like Python for example unless the instructor raises objections There are naming conventions for source code filename
141. ing and Page 77 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX automatically numbering either a single expression that spreads over several lines or multiple expressions while taking care of alignment for us The syntax is similar to that of the tabular and array environments except that no argument is necessary to declare the number and jus tification of columns The eqnarray environment does this without numbering any equations Thus begin eqnarray a b a b amp amp a 2 Qab b 2 a b a b amp amp a 2 b 2 end eqnarray will give a b a b a 2ab 0 3 1 a b a b b 3 2 See how we identify the columns so as to align the signs We can also leave entries empty The following output for instance sin x h sin z sing lim dx h gt 0 h ji sin x cos h cos z sin h sin x lim h gt 0 h sin x cos h 1 sinh lm cosg h 0 h h cosg has been produced from the input below begin eqnarray frac d dx sin x amp lim_ h rightarrow0 frac sin x h sin x h lim_ h rightarrow0 frac sin x cos h cos x sin h sin x h lim_ h rightarrow0 frac sin x cos h 1 h cos x frac sin h h 8pt amp amp cos x end feqnarray No first column entry is required The 8pt gives extra space Note also that displaystyle command is not required in eqnarray environ
142. ing list I still have to do the following things 1 Sort out LAN accounts for people on the course e Have new accounts created for those not already registered on the LAN e Make sure all users have a personal directory on the data drive e Add users to the appropriate LAN print queues 2 Have a TEX batch file added to a directory that is on a public search path 3 Finish typing these course notes and proof read them 4 Photocopy and bind the finished notes See how I lay the source file out in a readable fashion This is to assist myself not ATEX The description environment is unsurprisingly for making lists of descriptions begin description item itemize an environment for setting itemized lists item enumerate an environment for setting numbered lists item description an environment for listing descriptions like for words in a dictionary with boldface and a nice little indentation after the first line end description will typeset the descriptions shown in Figure 3 5 Note that the scope of the tt commands used in the item labels was restricted to the labels itemize an environment for setting itemized lists enumerate an environment for setting numbered lists description an environment for listing descriptions like for words in a dictionary with boldface and a nice little indendation after the first line Figure 3 5 The description environment Page 57 Chapter 3 Typesetting with ATRX 3 3 An in
143. ironment then the ensuing text will not be regarded as part of a new paragraph and so will not be indented end center In this case we left a blank line after the environment so the new text was regarded as starting a new paragraph gives the following text The center environment takes care of the vertical spacing before and after it so we do not need to leave any If we leave no blank line after the center environment then the ensuing text will not be regarded as part of a new paragraph and so will not be indented In this case we left a blank line after the environment so the new text was regarded as starting a new paragraph verbatim environment We can simulate typed text using the verbatim environment The tt typewriter text type style can be used for simulating typed words but runs into trouble if one of the char Page 54 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends acters in the simulated typed text is a specially reserved IATfX character For instance tt type newline would not have the desired effect because IAT X would interpret the newline as an instruction to start a new line The verbatim environment allows the simulation of multiple typed lines Everything within the environment is typeset in typewriter font exactly as it appears in our source file obeying spaces and line breaks as in the source file and not recognising the existence of any special symbols
144. iting that is appropriate in a paper submitted to the math department to complete Phase Two of MIT s writing requirement We review the general purpose of the requirement and the specific way of completing it for the math department Then we consider the writing itself the organization into sections the use of language and the special problems of presenting mathematics We conclude with a short example of mathematical writing 1 Introduction MIT established the writing requirement to ensure that its graduates can write both a good general essay and a good technical report Correspondingly the requirement has two phases which engage students at the beginning and toward the end of their careers The requirement is governed by an institute committee the Committee on the Writing Requirement CWR The requirement is administered by the Undergraduate Education Office which works in cooperation with the individual departments on Phase Two The general information given here about the requirement is taken from the MIT Bulletin and the CWR s brochure 3 which are the official sources MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Appendix B 1 Writing a Phase II Math Paper 1 Introduction To complete Phase One students must achieve a suitable score on the College Board Achievement Test or Advanced Placement Examination pass the Freshman Essay Evaluation pass an appropriate writi
145. itle contains no distracting secondary details and no formulas A strong title is concise The abstract is the most important section First it identifies the subject it repeats words and phrases from the title to corroborate a reader s first impression and it gives details that did not fit into the title Then it lays out the central issues and summarizes the discussion to come It is drawn completely from the paper However it includes no general background material The abstract is a table of contents in a paragraph of prose It allows readers to decide quickly about reading on While many will decide to stop there the potentially interested will continue The goal is not to entice all but to inform the interested efficiently Remember readers are busy They have to decide quickly whether your paper is worth their time They have to decide whether the subject matter is of interest to them and whether the presentation will bog them down A well written abstract will increase the readership The introduction is the place where readers settle into the story and often make the final decision about reading the whole paper Start strong do not waste words or time Your readers have just read your title and abstract and they have gained a general idea of your subject and treatment However they are probably still wondering what exactly your subject is and how you will present it A strong introduction answers these questions with clarity and
146. iven in full Rule 1 One should avoid giving the reader the impression that the subject matter can be mastered only with great pain In fact this is an ideal way to lose readers or audiences One should avoid using abbreviations like w r t with respect to iff if and only if and w l o g without loss of generality They simply do not look very nice and iff is offensive Rules 1 and 2 You should not begin a sentence with a math symbol This can confuse the printer as well as the reader Rules 1 and 2 Page 153 Appendix B 2 Some Hints on Mathematical Style 199 x As a example of such bad writing we have we want to prove the continuity of f x 2cos x sin x cos x being continuous This is corrected to f x 2cos x sin x Since cos x is continuous If your paper raises a natural question and you don t know the answer by all means say so This may turn out to be more interesting than the theorems that you prove Conversely refrain from making conjectures too hastily Use instead the words question or problem Remember that a good question should be answer able by yes or no To ask under what conditions does A hold is not a question worth printing It is often helpful to begin a new section of the paper with a summary of the general setting After the paper is finished it should be rerea
147. l TEX release 1982 the macro package TEX was born IXT X was written for general usage ATEX scores high points for its enhanced command syntax By far the majority of ATX users will never have to learn raw TEX for they will be shielded from direct exposure by the numerous powerful macro packages Pre amble Every ATEX document begins with a pre amble This consists of a set of commands that tells TEX how to process the document We will explain the important parts of this in the next two sections The first documentclass is mandatory whereas the others are all optional Document classes We have explained the concept of a document class It remains to name a few and indicate where they would be used One always has to choose a document class when preparing a document with TATExX The basic document classes in ATEX are article letter report and book Many more are available but these few cover the majority of straightforward applications This is because classes are not rigid you can impose your own parameter choices if you want So one chooses Page 40 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends the class that most closely approximates the document you have in mind and performs some minor tweaks here and there The article class is used for documents that are to have the appearance of a journal or magazine article and is the class that should be used for your reports in this course The rep
148. l that is to be printed must lie somewhere between the Page 46 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends documentclass article begin document Words within a sentence are ended by spaces One space between words is equivalent to any number We are only interested in separating one word from the next not in formatting the space between them For these purposes pressing Return at the end of a line and starting a new word on the next line just serves to separate words not to cut a line short The end of a sentence is indicated by a period followed by one or more spaces The end of a paragraph is indicated by leaving a blank line All this means that we can type without too much regard for layout and the typesetter will sort things out for us end document produces the result Words within a sentence are ended by spaces One space between words is equivalent to any number We are only interested in separating one word from the next not in formatting the space between them For these purposes pressing Return at the end of a line and starting a new word on the next line just serves to separate words not to cut a line short The end of a sentence is indicated by a period followed by one or more spaces The end of a paragraph is indicated by leaving a blank line All this means that we can type without too much regard for layout and the typesetter will sort things out for us Figure 3
149. lab The description below has been in this Manual since its first edition and is still valid if you are working in the UNIX command line Many integrated environments like Kile WinEdt Texnic Center or Scientific Word nowadays make processing a LaTeX document more comfortable Page 30 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX 3 1 9 Including source code in ETRX documents There are a couple of ways in which you can include the source code from your programs in your IATRX documents One way is to use the verbatim environment begin verbatim Paste a copy of your code here end verbatim Remember to break long lines by hand so that they fit the page width otherwise some details of your program will not be visible The other way to do so is to use lgrind which formats program sources in a nice style Comments are placed in Roman font keywords in bold face variables in italics and strings in typewriter font Source file line numbers appear in the right margin every 10 lines Suppose that you have a C program in the file sample c The first step towards including the file in the document is to run it through 1grind to produce a file say sample tex lgrind i lc sample c gt sample tex This generates a file sample tex which has the pretty printed version of sample c with a lot of TeX commands Note that your program and main document should have different names Now in the declarations at the start of your m
150. le for the margins being Page 53 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends indented on both sides during the quote This example has also been used to show how the commands that begin and end an environment restrict the scope of commands issued within that environment The em at the beginning of the quote did not affect the text following the quote We have also learned here that if we use em within already emphasized text the result is roman type and we do not require an italic correction here because the final letter of all was not sloping to the right Although MTFX does not care too much for how we format our source file it is obviously a good idea to lay it out logically and readably anyway This helps minimize errors as well as aids in finding them For this reason I have adopted the convention of always placing the environment begin and end commands on lines by themselves center environment This environment allows the centering of consecutive lines of text new lines being indicated by a If you do not separate lines with the command then you will get a centred paragraph the width of the page which will not look any different to normal If only one line is to be centred then no is necessary The tt center environment takes care of the vertical spacing before and after it so we do not need to leave any begin center If we leave no blank line after the tt center env
151. ls are often found by reading a differentiation formula in reverse For example the integrals in Table 5 1 were found in this way The notation in the table is standard 9 Page 149 Appendix B 1 Writing a Phase II Math Paper Advanced mathematics Table 5 1 A brief table of integrals a 1 fatde E2 C a 1 fa ldr nz C fsingdx cosxr C J cos xdg sinz C f fedr e C o A U N e p 178 the equation f ar Fle 0 is read The integral of f x dx is equal to F x plus C A longer table of integrals is found on the endpapers of the calculus textbook 9 Appendix Advanced mathematics In many treatments of advanced mathematics the key results are stated formally as theorems propositions corollaries and lemmas However these four terms are often used carelessly robbing them of some useful information they have to convey the nature of the result A theorem is a major result one of the main goals of the work Use the term theorem sparingly Call a minor result a proposition if it is of independent interest Call a minor result a corollary if it follows with relatively little proof from a theorem a proposition or another corollary Sometimes a result could properly be called either a proposition or a corollary If so then call it a proposition if it relatively more important and call it a corollary if it is relatively less important Call a subsidiary statement a lemma if
152. ls of the Greek letters constituting this word that the name T X was derived TFX is the art of typesetting Page 65 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX a Nalpha B beta y gamma delta e epsilon varepsilon zeta n Neta 0 theta Y vartheta y Niota k kappa A lambda H Amu Vv nu xi ma pi w varpi p rho o varrho o 6 sigma S varsigma T tau v upsilon phi ep varphi x Nchi Y psi w Nomega Table 3 4 Lowercase Greek letters T Gamma A Delta Theta A Lambda Mi I Pi Y Sigma Y Upsilon Phi Y Psi Q Omega Table 3 5 Uppercase Greek letters Calligraphic uppercase letters The letters A 2Z are available through use of the style changing command cal This command behaves like the other style changing commands em it etc so its scope must be delimited as with them Thus we can type for the filter cal F we have varphi cal F cal G to obtain for the filter F we have p F G There is no need to tabulate all the calligraphic letters since they are all obtained by just a type style changing command We will just list them so that we can see for reference purposes what they all look like Here they are ABCDEFGHIIKLMN OP QRSTUVWA YZ Binary operators IXT X has been taught to recognise binary operators and set the appropriate space either side of one i e it sets the first argument followed by a little space then
153. makes our function continuous everywhere Maple knows such tricks as extension by continuity and it automatically determines the y range necessary for the plot gt plot sin x x x 15 15 sin x Figure 4 2 Maple s graph of smooth function y x Let s try a graph with vertical asymptotes Consider the function y2 on p 89 which can be factorized as x 3 x 3 2 x 1 x 2 gt plot y2 x 10 10 The graph Figure 4 3 is not looking particularly illuminating The vertical range can be altered with this graph to enable a clearer picture Figure 4 4 left gt plot y2 x 10 10 y 40 40 Page 99 Chapter 4 Programming and graphing 4 3 Drawing graphs Figure 4 3 2 0007 1 0004 Maple s plot of y 1 000 x 3 a 3 2 x 1 x 2 10 4 20 4 30 4 40 Figure 4 4 Plot with restricted y range discontinuity exhibited left or hidden right Default view 10 20 4 30 4 40 gt Page 100 Chapter 4 Programming and graphing 4 3 Drawing graphs A discontinuity detector can be used to remove the unnecessary lines as on Figure 4 4 right gt plot y2 x 10 10 y 40 40 discont true Coordinates can be plotted using the following format yielding Figure 4 5 gt X 2 41 41 1 1 2 1741 0 0 1 2 1 4 1 1 12 431 X aa 1 4 z loo 5 a 1h
154. ment while it would be required if we were to produce the same result using array environment 3 4 6 Theorems Propositions Lemmas Suppose you document contains four kinds of theorem like structures theorems proposi tions conjectures and wild guesses Then near the beginning of the document you should have something like the following Page 78 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX newtheorem thm Theorem newtheorem prop Proposition newtheorem conjec Conjecture newtheorem wildshot Hypothesis make it sound good The first argument to newtheorem defines a new theorem like environment name of your own choosing The second argument contains the text that you want inserted when your theorem is proclaimed begin thm slshape X is normal if and only if each pair of disjoint closed sets in X is completely separated end thm begin wildshot remember we chose the name wildshot The property of Moore extends to all objects of the class Sigma end wildshot which will produce the following Theorem 1 X is normal if and only if each pair of disjoint closed sets in X is completely separated Hypothesis 1 The property of Moore extends to all objects of the class Notice that ATFX italicizes the theorem statement and that you still have to shift in to math mode when you want to set symbols and expression Typically it is the
155. mplete unit squares overlapping with the circle is vanishingly small Considerations of this sort can make a valuable part of the Mathematical details section or of the Results and Analysis section The subsection Program details should provide a detailed breakdown of your program so that the reader can see how the mathematical ideas of the solution method are coded Please learn to differentiate between a mathematical method or algorithm and its pro gramming implementation Sometimes the description of the method and of the program which implements it can be intertwined especially if the method is very straightforward In other cases you are better to explain the method or its more subtle elements within Mathemat ical details using conventional mathematical notation dot or void for the multiplication sign one letter variables subscripted if needed etc The explanation of a program involves the actual syntax of the programming language used with its own conventions for multiplica tion multi letter names of variables etc If necessary explain the correspondence between mathematical variables and their counterparts in the program Page 15 Chapter 2 Technical writing 2 3 Organization of report What is the best way to explain a computer program On the one hand from the end user perspective the program is a black box that takes a specified input and produces an output which the user should be in position to interpret
156. mplify command applies a bunch of algorithms to transform expressions to a simpler form For example it will identify common factors in the numerator and denominator and remove them In our fraction y2 defined above Maple finds that the common factor a 2 can be canceled Page 88 Chapter 4 Programming and graphing 4 2 An introduction to Maple gt simplify y2 x 3x 9x 27 2 x 3x 2 The simplify command also knows trigonometric identities gt simplify sin theta 2 cos theta 2 1 Maple s simplification algorithms are powerful but not perfect For example Maple fails to notice that x 1 a 2g 1 x 1 x 2x 1 0 gt simplify x 1 2 n x 2 2 x 1 n x 1 x 2x 1 For any particular n Maple will simplify correctly but it can take a long time gt simplify x 1 2 700 x 2 2xx 1 700 0 Another useful command is substitution subs gt subs x Pi 4 sin x simplify 1 V2 ne The colon suppresses printout of a result try to put a semicolon instead to see the effect The percent sign refers to the most recent result 4 2 2 Equations Maple has built in commands to solve equations automatically gt solve x 2 x 12 0 x 3 4 gt XX solve x7 2 6 x 3 x 3 v6 3 v6 The command evalf takes exact answers like those above and spits them out in decimal form gt evalf XX 550510257 5 449
157. n accordance with the method you intend to use to render your graph Every pair of numbers must be framed with opening symbol or keyword preceding the x value and closing symbol or keyword following the y value and a separator must be inserted between the x and y values The list of coordinates as a whole has its own opening before the first point closing after the last point and a separator between the successive points Some of these can be void or blank space Graphing facility LaTeX picture Postscript Maple Gnuplot Before x none none Between x and y space space After y moveto or lineto none List opening join newpath none Between points none line break A line break List closing none stroke or fill none Table 4 1 Openings closings and separators for coordinates A summary of the various coordinate formats mentioned in this Manual is given in Table 4 1 Consider for example a line defined by three points 1 1 0 0 and 1 1 a very rough approximation to a graph of y 2 Below we show what the data file produced by your program should look like in different cases In ATFX and Postscript a change of scale may be necessary to actually see the picture e IXT X you must include package 2130 sty or curvesb sty to enable the join command Import the data file by the input command see p 120 join 1 17 0 0741 1 e Postscript you must add the
158. n your report for example a calculus book it must be listed as a reference You should provide specific page number to enable the reader to easily find the place definition theorem historical fact you are referring to Example In the body of the paper put the reference number and the page number If we substitute the elliptic arc equation 2 into the arc length formula 3 p 548 b f VI FP da we obtain the expression In the References section describe the source 3 J Stewart Calculus Early Transcendentals 5th ed Thomson Brook Cole 2003 In this case the publisher is a worldwide company and the place of publication is not indicated There are different reference styles Follow one style consistently Check with your instructor as to whether a particular style is preferred Quoted online resources must also be given proper attribution For instance there is a webpage at http mathworld wolfram com ContinuityPrinciple html It has a title and unlike say many pages in Wikipedia it is not anonymous we can name an author For this particular page a bibliographic entry would look like this 1 Eric W Weisstein Continuity Principle http mathworld wolfram com ContinuityPrinciple html Accessed Dec 5 2008 Alternatively web sites may be cited in running text instead of in an in text citation The Chicago Manual of Style Online section Website This very line is an example The sections Ack
159. nd they will be penalized heavily However be warned the spell checker will not find every error in spelling nor can it pass judgement on a sentence like A program too gene rate asset off inter resting numb hers Some common spelling errors e their whose there where e its whose it s it is e separate not seperate e occurence not occurance e one s once e two to too e then if then than more than e lablo ratory not labratory 2 4 2 Squeeze water out Eliminate unnecessary words Compare 1 It can be shown by the implementation of the Cosine theorem that the distance AB is equal to 5 2 Applying the Cosine theorem we see that AB 5 Page 20 Chapter 2 Technical writing 2 4 Suggestions about style 2 4 3 A note on strong words Students often write it is necessary one must etc Such strong expressions may justly raise objections Example Suppose we are considering the equation z 6x 5 0 Bad description It is necessary to use the Quadratic Formula Thus we obtain Is it necessary Absolutely not Any one competent in quadratic equations will factor this one on the spot If you want to emphasize the method better say The roots as given by the Quadratic Formula are 3 6 VD where D 6 4 x 5 16 Thus x1 6 4 2 5 z2 6 4 2 1 Better even if the method is of no special import
160. nd your mathematical explanations determine the research value of your paper more than anything else Remember that this is a mathemat ics course and a large component of your grade will be based upon the paper s mathematical content Don t just state observations Analyse them and justify them If the analysis and or explanation of the results requires a piece of theory that has not been discussed in the Math ematical details section include the necessary definitions and facts here along with your own calculations and arguments In this section you can also explore the efficiency of your code how fast or slow it is as the size of data fed to the program increases 2 3 8 Acknowledgements and References Any help that you have received from another person must be acknowledged An acknowledge ment should be expressed in the form of a grammatically complete sentence If possible specify the kind of help obtained It also helps to characterize the status of the person so that those who come across your paper in a few years will know Don t just say e John Smith for his help with this assignment Say instead John Smith a Computer Science major has provided advice about the input output functions in Java Or I acknowledge help from Mr John Smith a tutor in justifying the pattern as described in the Results section Page 18 Chapter 2 Technical writing 2 3 Organization of report If you quote any printed material i
161. ng subject in Course 21 or write a satisfactory five page paper for any MIT subject Wellesley exchange subject or UROP activity In level format and style a paper should be like a magazine article for an informed but general readership Papers are judged on their logical structure language and tone technical accuracy and mechanics grammar spelling and punctuation by the instructor of the subject and by evaluators for the Undergraduate Education Office A paper judged not acceptable may be revised and re submitted twice Students must complete Phase One by the middle of their third semester at the Institute To complete Phase Two students must receive a grade of B or better for the quality of writing in a cooperative subject approved by the student s major department receive a grade of B or better in one of several advanced subjects in technical writing or write a satisfactory ten page paper for any MIT subject or UROP activity approved by the major department A student with two majors needs only to complete the requirement in one department In level format and style a Phase Two paper should be like a formal professional report Thus a term paper or laboratory report may have to be reworked substantially before it is acceptable as a Phase Two paper A paper is judged by its supervisor and by departmental evaluators Students must complete Phase Two by the end of registration day of their last semester otherwise they cannot graduat
162. nowledgments and References as well as Abstract are not numbered See Sect 3 2 regarding ATFX typesetting conventions for these sections 2 3 9 Appendix Material that does not naturally fit in the flow of your paper yet is important for your project s completeness should be put in an Appendix Many papers will not have an appendix Where an appendix is present the following kinds of material are found in it e Computer code e Graphs and illustrations e Particularly long mathematical calculations or proofs Page 19 Chapter 2 Technical writing 2 4 Suggestions about style A listing of your program is the most common thing to put in the Appendix Sect 3 1 9 suggests how to get a nice printout A Math 2130 paper having more than one appendix should be an exception but if that happens identify the appendices alphabetically Appendix A Appendix B We urge you to learn quickly how to include graphs and illustrations in the body of your report You may use gnuplot xfig the IATFX picture environment Maple or PostScript Graphs and illustrations which are not part of the text can comprise Appendix A of your report while the computer programs can be presented in Appendix B 2 4 Suggestions about style 2 4 1 A note on spelling There are many spelling checkers available Use them On Linux you can use ispell The Kile editor has a built in spell function which uses the ispell program There is no excuse for spelling errors a
163. ns of classes of documents teaching TEX just how each class likes to be formatted This is taught in terms of font preferences default page sizes placement of title author date etc For instance a paper style file could teach TEX that when typesetting a theorem it should embolden the part that states the theorem number and typeset the text of the theorem statement in slanted Roman typeface as in many journals The typist simply provides and indication that a theorem is being stated and then types the text of the theorem without bothering to choose any fonts or do any formatting all that is done by the style file Style files exist for all manner of document letters articles papers books proceedings review articles and so on There are many other motivations one could cite for the superiority of TEX But it is time that we started to get our hands dirty The novice reader will still have no idea of what a T X source file looks like Indeed why do we keep referring to it as a source file The fact of the matter is that TFX is essentially a programming language Just as in any compiled language e g Fortran C one prepares a source file and submits it to the compiler which attempts to produce an object file dvi file in the T X case To learn TFX is to learn the command syntax of the commands that can be used in the source file Typical T X interfaces By the nature of TFX most time is spent editing the source document before
164. ntence or paragraph in such a manner that the material stands out from the rest of the text This can be used to enhance readability or to simply emphasize something Its syntax is simple Horace smiled and retaliated begin quote em You can mock the non WYSIWYG nature of TeX all you like You do not understand that that is precisely what makes TeX enormously more powerful than that lame excuse for a typesetter you use And I will bet that from start to finish of preparing a document I am quicker than you are even if you do type at twice the speed and have the so called advantage of WYSIWYG In your case what you see is em all you get end quote and then continued with composing his masterpiece of the typesetting art produces the following typeset material Horace smiled and retaliated You can mock the non WYSIWYG nature of T X all you like You do not understand that that is precisely what makes TEX enormously more powerful than that lame excuse for a typesetter you use And I will bet that from start to finish of preparing a document I am quicker than you are even if you do type at twice the speed and have the so called advantage of WYSIWYG In your case what you see is all you get and then continued with composing his masterpiece of the typesetting art That is a much more readable manner of presenting Horace s piece of mind than embedding it within a regular paragraph The quote environment was responsib
165. o perform some action Thus we are either typing material that will go straight into the document with some beautification or we are giving commands to ATEX Some commands are implicit in that we do not have to do anything much extra For instance we command TFX to end the present sentence by typing a period that does not follow a capital letter These are not so much commands as part of having to describe the logical structure of a document A control word is something of the form commandname where the command name is a word made up only of the letters a to z and A to Z A control symbol consists of a followed by single symbol that is not a letter Here are some examples e we have met the control space symbol u before e the commands to set symbols like and are control symbols e AC is a control symbol that told TEX that the very next period did really end the sentence e LaTeX is a control word that tell TEX to insert its own name at the current point e pm instructs that a be inserted e div inserts a symbol e infty inserts a oo symbol e em makes the ensuing text be emphasized Page 42 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends These examples show that control sequences can be used to access symbols not available from the keyboard do some typesetting tricks like setting the word TX the way it does and change the appearance of whole chunks of text as with em We will
166. ode eqnarray Here we usually mean a set of equations Use beginf eqnarray lt formula gt amp lt connective gt amp lt formula gt lt formula gt amp lt connective gt amp lt formula gt end eqnarray It is possible that some of the lt gt are empty fields Also the XX can be replaced by ME as indicated in the section on vertical space above If the is omitted the equations will automatically be numbered If a line is not to be numbered then the command nonumber must be entered somewhere in that line Math array The array environment is used within displayed math in the cases when an additional flexi bility as compared to eqnarray is required Details can be found in Maltby In both array and eqnarray environments MTpX is by default in the inline math mode so you have to use the displaystyle command to display fractions sums etc properly Moreover this command only has effect between two ampersands or between an ampersand and the endline command So you may have to issue the displaystyle command repeatedly That s why the abbreviation shown on p 25 makes a lot of sense Page 29 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX 3 1 7 Advanced math typesetting The formula sin 2 lola J Malas is obtained from frac x sin x cos x x int_ sqrt x infty f x dx To the mathematically literate many math c
167. oduction Fut tn ees BR as be ek eee 114 ACAD o Lines e Be PR Sh Sule oe Bed pl ee Paes 115 44 3 Enhanced Pictures siae 3 5 ti Pe ok eo 115 4 4 4 Superimposition 2 2 ee 122 5 Local system particulars 123 5 1 Wlectronie submissions y s c s00 ao A A He ek A Poe ee 123 5 2 Laboratory computers on campus 2 e a e e 124 DEZA WHEE ised pec ee A US oe BER eee ot Syd td 124 5 2 2 Your computer account e a a e ar n a aa DE a a AEE e E S 124 A Printing nh eg a e a a a Ee aa ae a ae eee Des 125 DO SSOMWALC 2 Gr Sx Boke Redes EA A a Bee Bo A a eed bee Ee RN 126 5 3 1 Processing ATFX files in the command line 126 5 3 2 Kile integrated ATEX environment o a 127 Diora COMPpilerse som dr de Ghee doen ke Roar ele Boe Gea ind Dee Ae kale 127 DIA Maple aia a la We ae da a 128 5 3 5 Miscellaneous 128 Appendix A Quick reference on UNIX 130 Aol LLOSA A A hes A A DAA a e 130 A2 Directories ia DA A A AAA 131 A3 Dath aMes o sala e eon AS da a a talar 133 DOA Shell a A ee a a ta A o 133 A 5 Basic UNIX commands 0 0002 ee ee 134 A 6 Working with directories and files o o e e o 135 A 7 Redirection of output ee 138 A 8 Access privileges 2255 4 5 ek dee aS PR ee aA ee es 138 Appendix B Two papers on mathematical writing 139 B 1 Writing a Phase II Math Paper S Kleiman MIT 139 1 Introductions A eh a Behe Re a a 139 2 Oreanization
168. oduction to TX and friends more stretchable than normal inter word space and that space after a sentence ending period should be stretched more than space after a mid sentence comma TEX knows the nature of punctuation if you stick to the simple rules outlined here As we have already said those rules tell ATRX how to distinguish consecutive words sentences phrases etc Actually there is more to ending sentences than mentioned above Since ATEX cannot speak English it works on the assumption that a period followed by a space ends a sentence unless the period follows a capital letter This works most of the time but can fail To get a normal inter word space after a period that does not end a sentence follow the period by a control space a u a character followed by a space or return Very rarely you will have to force a sentence to end after a period that follows a capital letter remember that TEX assumes this does not end a sentence This is done by preceding the period with a command you can guess from the odd syntax that this is rarely needed It is time we saw some examples of this After all this is our first experience of control symbols do not worry there are many more to come We must be careful not to confuse intra sentence periods with periods that end a sentence i e we must remember that our task is to describe the sentence structure Periods that the typesetter requires a little help with typically re
169. of all numbers x such that x lt 1 3 DO NOT START A SENTENCE WITH A SYMBOL BAD ax bx c 0 has real roots if b 4ac gt 0 GOOD The quadratic equation ax bz c 0 has real roots if b 4ac gt 0 4 BEWARE OF USING SYMBOLS TO CONVEY TOO MUCH INFORMATION ALL AT ONCE VERY BAD If A b 4ac gt 0 then the roots are real BAD If A b 4ac is nonnegative then the roots are real GOOD Set A b 4ac If A gt 0 then the roots are real 5 IF YOU INTRODUCE A CONDITION WITH IF THEN INTRODUCE THE CONCLUSION WITH THEN BAD If A gt 0 the roots are real 6 USE CONSISTENT NOTATION DO NOT SAY Aj WHERE 1 lt j lt n ONE PLACE AND A WHERE 1 lt k lt n ANOTHER Page 147 Appendix B 1 Writing a Phase II Math Paper 5 Example 7 KEEP THE NOTATION SIMPLE FOR EXAMPLE DO NOT WRITE a IS AN ELEMENT OF X IF IS AN ELEMENT OF X WILL DO 8 PRECEDE A THEOREM ALGORITHM AND THE LIKE WITH A COMPLETE SENTENCE BAD We now have the following Theorem 4 1 H x is continuous GOOD We can now prove the following result Theorem 4 1 The function H x defined by Formula 4 1 is continuous 5 Example As an example of mathematical writing we discuss the two fundamental theorems of calculus Our discussion is based on that in Apostol s book 2 pp 202 7 The First Fundamental Theorem says that the process of differentiation reverses that of integration
170. ommands are intuitive If you want a symbol and cannot remember it try the obvious and most times you will be correct You now should read Section 3 3 An Introduction to TREX and friends by Gavin Maltby The definitive book is the IATfX User s Guide and Reference Manual by Leslie Lamport 3 1 8 Processing and viewing KTpX files Every ATEX file must be saved with the tex extension You process the file mylab tex with the command latex mylab Note that there is no need for the extension tex At this point a lot of information will come across your screen With time much of it will even make some sense Everything you see on the screen and more gets written to a log file If you processed mylab tex ATEX will create mylab log for you If you are lucky and have made no errors AT RX will eventually stop and report that the output was written to mylab dvi If you are less fortunate ATX will stop at the first error and leave you hanging at a question mark on the screen At this point if you answer r for run ATEX will finish processing to the best of its ability writing all errors to mylab log which one can then review in one window while correcting mylab tex in another To view mylab dvi you use a UNIX program called xdvi which is run like this xdvi mylab Again there is no need for the extension dvi A dvi can be converted to a pdf file by the command like this dvipdf my
171. on the left rfoot thepage page number in the footer on the right underheadoverfoot dividing lines under header and below footer 3 2 2 Table of contents Assuming you use the standard ATEX commands to structure your report section subsec tion all that remains to produce the table of contents TOC is to insert the command tableofcontents after the title page code You have to run TFX compiler two times to obtain a correct TOC as the first run just creates an auxiliary file where the information about sections and subsections found is collected but IATRX is not able to incorporate that information into its dvi output immediately Some complication occurs with References and Appendix assuming they are formatted as suggested below The command thebibliography which generates the list of references does not automatically yield an entry in TOC You have to do some work by hand Somewhere soon after your thebibliography command perhaps immediately after in sert the following line addcontentsline toc section References The heading References will then appear in your TOC and it will be printed in the same style as section headers If you want to somewhat de emphasize References in TOC modify the above line addcontentsline toc subsection References Similarly if you formatted your Appendix A using section command you should put the corresponding TOC line immediately after it for example add
172. onditionals and calls to other procedures or to Maple s built in functions There are also commands to test whether inputs are real complex matrices or whatever gt type 4 realcons type c realcons true false These could be used in if then statements For example the following procedure returns the square root of the argument if the root is a real number and prints an error message otherwise Page 95 Chapter 4 Programming and graphing 4 3 Drawing graphs gt SafeSqrt proc x local sqrtx sqrtx sqrt x if type sqrtx realcons then return evalf sqrtx else print Sqrt Error end if end proc gt SafeSqrt 3 1 732050808 gt SafeSqrt 3 Sqrt Error gt SafeSqrt x 2 Sqrt Error 4 3 Drawing graphs Knowing how to generate graphs and incorporate them into a paper is a valuable skill for all technical writers In this chapter we review a number of ways to generate plots with software The most common method to import computer generated graphs into a IXTRX document involves Encapsulated Postscript files We begin this section with basic information about Postscript Encapulated Postscript and MTFX imports We then explain how graphs can be generated in a Maple worksheet and include brief descriptions of the Gnuplot and Xfig graphing packages IAT X has its own graphical facility the picture environment Its drawing functions are very limited but there are powerful enhancements in partic
173. ons The reader can rightly be curious about the command s name look it up gt numapprox infnorm x cos x x 0 2 0 8322936731 Here we encounter for the first time an example of a function from a Maple package The whole package whose name is numapprox can be uploaded by the command with numapprox and then you can use the infnorm command without prefix numapprox Maple is quite knowledgeable in Calculus It knows limits and Taylor series gt limit sin 2 x 1n 1 x x 0 2 gt taylor tan t t 6 1 3 2 5 7 tit rl O t E O t We leave it to the reader to find out the meaning of the big Oh symbol 0 Page 91 Chapter 4 Programming and graphing 4 2 An introduction to Maple 4 2 4 Arrays Data in Maple can be grouped to form an array An array is bounded by square brackets and elements are separated by commas The elements of an array can be objects of like or different nature they can themselves be arrays For example gt A 1 2 red bluel x72 5 x 6 plot1 The elements can be referenced using forward or backward indexing gt Afi 1 gt A 3 red blue gt A 3 2 blue gt A 1 ploti The command nops returns the number of elements in an array gt nops A 5 A sub array can be selected gt A 3 4 red bluel x 2 5 x 6 It is straightforward to change the values of elements of an existing array by assignments like A 1 but adding new elements is
174. ope LOngleftrightarrow produces gt compare Longleftrightarrow which produces gt LOngleftarrow produces LOngrightarrow produces gt IFF produces lt gt compare iff which produces gt Page 33 Chapter 3 Typesetting with ATEX 3 2 Formatting your Math 2130 report in AT px 3 2 Formatting your Math 2130 report in BTRX 3 2 1 Title page footers and headers A typical title page is shown on Figure 3 2 A IATFX code used to produce it is as follows begin titlepage begin center large SHAPE MANIPULATION AND MATRIX ALGEBRA end center vspace 6cm hfill begin tabular 11 AM 2130 amp Lab 2 Submitted by amp Unlikely Student amp 200765432 Submitted to amp Dr Good Professor Feb 18 2009 end tabular end titlepage SHAPE MANIPULATION AND MATRIX ALGEBRA AM 2130 Lab 2 Submitted by Unlikely Student 200765432 Submitted to Dr Good Professor Feb 18 2009 Figure 3 2 A sample title page for an AM2130 report Page 34 Chapter 3 Typesetting with ATRX 3 2 Formatting your Math 2130 report in ATEX Your document will look nicer with running footers and headers The following few lines can be placed in the preamble or after the title page The effect is explained in the comments lhead AM2130 appears in the header on the left rhead Lab 1 Title appears in the header on the right lfoot Your Name appears in the footer
175. or text via the coordinates in the put command begin figure H begin verbatim Text of the Postscript program end verbatim begin picture 400 1 put 300 30 includegraphics triangles end picture caption A simple Postscript program and its effect end figure The main difficulty in such cases is determining the coordinates where to put an object It is essentially a trial and error business the convergence rate of the process and precision with which you can drop the thing where you want it to be greatly improves as you gain experience Using superimposition within the master ATEX document it is possible to insert labels on graphs created by various software tools The advantage of this approach is that your labels will always be in the same font style as the rest of your document and their size will not depend on the scaling you apply to the imported graphics The pattern is simple begin picture put 0 0 includegraphics your eps file put label or text end picture For the dimensions of the picture in points you can take the dimensions of the EPS graph which can be calculated based on BoundingBox information The BoundingBox line can be found in most EPS files near the top of the file Suppose for example that the BoundingBox numbers are 50 60 410 302 Then the horizontal size of the graph is 410 50 360 and the vertical size is 302 60 242 Thus you can u
176. ort class is usually used for larger documents than the article class These classes really only differ in their choice of default page size font placement of title and author sectional units etc and on how they format certain ATX constructs You use the same MIX commands in each Since the examples here will be small we will choose to use the article document class There are a number of possible options with each document class The syntax for choosing a document class follows Do not worry if this leaves you with no idea of how to choose a document style for we will soon be seeing some examples Also remember that an argument in square brackets is optional and can omitted altogether including the brackets documentclass options class where class is the main document class eg report and the optional argument options is a list of document style options chosen from for example the following list 11pt chooses 11 point as the default font size for the document instead of the default 10 point 12pt chooses 12 point as the default font size twoside formats output as left and right pages as in a book twocolumn produces two column magazine like output titlepage applies to the article style only causing the title and abstract to appear on a page each In fact there are many many more document class options but we will not mention any more here Packages To modify further the main document class we make use of style f
177. ort mathematical paper is broken into sections We consider the purpose and content of the individual sections the abstract the introduction the several sections of the main discussion the conclusion which is rare in a mathematical work the appendix and the list of references Section 3 below deals with language that is the choice of words and symbols and the structuring of sentences and paragraphs We consider seven goals of language precision clarity familiarity forthrightness conciseness fluidity and imagery We discuss the meaning of these goals and how best to meet them Sections 2 and 3 are based mainly on Alley s book 1 Section 4 deals with a number of special problems that arise in writing mathematics such as the treatment of formulas the presentation of theorems and proofs and the use of symbols The material is drawn from all five sources cited above Section 5 gives an illustrative sample of mathematical writing We treat the two fundamental theorems of calculus for the most part paraphrasing the treatment in Apostol s book 2 pp 202 4 we state and prove the theorems and explain their significance Finally the appendix deals with the use of such terms as lemma proposition and definition which are common in treatments of advanced mathematics and appear every year in a few Phase Two papers 2 Organization Most short technical papers are divided up into sections which are numbered and titled The pag
178. orward tool to plot graphs given as pairs of coordinates On the other hand Maple s versatility and symbolic manipulation power is incomparably higher The best way to use Gnuplot is to interactively piece together step by step vary and adjust all the essentials for the desired plot all the while watching the plot displayed in its own window at every stage Once the desired plot is generated and fine tuned it is easy to redirect the plot into a file To start a Gnuplot session simply type gnuplot in the command line and the Gnuplot prompt will appear A Gnuplot session is ended by typing quit at the prompt The two main plotting commands are plot for 2D data and splot for 3D data Their behaviour is controlled by a wide range of options Most of the options are introduced by the command set Gnuplot s originally intended and still most popular use is to render plots based on externally prepared data fed to it from a file Yet modern Gnuplot knows many standard mathematical functions and it is quite capable of plotting on its own as sample graphs that follow demonstrate Here we are only able to help you get started with Gnuplot An interested reader can find out about numerous options and features in Gnuplot s Help and in online tutorials for example http www ibm com developerworks library 1 gnuplot Plotting functions with Gnuplot The figures on the next page demonstrate how Gnuplot can be used directly without data importin
179. ously powerful and friendly package In fact they do but that fact is well hidden in one s initial THX experiences In this section we describe a little of what makes TX great and why other packages cannot even begin to compete Be warned that a little patience is required TRX s virtues are rather subtle to begin with But when the penny drops you will wonder how you ever put up with anything different TEX is a typesetter not a word processor TpX was designed with no limiting application in mind It was intended to be able to prepare practically any document from a single page all text letter to a full blown book with huge numbers of formulae tables figures etc Conventional word processors have a fundamental limitation in that they try to keep up with you and typeset your document as you type This means that they can only make decisions at a local level eg it decides where to break a line just as you type the end of the line TEX s secret is that it waits until you have typed the whole document before it typesets a single thing This means that TFX can make decisions of a global nature in order to optimise the aesthetic appeal of your document It has been taught what looks good and what looks bad having been given a measure of the badness of various possibilities and makes choices for your document that are designed to make it minimally bad But T X s virtues run much deeper than that which is just a
180. p 10pt amp 11pt hline tt large amp 12pt amp 12pt amp 14pt hline end tabular produces the following table IATRX size changing commands Style option 10pt default 11pt 12pt footnotesize 8pt 9pt 10pt small 9pt 10pt 11pt large 12pt 12pt 14pt Page 59 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends figure and table environments Figures diagrams pictures etc and tables perhaps created with the tabular environment cannot be split across pages So ATEX provides a mechanism for floating them to a nearby place where there is room for them This may mean that your figure or table may appear a little later in the document than its declaration in the source file might suggest You can suggest to ATFX that it try to place the figure or table at the present position if there is room or failing that at the top or bottom of the present or following page You can also ask for it to be presented by itself on a page of floats You suggest these options to TEX through an optional argument to the environment One lists a combination of the letters h t b and p with the following meaning h the object should be placed here if there is room so that things will appear in the same order as in the source file t the object can be placed at the top of the of a text page but no earlier than the present page b the object can be pl
181. p 85 amp Pleasing H Hosepipe amp 829134 amp 5 amp 10 amp Improving I N Middle amp 853931 48 amp 47 amp Can make it end tabular will produce the following no frills table Student name Number Test 1 Test 2 Comment F Basset 865432 78 85 Pleasing H Hosepipe 829134 5 10 Improving I N Middle 853931 48 47 Can make it Note that a was not necessary at the end of the last row Also note that once again the alignment of the amp characters was for human readability It is conventional to set columns of numbers with right justification The bf directives apply only to the entries in which they are given A typed in the tabular environment s argument causes a vertical line to be drawn at the indicated position and extending for the height of the entire table An hline given in the environment draws a horizontal line extending the width of the table to be drawn at the vertical position at which the command is given A Xclinefi j draws a line spanning columns to j at the vertical position at which the command is given A repeated line drawing command causes a double line to be drawn We illustrate line drawing in tables by putting some lines into our first table We will type this example in a somewhat expanded form trying to make it clear why the lines appear where they do Page 58 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends begin tabular 1 1 rlr 11 hline bfseries
182. p that follows them as a sub and superscripts to the group that precedes the sub and superscript symbols We see now now that our initial examples worked by considering a single character to be a group by itself Here are some examples Type To produce a 2b 3 a p 27 1213 ge 2 21 2 1 a x 17 att ar x72 1 a7 tt 1 73 a 1 Gamma_ alpha beta gamma Tagy _1A_2 143 In the very last example we see a case of setting a subscript to an empty group which resulted in a kind of pre subscript With some imagination this can be put to all sorts of uses In all of the above examples the sub and superscripts were set to single character groups Nowhere did we group an expression before sub or superscripting it Even in setting the expression x 1 the superscript was really only set to the character If we had wanted to group the x 1 before setting the superscript we would have typed x 1 3 which gives x De with the superscript slightly raised One has to go to this trouble because to most people something like x is just as acceptable and as readable as 12 It also has the advantage of aligning the base lines in expressions such as ab ab fb La 12 b la 1p la 1 which looks more pleasing than if we use additional grouping to force ab ab 1 pa ota teat and the latter has rather more braces in it that require balancing Here are some more exam
183. perform all the usual functions end itemize produces the following itemized list e an item is begun with item e if we do not specify labels then TX will bullet the items for us e I indent lines after the first in the input file but that is just to keep things readable As always ATEX ignores additional spaces e a blank line between items is ignored for TX is responsible for spacing items e TFX is in paragraph setting mode when it reads the text of an item and so will perform all the usual functions Lists can also be embedded within one another for they are just environments and we said that environments have this property Remember that we must nest them in the correct order We demonstrate with the following list which also shows how to use the enumerate environment Page 56 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends noindent I still have to do the following things begin enumerate item Sort out LAN accounts for people on the course begin itemize item Have new accounts created for those not already registered on the LAN item Make sure all users have a personal directory on the data drive item Add users to the appropriate LAN print queues end itemize item Have a TeX batch file added to a directory that is on a public search path item Finish typing these course notes and proof read them item Photocopy and bind the finished notes end enumerate will give the follow
184. ples showing how ATFX will set things just as we want without any further work on our part Page 71 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Type To produce x7 y z ae 27 272 202 27 27 27 aleph_0 38 a Gamma z_c7d pe We can also make use of empty groups in order to stagger sub and superscripts to an expression as in Gamma_ alpha beta gamma _ delta which will yield Tae s One can specify the sub and superscripts to a group in any order but it is best to be consistent The most natural order seems to be to have subscripts first but you may think otherwise It is also a good idea to always include your sub and superscripts in braces i e make them a group whether they consist of just a single character or not This enhances readability and also helps avoid the unfortunate case where you believe that a particular control word gives a single symbol yet it really is defined in terms of several Primes LXT X provides the control word prime for priming symbols Note that it is not automati cally at the superscript height so that to get f you would have to type f prime To make lighter work of this XIX will interpret a right quote character as a prime if used in math mode Thus we can type f g x g x h x in order to get f g g w h 2 Fractions IXT X provides the frac command that accepts two arguments the
185. plicit meanings the wrong connotations can trip up your readers by suggesting unintended ideas For example the word adequate means enough for what is required but it gives you the feeling that there is not quite enough its connotation is the exact opposite of its denotation Strong writing does not require using synonyms contrary to popular belief Indeed by repeat ing a word you often strengthen the bond between two thoughts Moreover few words are exact synonyms and often using an exact synonym adds nothing to the discussion Being precise means giving specific and concrete details Without the details readers stop and wonder needlessly On the other hand readers remember by means of the details Being precise does not mean giving all the details but giving the informative details Giving the wrong details or giving the right ones at the wrong time makes the writing boring and hard to follow Being specific does not mean eradicating general statements General statements are important particularly in summaries However specific examples illustrations and analogies add meaning to the general statements Being clear means using no wrong words An ambiguous phrase or sentence will disrupt the continuity and diminish the authority of an entire section A common mistake is to use overly complex prose Do not string adjectives before nouns lest they lose their strength and precision instead use prepositional phrases and dependent
186. pmattin e s i a Se ove A wont aed Seas 45 3 3 5 Document structure 2 ee 52 3 4 Mathematical typesetting with WT X G Maltby 61 3 41 Tntroductiony os 1 egos eg eee A ek ee a es 61 3 4 2 Displaying a formula e 64 3 43 Using mathematical symbols e o 65 3 4 4 Some common mathematical structures 70 3 4 5 Alignment o ack yk ba ae a a aa oe a ee es 77 3 4 6 Theorems Propositions Lemmas a a a 000000 78 4 Computer assisted research programming and graphing 80 4d Programming dnde Roe de he a A bal oe aE 80 4 1 1 Development process e 80 4 1 2 Programming style o a 83 4 1 3 Generating graphics data with your own program 84 4 2 An introduction to Maplex s mios bee HO bee RA oh ES RS 87 4 2 1 Basic Arithmetic and Algebra 2 0 2 0 ee ee 87 Page ii Contents AD QUAN a rs e A AM er OR a Pe 89 ADD Calcula a e a as ra 90 ADA GATTO ide aoe ee La ee eos he he oe ee ee 92 4 2 5 Linear Algebra e 93 42 6 Programming E eo a a 94 4 3 Drawing graphs i244 44 80 A AS ee ee A es 96 4 3 1 Postscript Files oss marao sa 84 re Oe Pe ee DA 97 4 3 2 Maple graphics ee 99 Aaa Gaupl t 4 Bok lek ge San bat we Ak Gs A Atte oes ren 107 4 3 4 Using XFig to make diagrams 0 02 0000002 eee 112 4 4 The TEX picture environment and enhancements 114 AAA Tntr
187. problem as required As long as that principal condition is met further criteria pertaining to contents typically include the following Page 2 Chapter 1 Introduction 1 3 Policies e Usefulness of the paper relevance informativeness mathematical and factual correct ness e Research quality understanding of underlying mathematics appropriateness and effec tiveness of tools used scope and depth of analysis e Quality of computer programs supporting the research validity of code efficiency of algorithm readability structure comments self explanatory identifiers etc and ex planation of the program s workings Depending on the nature of a problem at hand the relative importance of the listed elements may vary and other elements may be emphasized If in doubt ask your instructor what to pay attention to The criteria pertaining to presentation are very similar to those used in non technical writing e Quality of exposition structure style level appropriate to the assumed readership clarity with which technical ideas are explained consistent use of terminology and notation e Conformance to language standards grammar spelling e Conformance to typographical standards I4TpX typesetting quality of graphics e Proper citations and quotations Chapters 2 4 elaborate on many of these points This course gives you an opportunity to put the skills you acquired in other courses to work Some students
188. put the period after the citation not before the brackets or inside them 3 Language In the subject of writing the word language means the choice of words and symbols and their arrangement in phrases It means the structuring of sentences and paragraphs and the use of examples and analogies When you write watch your language When it falters your readers stumble if they stumble too often they will lose their patience and stop reading Write rewrite then rewrite again improving your language as you go there is no short cut Alley 1 pp 25 130 identifies seven goals of language two primary goals precision and clarity and five secondary goals familiarity forthrightness conciseness fluidity and imagery These goals often reinforce one another For example clarity and forthrightness promote conciseness precision and familiarity promote clarity We will now consider these goals individually Page 143 Appendix B 1 Writing a Phase II Math Paper 3 Language Being precise means using the right word However finding the right word can be difficult Consult a dictionary not a thesaurus because the dictionary explains the differences among words For example the American Heritage Dictionary is a good choice because it has many notes on usage Consult a book on usage such as Webster s Dictionary of English Usage Al ways consider a word s connotations associated meanings along with its denotations ex
189. reate arbitrary lines However with enhancements provided by additional packages I4TRX s picture environment becomes competitive in its ability to generate interesting quality graphics From now till the last part of this chapter Section 4 4 4 we will stay entirely within a ATEX document No other graphics formats or imports will be involved We will describe in some detail the enhancements offered by the math2130 sty package In particular a necessity to decide which unit length to set for the given picture can be avoided by use of an enhanced picture environment called scaledpicture It is used thus begin scaledpicture percent xlen ylen leftcornerx leftcornery end scaledpicture Here percent is a number less than or equal to 100 where 100 gives a diagram that almost fills the entire text width and any smaller number gives a diagram that spans a percentage of the corresponding 100 diagram In most respects scaledpicture behaves like the standard ATX picture environment but it has additional features to make it easier to produce diagrams quickly and easily Page 114 Chapter 4 Programming and graphing 4 4 The ATEX picture environment 4 4 2 Lines A major restriction in the TeX picture environment lies with the available slopes of lines that can be drawn These slopes are restricted to rationals of the form p q where p q are coprime and less than or equal in size to 6 The slopes are written as ordered pairs
190. rectory One difference between mv and cp is that cp will not copy a directory whereas mv can rename it or move it into another directory The command to remove a file is rm The arguments to rm are the files you want to remove Be careful with this command Once you remove a file it is difficult to get it back All the files on the system are saved every night so if you do accidentally remove a very important file the system administrator may be able to help you Be especially careful with rm command The command to create a directory is mkdir It takes one argument the pathname of the directory you wish to create For instance if Bob ran mkdir lab4 in his m2130 directory he would see lumsden mkdir lab4 lumsden Is labi lab2 lab3 lab4 The command rmdir takes one argument the pathname of a directory you wish to remove If the directory is not empty rmdir will not function The command p is actually a shorter name for the command less This is a program you can use to quickly look at text files p will display a screenful of the file and then stop with a prompt at the bottom of the screen You can hit the space bar to see the next page or the u key to go upwards in half screenfuls When you reach the end of the file p will prompt with the name of the file followed by END Type the q key to quit from p Page 137 Appendix A Quick UNIX reference A 8 Access permission A 7 Redirection of output Most studen
191. rences and citations The caption command within a figure or table environment assigns a number to the figure or table This number can be captured by the label command put right after For example the command label xyz allows you to refer to your figure elsewhere in your document in the following way See Figure ref xyz on page pageref xyz Similarly labels can be assigned to sections subsections Sect 3 2 4 equations Sect 3 1 5 and theorem like environments described in Section 3 4 6 References to sources listed under thebibliography command can be done as follows Fourier s memoir On the Propagation of Heat in Solid Bodies was read to the Paris Institute on 21 December 1807 cite fourier bio Page 37 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends 3 3 An introduction to TEX and friends Original text by Gavin Maltby 1992 adapted by Math 2130 Instructors 1995 1998 2008 3 3 1 An Introduction to TREX TEX is well known to be the typesetting package and a vast cult of TFX lovers has evolved But to the beginning T X user or to someone wondering if they should bother changing to TEX it is often not clear what all the fuss is about After all are not both WordPerfect and Microsoft Word capable of high quality output Newcomers have often already seen what TpX is capable of many books journals letters are now prepared with T X and so expect to find a tremend
192. rmula 2 3 referring to the Mathematical details section The variable DT in the program is time step denoted by 7 in the description of the method Note that the value SPEED TMIN is not included since it has been included in the previous summation The better your programming style the easier it is to explain the program s overall design and logic Look at Example 1 again Perhaps replacing the whole body of the loop dozens of lines of code by a framed summary was a good writing trick But it becomes altogether unnecessary if a subroutine is used instead Page 16 Chapter 2 Technical writing 2 3 Organization of report DO N 1 MAXN CALL NUM_PARTITIONS N END DO Self explanatory names of variables short functions transparent if else conditions avoiding fancy syntax constructions like cond i i gt 1 in C all this helps Do not teach the reader the basics of programming A general definition of a for loop copied from the Internet or a general discussion of the organization of computer memory or a definition of common data types int double is not what is needed If you really feel a need to remind the readers about some syntaxic details or other particulars of the programming language used for instance if you are writing for your own future reference then ok find a place but don t make it a big story Even if you think possibly correctly that your instructor is not a Java or Python guru it is not a r
193. rrection after the emphasized text earlier in this paragraph One might expect by now that ATFX would insert an italic correction for us But there are enough occasions when it is not wanted and there is no good rule for TFX to use to decide just when to do it for us So the italic correction is always left up to the typist Sentences and paragraphs Let us create our very first ATEX document which will consist of just a few paragraphs As mentioned above paragraph input is free form You type the words and separate them by spaces so that IATFX can distinguish between words For these purposes pressing Return is equivalent to inserting a space it does not indicate the end of a line but the end of a word You tell ATFX that a sentence has ended by typing a period followed by a space TFX ignores extra spaces typing three or three thousand will get you no more space between the words that these spaces separate than typing just one space Finally you tell ATEX that a paragraph has ended by leaving one or more blank lines In summary FTX concerns itself only with the logical concepts end of word end of sentence and end of paragraph Sounds complicated The example in Figure 3 3 should clear things up Try running MTFX on this input We have learned more than just how TEX recognises words sentences and paragraphs We have also seen how to specify our choice of document class and how to tell ATEX where our document begins and ends Any materia
194. ructure Do not worry about varying your sentences and paragraphs at first wait until you polish your writing Remember though if you have to choose between fluidity and clarity then you must choose clarity The very structure of a sentence conveys meaning Readers expect the stress to lie at the beginning and end They take a breath at the beginning but will run out of breath before the end if the structure is too complex for instance if the subject is too far from the verb Most people think and remember images not abstractions and images are clarified by illustrations Illustrations also give readers rest stops so complex ideas can soak in Moreover illustrations can make a paper more palatable and less intimidating However illustration can be overdone it must fit the audience and the subject Illustrations cannot stand alone they must be introduced in the text Assign them titles like Figure 5 1 or Table 5 1 for reference Assign them captions that tell independently of the text what they are and how they differ from one another without being overly specific In addition clearly label the parts of your illustrations label the axes of graphs with words not symbols identify any unusual symbols of your diagrams in the text Do not put too much information into one illustration because papers without white space tire readers For the same reason use adequate borders Smooth the transitions between your words and pictures First
195. ry mistake and a deliberate forge is shaky An argument that pretends to be a mathematical proof but fails to be such due to a logical error can be treated as a forge if there is an evidence that the author has been aware of the error and has chosen to disregard it If you think that something goes wrong in your project you should consult with your professor or laboratory assistant at the earliest opportunity Their advice will likely get you on track Yet quite a few students find themselves in a situation where the assignment is due the next day and things do not work their way What should they do Desperately filling up pages with material that is not supported by your actual findings is a bad idea One solution is to to buy additional time at the expense of losing 5 marks as allowed by the evaluation policy Sect 1 3 1 Another possibility is to frankly admit a problem and describe your approach in as much detail as possible If you feel that your method program is sound but perhaps some detail escaping your view prevents it from yielding satisfactory results report the research as is Do not beg for an excuse instead try to present an educated guess as to where a weak link could be B Plagiarism We urge all students to familiarize themselves with Section 4 11 Academic Misconduct in the Memorial University Calendar http www mun ca regoff calendar In particular read carefully Section 4 11 4 Academic Offences which defines wh
196. s alignment environments that allow us to prepare material like multi line expressions and arrays Subscripts and superscripts Specifying a sub or superscript is as easy as you would hope you just give an indication that you want a sub or superscript to the last expression and provide the material to be placed there and ATX will position things correctly So sub and superscripting a single symbol an operator or a big array all involve the same input and TX places the material according to what the expression is that is being sub or superscripted N 411 412 013 2 T x a21 Q22 023 i 1 431 432 433 To tell ATX that you want a single character set as a superscript to the last expression you just type a before it The last expression is the preceding group or if there is no preceding group the single character or symbol that the follows Type To produce x72 x a b a Y7X y gamma 2 y A B 72 A BY left Mracix 2 1Hx 2 y 2 Vrightl n E Subscripts of a single character are equally easy you just use the underscore character _ where you used for superscripting Page 70 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX Type To produce x_2 T2 x_i Li Gamma_1 x P x Now let us see how to set a sub or superscript that consists of more than just one character This is no more difficult than before if we remember the following rule _ and set the grou
197. s boxed Figure 4 9 Page 103 Chapter 4 Programming and graphing 4 3 Drawing graphs For more advanced tasks we can load the plotting library plots gt with plots Interactive animate animate3d animatecurve arrow changecoords complexplot complexplot3d conformal conformal3d contourplot contourplot3d coordplot coordplot3d cylinderplot densityplot display display3d fieldplot fieldplot3d gradplot gradplot3d graphplot3d implicitplot implicitplot3d inequal interactive interactiveparams listcontplot listcontplot3d listdensityplot listplot listplot3d loglogplot logplot matrixplot multiple odeplot pareto plotcompare pointplot pointplot3d polarplot polygonplot polygonplot3d polyhedra_supported polyhedraplot replot rootlocus semilogplot setoptions setoptions3d spacecurve sparsematrixplot sphereplot surfdata textplot textplot3d tubeplot Plotting the graph of an implicit equation f x y 0 now becomes possible Try gt 4 x72 9 y 2 25 gt implicitplot f x 4 4 y 2 2 scaling constrained The result is identical to Figure 4 6 It should not be surprising the parametrized coordinates r 3 cost and y 2 sint satisfy exactly our present equation 4z 9y 25 Note however that plotting functions implicitly is more difficult for Maple than plotting parametric curves with a command like that on p 101 The quality of parametric plots will generally be better
198. s chosen accordingly to the percent param eter You may override this by the usual font sizing commands Compare begin Scaledpicture 36 12 6 begin Scaledpicture 36 12 6 grid 12 6 4 3 5 2 large grid 12 6 4 3 5 2 end scaledpicture end scaledpicture 5 9 13 17 5 9 13 17 8 8 8 8 5 5 5 5 2 2 2 2 5 9 13 17 5 9 13 17 A scaledpicture is always centered In fact the environment used here was Scaledpicture which produces an uncentred scaledpicture This is useful for putting several diagrams on one line Page 119 Chapter 4 Programming and graphing 4 4 The ATEX picture environment To further demostrate the use of labeling commands provided by scaledpicture here is a set of commands for a cubic graph begin scaledpicture 70 8 6 4 3 xaxis yaxis xnums 1 ynums 1 ticks 1 0 1 thicklines input cubic_graph put 2 07936 0 circle 0 1 put 0 46295 0 circle 0 1 put 3 1164 0 circle 0 1 put 2 2 33333 circle 0 1 put 1 2 16667 circle 0 1 put 0 1 circle 0 1 put 4 3 7 large The graph of f x frac13 x 3 frac12 x 2 2x 1 end scaledpicture Figure 4 15 The graph of f x iz ig 2x 1 The input cubic_graph command imports the contents of the file cubic_graph tex whose first few lines are join 2 50 2 333 2 48 2 200 2 46 2 068 2 44 1 939 2 42 1 812 2 400 1
199. s file into a tex file is easy 1 First you must have the line usepackage graphicx in the preamble of you document between the documentclass and begin document Note the peculiar x at the end of the package name 2 At the spot where you want to drop the eps file into your document use the command includegraphics For example if the name of your graph is figl eps the following line will include it into the TAT X file includegraphics fig1 The extension eps in the file name should be omitted Often the includegraphics command is used within the picture environment or figure environment See p 60 and p 114 for information about these environments 3 Then proceed with your ATFX file in the usual way For most students the above algorithm of integration of EPS with IATFX is all that is needed For all practical purposes the only difference between ps and eps files is that the latter have a BoundingBoz line which is usually the second line in the file but sometimes it is found at the very end If your graphing program generates ps file but not an eps you need to convert it see instructions on p 128 Unless you use raw Postscript programming or older versions of Gnuplot you will likely never need this Optional arguments of includegraphics Consider a more sophisticated version of the above example includegraphics height 8cm angle 90 fig1 The expressions height 8cm and angle 90 are optional
200. s loops a lot slower than compiled programs also it runs out of memory on much smaller sizes of data Yet for many applications and many Math 2130 projects these issues are not critical Our first example is a summation loop which computes the arithmetic sum 11 32 53 74 95 Remember to use Shift Enter to type multi line commands into Maple cf page 87 Page 94 Chapter 4 Programming and graphing 4 2 An introduction to Maple gt tot 0 for i from 11 by 21 while i lt 100 do tot tot i end do tot 0 tot 11 tot 43 tot 96 tot 170 tot 265 If you are not interested to see the intermediate results simply replace the semicolons by colons in the above program and add the line gt tot to print the final result There are usual conditional commands if then else For example the following command finds the maximum of two numbers gt a 4 b 2 if a gt b then a else b end if 4 gt a 1 b 7 if a gt b then a else b end if 7 The closing commands end do and end if can be replaced by less traditional od and fi respectively Consider an example of a very simple user defined function or procedure It just adds one to a given number gt increment proc x return x 1 end proc gt increment 2008 2009 Procedures can be much more involved they may have many input values local variables and return values of any type Procedures can contain loops c
201. s of the file by default should be a collection of ordered pairs x y separated by white space one pair per line Let s say that you wish to plot two curves on the interval x 2 2 1 y a 32 and y qe e Choose the number of points to be used Let s say 100 points Since the length of our interval is 4 the value of x will be incremented by 0 04 from one point to the next e Write a program to generate the data sets for both functions For example here is a fragment of a C program that does it for the first function for x 2 x lt 2 x x 0 04 printf f f n x pow x 3 3 x This code prints the data to the terminal but you can re direct the output to a file type a out gt plot1 dat see Section A 7 e A data file named plot1 dat has been created with 100 data pairs For example the first and the last lines in the file will be like these 2 000000 2 000000 2 000000 2 000000 Modify the program and create the file plot2 dat for the second function similarly e Now the command gnuplot gt plot ploti dat with lines plot2 dat with lines generates the plot displayed in Figure 4 13 On your terminal the curves will be drawn in like style but with different colours When a hard copy is generated gnuplot knows that colour is not generally available and thus differentiates between different curves on the basis of different line styles Displaying a surface in 3D space Gnuplot accepts
202. s well because it is possible to get satisfactory though imperfect results from some word processors One of TRX s strongest points is its ability to typeset complicated formulae with ease Not only does T X make hun dreds of special symbols easily accessible it will lay them out for you in your formulae It has been taught all the spacing size font conventions that printers have decided look best in typeset formulae Although of course it does not understand any mathematics it knows the grammar of mathematics it recognises binary relations binary operators unary operators etc and has been taught how these parts should be set It is consequently rather difficult to get an equation to look bad in T X Another advantage of compiling a document after it is typed is that cross referencing can be done You can label and refer back to chapters sections tables etc by name rather than Page 38 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends absolute number and T X will number and cross reference these for you Similarly it will compile a table of contents glossary index and bibliography for you Essential to the spirit of TFX is that it formats the document whilst you just take care of the content making for increased productivity The cross referencing just mentioned is just part of this Many more labour saving mechanisms are provided for through class and style files These are generic descriptio
203. s which must be adhered to with each of the various compilers FORTRAN There are two compilers 95 and ifort and program source filenames must end in f C The compiler is gcc and program source filenames must end in c C The compiler is g and program source filenames end in c cc or cxx java The compiler is javac and the program source file names end in java For example suppose we have a FORTRAN program named assign1 f 1 Compile the program with the command lumsden f95 assign1 f which creates the executable file a out If you want to have the executable file named differently use the o option as in lumsden f95 assign1 f o assign1 which will name the executable file assign1 instead of the default a out If you just want to get an error report use lumsden f95 assign1 f c assign 1 Any syntactical errors in your program will be reported by the compiler If any are found you will have to go back to the first step and re edit your source file 2 Run your program which is done simply by typing the name of the executable file For example if you created the executable file assign1 as in Step 1 it is run with the com mand Page 127 Chapter 5 Local system particulars 5 3 Software lumsden assign1 otherwise the command would be lumsden a out 5 3 4 Maple To enable access to Maple in your account a licence information must be set This needs to be done only once by issuing the command e
204. same Whenever you create a file and save it it does not get saved on the local or remote workstation rather it is written in your home directory on the student disk and it is then available to you from any other workstation This is all done in a seamless fashion so you really need not concern yourself Organize your work Create a separate subdirectory in your home directory for each course Within it create a separate subdirectory for each project In your Math 2130 directory you may also create a subdirectory for ATEX and Maple samples provided by the instructor or for your own experiments with these software systems We suggest that you manage your home directory carefully regularly deleting unnecessary files Though disk space limitations may not be a big concern these days regular clean up will keep your directory well organized otherwise you will feel an increasing discomfort due to accumulating junk files Rules of conduct You are strongly encouraged to read and heed the university s policy concerning the appropriate use of campus computers It can be found at http www mun ca scac 5 2 3 Printing A laser printer is available in each lab It is important to replenish your paper account in advance of the submission deadline Inability to get a printed copy of your work due to insufficient funds is not an excuse for missing a deadline There are several stations across Campus where you can deposit funds onto your Mun One Card
205. se begin picture 360 242 Setting the picture dimensions precisely is not necessary and you can always make adjustments if you don t like the way the compiled ATEX document looks Page 122 Chapter 5 Local system particulars The information in this chapter is believed to be mostly valid as of December 5 2008 As the computer systems undergo updates and upgrades some of it will become obsolete 5 1 Electronic submissions The command submit is to be used to submit your assignments electronically Run it from your local shell window prompt in Linux You should place all the files you wish to submit for your assignment in a directory with a certain name determined by your instructor math2130 al math2130 a2 etc We recommend that this directory be different from your working directory for the current assignment it is convenient to make it a subdirecotry After you have completed your work the working directory will contain files with extentions log aux bak which should not be included in the submission The working directory can also contain drafts that you do not want to submit Copy only those files to the submission directory that are needed to reproduce your work in a form identical to the printed copy you are submitting Include the tex file or files if there are several and all graphics files eps pdf eepic etc that your master file refers to Also include a copy of your computer program f c etc or Maple
206. setting needs Another thing to look out for is the use of braces in an expression Typing x x gt 0 will not produce any braces This is because as we well know braces are reserved for delimiting groups in the input file Looking back to section 3 3 3 we see how it should be done x f x gt 0 Y Math shift commands also behave as scope delimiters so that commands issued in an expression cannot affect anything else in a document Page 63 Chapter 3 Typesetting with ATRX 3 4 Mathematical typesetting with ATRX 3 4 2 Displaying a formula I4TRX considers an expression to be word like in the sense that it considers it to be eligible for splitting across lines of a paragraph but without hyphenation of course BTEX assigns quite a high penalty to doing this thus trying to avoid it remember that TAT X tries to minimize the badness of a paragraph When there is no other way it will split the expression at a suitable place But there are some expressions which are just too long to fit into the running text without looking awkward These are best displayed on a line by themselves Also some expressions are sufficiently important that they should be made to stand out These too should be displayed on a line of their own The mechanism for displaying an expression is the display math mode which is begun by typing and ended by typing the same sequence which again means that we had better be s
207. ssigned problem and the results of computations Is it to decipher a cryptic message Or is it possibly to describe a series of computer assisted experiments with a logical game Knowing the purpose will prevent you from going off on tangents when writing e Decide about scope Narrow down the subject so as to avoid excessive generality Decide what theory which results how many graphs and tables you want to include Keep focused when writing It is better to present a small circle of ideas accurately and precisely than to attempt to embrace a larger area in vague terms e Decide who is your assumed readership is In most cases the best assumption is that the reader is a fellow student with a background like yours In some projects especially those of an entertaining nature younger math students can be the target audience Stick with the interests and level of your readers Do not go over their head but do not use baby talk Aiming your paper at a graduate level audience or professors will only work in exceptional cases Never address the paper directly to your professor as if he she were the only reader In summary Identify the purpose Limit the scope Speak to your audience Now we come to the main point how to actually put things down Writing is a creative process One s writing strategy reflects one s personality There is no such thing as a magic writing algorithm suitable for everybody Some people write easily most
208. struggle Find what works best for you making writing less painful and more enjoyable As food for thought here are several possible approaches that different people use Your writing strategy will likely be a mix of these or possibly even entirely different e Top down approach Start with a plan set the goal or goals and proceed section by section This approach generally speaking requires good self discipline and ability to comprehend the material of the paper in its entirety otherwise it is easy to miss important points at the outset The suggested format of a Math 2130 paper Section 2 3 will Page 8 Chapter 2 Technical writing 2 3 Organization of report hopefully help You will still need to return to sections already written and to make changes as your work progresses Bottom up approach Begin by stating the results then trace back A method by which the results were obtained must be fully explained Terminology involved must be defined Elaborate fill in details Make sure the final order of parts makes logical sense concepts should be introduced before they are referred to Free flow approach Start writing up your thoughts as they come Write an introduc tion Put down relevant definitions facts considerations Describe the work done and the results obtained State a conclusion Then edit the obtained loose draft organize the material into structural units improve explanations expand where needed remove redund
209. sult from abbreviations as in etc and others We have to work somewhat harder to break a sentence after a capital letter but that should not bother us to much if we keep up our intake of vitamin E All this goes for other sentence ending punctuation characters so I could have said vitamin E Fortunately these are rare occurrences results in We must be careful not to confuse intra sentence periods with periods that end a sentence i e we must remember that our task is to describe the sentence structure Periods that the typesetter requires a little help with typically result from abbreviations as in etc and others We have to work somewhat harder to break a sentence after a capital letter but that should not bother us to much if we keep up our intake of vitamin E All this goes for other sentence ending punctuation characters so I could have said vitamin E Fortunately these are rare occurrences Quotation marks is another area where ATEX will do some work for us Keyboards have the characters and but we want to have access to each of and So we proceed like this LaTeX is no conventional word processor and to to get quotes like this we type repeated tt and tt characters Note that modern ec convention is that punctuation comes after the closing quote character which gives just what we want ATEX is no conventional word processor
210. t set terminal postscript eps gt set output figurel eps gt replot The first of these abbreviations term and post can be used tells Gnuplot you wish to produce data in Encapsulated Postscript format the second redirects the output into a file in this case named figure1 eps and the last command just redraws the plot last displayed into the file The file figure1 eps has now been created in your working directory You can view it with Ghostview or insert it in your ATEX document as descrined in Section 4 3 1 A scaling option height or width in Nincludegraphics may be helpful If you set term post without the eps option then also conversion ps to eps and rotation by 270 will be required The size of the picture as it will appear in your paper will often be smaller than what you see when previewing the generated file in Ghostview Have mercy on your instructor s eyes use larger font size in labels This can be done as follows gt set term post eps Helvetica 24 Page 111 Chapter 4 Programming and graphing 4 3 Drawing graphs 4 3 4 Using XFig to make diagrams The program XFig is a handy tool that allows you to quickly draw diagrams consisting of simple shapes to drag and drop objects and even to put labels and formulas on your figures in a JATRX format It is great for creating hand drawn diagrams but less suitable when it comes to graphs where the positions of objects must be specified by coordinates In X
211. t a number or it can be an array of numbers a table or a graph As a bare minimum your presentation of results should include e evidence that your mathematical method and your program are correct Run sample cases that can be checked by hand calculation Or demonstrate the workings of your program in cases where the solution is intuitively obvious e the solution s corresponding to those data provided in the assignment if such data are indeed provided Page 17 Chapter 2 Technical writing 2 3 Organization of report If correctness of the method program cannot be demonstrated because the program doesn t work correctly read Sect 1 3 2 Many projects in this course are to some degree open ended They ask you to go beyond the prescribed sets of data and to explore the problem further on your own The assignment sheet may or may not give a hint on how to choose data for such experimentation Some outcomes of your experiments will end up in a trash bin and some will make it into the paper In the end we want your Results to be more than just plural for a single result Interpret them present them as a manifestation of a certain idea or phenomenon We want you to spot a trend to observe a pattern to discover some sort of law e Tell the reader why or how each example presented is relevant to the conjectured law e Explain the observed pattern law at least partially The quality of your analysis of results a
212. t hurt to be familiar with an old fashioned but always reliable command line mode To enter the command line mode you need to open a terminal shell window click on the icon that looks like a display Now what you type is interpreted by a special program called the shell It launches and runs other programs for you The shell tells you it is waiting for input by displaying a prompt like lumsden at the beginning of a line Two combinations of keys deserve a special mention e Almost any program started from the command line can be stopped by typing Ctrl C Page 133 Appendix A Quick UNIX reference A 5 Basic UNIX commands e The combination Esc K returns the most recent command entered in the shell Pressing Esc K twice will quickly bring back the second most recent command etc Knowing this is especially convenient for those who run compilers in the command line In another type of shell the single key f scrolls up the commands history A command followed by the ampersand character amp launches a program in a mode de tached from shell s interactive session so that you can enter other commands in the same window while the program is running For example you can open a text editor and modify your program in it while the command line will be available for compilation of the program lumsden kile myprog f amp A 5 Basic UNIX commands A UNIX command consists of one or more words separated by spaces The first word is
213. t language Notice the default here will be to create a file named diagram eps which you can subsequently include in your document by following the instructions in Section 4 3 1 You will likely want to label your diagrams on occasion sometimes even using the math mode of I4TRX to display mathematical symbols For this you ought to start XFig with the command xfig P specialtext latexfonts Page 112 Chapter 4 Programming and graphing 4 3 Drawing graphs Using the text drawing tool in XFig you can then label your figures as you please even including math mode text which you can accomplish by using dollar signs While XFig will not display your math mode labels very nicely they will come out just fine in your document such as in the following figure However when using math mode you need to select the export option of Combined PS LaTeX rather than Encapsulated Postscript You also should use the magnification option of the XFig Export window in order to fine tune the size of your figure as it appears in your document This time to include the diagram in your master IATFX file use a different IATFX command input diagram pstex_t In this import mechanism only the intermediary file with extention pstex_t must be directly referenced from your ATFX document yet the actual figure is still an eps file which in this case has extension pstex Thus your electronic submission must include both the pstex_t an
214. ted or enforced by certain programs while others are merely conventions Some file types most relevant to this course are e Text files They are human readable and can be edited by means of a text editor There are many different kinds of text files Program source files These files are source code written by programmers in a high level language like FORTRAN or C The compilers for these languages require the source file names to end in f or c respectively Data files Input data files contain data that will be fed into a program Output data files contain output produced by a program that you want to keep in a file ATpX files These files are source files for documents such as the one you are reading ATEX software requires that the file name end in tex Webpages are files with extensions htm html They stand for Hypertext Markup Language MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Appendix A Quick UNIX reference A 2 Directories e Executable files These files are programs that can be run directly that is you can type their names into the shell like the UNIX commands UNIX shell commands compilers text editors Internet browsers belong to this category Also this type of file is produced by a compiler from a source file written in FORTRAN C or another language The FORTRAN and C compilers name this file a out by default e dvi files These
215. tegers from 1 to 1000 and print the result include lt stdio h gt define N 1000 int Sum int maxnum int main printf The sum of the integers from 1 to d is d n N Sum N return 0 int Sum int maxnum int i int total 0 for i 1 i lt maxnum i total i return total Figure 3 1 Source code printed A using lgrind and B using verbatimfile Page 32 10 20 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX 3 1 10 Some commands defined in 2130 sty Text commands TODAY produces dates in the form 22 December 2008 TODAYAT produces dates and time in the form 22 December 2008 at 14 57 Cents produces INDENT forces an indented line when indent fails tildechar produces hatchar produces boxit object produces object 1bk short for linebreak produces a line break with horizontal justification pbk short for pagebreak produces a page break with vertical justification fsize number is an alternative way of changing font size This was recommended by Lam port normalsize is fsize 0 Positive integers increase and negative integers decrease from here For example fsize 1 is equivalent to large and fsize 4 is equivalent to tiny Inte gers too large default to the smallest or largest fonts available Math commands di is short for displaystyle toi produces co dist produces dist slope produces sl
216. than you would spend via the input prompt Syntax errors that depend on a programming language and a compiler used cannot be discussed here in any depth We will just mention some common errors that appear frequently e Unmatched bracket in a mathematical expression or unmatched opening of a structure in a program like DO loop without closing END DO in FORTRAN Most notably when you find such an error and try to fix it there is a danger that you misplace the closing bracket or the closing keyword and make the problem worse more difficult to detect e All variables in the program must be assigned values before their values are used for the first time A randomly looking output is the most common consequence of the failure to initialize However a compiler may initialize your variables to 0 by default not to the values that ought to be there the results may look OK at first sight but still be wrong Page 81 Chapter 4 Programming and graphing 4 1 Programming e Initializations should be placed outside loops that they are supposed to initialize If the variable SUM is an accumulator for a sum computed by a loop you should put the initialization SUM 0 outside the loop This problem is especially common with nested loops You must carefully identify fast variables which must change in the inner loop and slow variables which change only once per the outer loop e Off by one error is common even with seasoned
217. the name of the program you want to run either a standard system program or one you created yourself The rest of the words are arguments to the program which usually are either the names of files or options which tell the program to modify its usual behaviour Options usually begin with a dash for instance 1 Notation used This typeface is anything you type in literally Anything in italics is not typed in literally For example file means that you should not type the word file but that you should type a file name instead Anything followed by the ellipses can be repeated For example file means you can type in several file names In the next section examples this typeface will denote what the computer displays as opposed to what the user types Commands Is list the names of all files in the current directory cp original name new name create a copy of the original file with a different name mv original name new name rename the file with a different name or move the file to another place rm file name remove the file s cat file name display the contents of the file s p file name or more file name Page 134 Appendix A Quick UNIX reference A 6 Working with directories and files display the contents of the file s one screen at a time cd directory name changes to the directory named mkdir directory name create a new directory rmdir directory name
218. thematics a reference preferably in the text just before the statement If you give the reference in the statement then do so after the heading like this Theorem 5 1 2 p 202 Tell whether the omitted proof is hard or easy to help readers decide whether to try to work it out for themselves If the theorem has a name use it say by the First Fundamental Theorem not by Theorem 5 1 State a theorem before proving it Keep the statement concise put definitions and discussion elsewhere Prefer a conceptual proof to a computational one ideas are easier to communicate under stand and remember Omit the details of purely routine computations and arguments ones with no unexpected tricks and no new ideas Beware of any proof by contradiction often there is a simpler direct argument Finally when the proof has ended say so outright for instance say The proof is now complete In addition surround the proof and the statement as well with some extra white space Here are some more principles 1 SEPARATE SYMBOLS IN DIFFERENT FORMULAS WITH WORDS BAD Consider Sy q 1 n GOOD Consider Sy for g 1 n 2 DO NOT USE SUCH SYMBOLS AS J V A gt gt IN TEXT REPLACE THEM BY WORDS THEY MAY OF COURSE BE USED IN FORMULAS PLACED IN TEXT BAD Let S be the set of all numbers of absolute value lt 1 GOOD Let S be the set of all numbers of absolute value less than 1 GOOD Let S be the set
219. ting with IATRX 3 1 Elements of BTRX 3 1 1 Preamble Every TEX file has a structure like this documentclass 12pt article usepackage 2130 end document The part of the file before the line begin document is called preamble while the subsequent part is called body of the document The first line in the file tells ATX to use a file called article sty as the main source of formatting commands The style file contains certain default parameters that determine layout of the document in particular textwidth textheight topmargin oddsidemargin evensidemargin The subsidiary style indicated by the argument 12pt sets up the regular font size for the document to be 12pt Line spacing and sizes of fonts described in relative terms Large large small tiny thus become determined The first line may be followed by lines that import additional commands from various packages The package 2130 sty which the second line in our document refers to makes it MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Chapter 3 Typesetting with ATRX 3 1 Elements of AT RX easy to format a report for this course For example it will default to one inch margins all around the standard size of paper It also makes it easy to create the title page headers and footers using the commands headers footers underhead nounderhead overfoot noo
220. tion vs in C and Java vs in Maple and Pascal Make sure you understand the difference Other symbols to watch carefully are comma vs semicolon and various kinds of brackets Students often get lost when a program does not behave the way it is supposed to How is it possible to find errors that affect functionality and are not easy to catch A regular approach to find and fix a mistake is to insert temporary output operators and using simple test data cf p 2 3 6 to trace the intermediate results comparing them with those calculated by hand If the program s functioning disagrees with your mathematical algorithm most often due to a typo you will detect a discrepancy at some point Debugging is more complicated if the mathematical method is flawed in itself Dissecting the problem and the program into smaller steps is still a dependable approach Page 82 Chapter 4 Programming and graphing 4 1 Programming 4 1 2 Programming style Your program code should be reasonably self contained and documented Put the following at the top of a program e Author s name e Date e Course and project number e A brief description of the program what it does e Additional information if several programs have been written for this project Note that the readability of a program is improved and debugging is helped immensely by the generous insertion of comments Ask yourself will you be able to understan
221. tion indefinite and definite integration gt yl t3 9 A acs es 2x 6 gt diff y1 x 3 ae SOO 2 gt Iy1 int y1 x 1 3 Iy1 xf x x 6x a E gt int y1 x 1 1 9 Page 90 Chapter 4 Programming and graphing 4 2 An introduction to Maple Maple has commands that find extreme values of functions gt maximize ly1 gt minimize ly1 ee ral 44 2 7 24 1247 The percent symbol can be used as a substitute for the result of the last executed command gt eval 302 1620735 The symbols etc refer to the results obtained so many steps back By Maple s design you can execute commands that are typed in your worksheet in any order moving back and forth across the worksheet simply by hitting Enter on a command This practice should be avoided in worksheets that are to be saved and later read by you or another person otherwise the results can mislead the reader In particular instead of using the percent sign it is preferable to assign symbolic names to the results you want to re use The maximize and minimize commands work only on certain functions namely where no critical points exist or the equation for critical points can be solved exactly Not the case here gt maximize x cos x x 0 2 RootOf tan _Z _Z 1 0 8603335890 cos RootOf tan _Z _Z 1 0 8603335890 The command numapprox infnorm can find the maximum abslolute value of more general functi
222. tivation and historical background can be included although some of it can be scattered over later sections too The Introduction should also indicate what the reader will find in the remainder of the report The context and language of the Introduction often Page 11 Chapter 2 Technical writing 2 3 Organization of report makes it clear who the target audience is Otherwise state any special assumptions about the readers background explicitly e g We assume the reader is familiar with eigenvalue theory for matrices When writing the Introduction assume that the original assignment is not available to the reader Your paper must be self contained Do not copy the assignment s language use your own words Some assignments might introduce a little story and characters like Alice and Bob In this case again your own Introduction must independently describe the situation so that the reader who didn t see the assignment sheet would know what you are talking about The introduction can be viewed as an extended abstract but it has a broader mission Hook the readers make a promise that makes them want to stay with your paper A potential reader may never get to appreciate the rich and interesting contents if the introduction fails in its mission For a typical paper in this course the Introduction should be from 1 4 of a page to a full page long It should not tire the reader It should be rather easy reading not so tec
223. to an area rather than affecting the whole document Apart from enhancing usability this also in a sense protects distinct parts of a document from each other The XIX commands for changing type style are given in table 3 2 and those for changing type size are given in table 3 3 Commands for selecting fonts other than these are not discussed here rm Roman Nit italic sc CAPITALS em Emphasized sl slanted tt typewriter bf boldface sf sans serif Table 3 2 Commands for selecting type styles Each of the type style selection commands selects the specified style but does not change the size of font being used The default type style is roman you are reading a roman style font now To change type size you issue one of the type size changing commands in table 3 3 which will select the indicated size in the currently active style size default 10pt 11pt option 12pt option tiny 5pt 6pt 6pt scriptsize 7pt 8pt 8pt footnotesize 8pt Opt 10pt small Opt 10pt 11pt normalsize 10pt 11pt 12pt Marge 12pt 12pt 14pt Large 14pt 14pt 17pt LARGE 17pt 17pt 20pt huge 20pt 20pt 25pt Huge 25pt 25pt 25pt Table 3 3 TEX size changing commands Page 45 Chapter 3 Typesetting with ATRX 3 3 An introduction to TX and friends The point size option referred to in table 3 3 is that specified in the documentclass com mand issued at the beginning of the input file Through it you select that base
224. tricky We need the command op whose effect is just to remove the bounding brackets around the whole array gt op A 1 2 red blue x 2 5 x 6 plot1 To add a new element say elem6 the following command can be used gt A op A elem6 A 1 2 red bluel x72 5 x 6 ploti elem6 The command seq provides a convenient way to initialize an array with elements generated according to a given rule gt B seq i72 i 3 9 B 9 16 25 36 49 64 81 The command map performs the specified action on all elements of the array at once gt map sqrt B 3 4 5 6 7 8 9 In the commands seq and map it is possible to use your own function For example the following will increment all elements of the array B by one gt map x gt x 1 B 10 17 25 37 50 65 82 Page 92 Chapter 4 Programming and graphing 4 2 An introduction to Maple 4 2 5 Linear Algebra Linear algebra is available in Maple via either of two packages linalg or LinearAlgebra The former is not being updated anymore and will be eventually phased out We will work with the latter package First load the library gt with LinearAlgebra Here are some basic operations to create a matrix to find the inverse the determinant the transpose the characteristic polynomial the eigenvalues and eigenvectors gt A Matrix 2 4 6 8 gt A 1 gt Determinant A gt Transpose A 2 6 4 8 gt CharacteristicPolynomial A lambda
225. troduction to TX and friends tabular environment The tabular environment is used to produce tables of items particularly when the table is predominantly rectangular and when line drawing is required TFX will make most decisions for us for instance it will align everything for us without having to be told which are the longest entries in each column This environment is the first of many that use the TFX tabbing character This character is used to separate consecutive entries in a row of a table array etc The end of a row is indicated in the usual manner by using In this way the individual cells of the table or array are clearly described to ATEX and it can analyse them to make typesetting decisions Commands issued within a cell so defined are again local to that cell The tabular environment is also our first example of an environment with arguments The arguments are given in braces as usual just after the closing brace after the environments name In the case of tabular there is a single mandatory argument giving the justification of the entries in each column 1 for left justified r for right justified and c for centred There must be an entry for each column of the table and there is no default Let us start with a simple table begin tabular llrr1 bfseries Student name amp bfseries Number amp bfseries Test 1 amp bfseries Test 2 amp bfseries Comment F Basset amp 865432 amp 78 am
226. ts have little trouble making their programs to print on the screen but they expe rience more difficulties in creating programs that would flush their output to a file Not that creating such a program in any language is very difficult but it certainly requires more effort and time Redirection is a trick that can help to work around this problem Every program running under UNIX has a file already opened standard output Nor mally it is your shell terminal s window You can redirect it to a text file in your directory For instance if you want your program a out to print the output to a file data out instead of the screen you can run it like this lumsden a out gt data out Note that this could be a problem if you have messages printed out prompting for certain kinds of input those messages will also be redirected into the file instead of the screen You should in this case write your programs so that they not be prompting for input Or at least know how many numbers and in what sequence the program wants you to enter you can then feed the data into your program blindfold Note also that if you run the same command again the old contents of the file data out will be lost A 8 Access privileges We mentioned previously that the system will deny Bob to access Lisa s directory and vise versa Technically the access is governed by certain attributes assigned to each directory and file on the system Each file has its owner who
227. ttle extra space and using a larger font It will also start a new page in the case that a new chapter is begun It is always a good idea to plan the overall sectional structure of a document in advance or at least give it a little thought Not that it would be difficult to change your mind later you could use the global replace feature of an editor for instance but so that you have a good idea of the structure that you have to describe to ATEX The sectioning command that began the present sectional unit of this document was subsection Document structure and that was all that was required to get the numbered section name and the table of contents entry There are occasions when you want a heading to have all the appearance of a particular sectioning command but should not be numbered as a section in its own right or produce a table of contents entry This can be achieved through using the form of the command as in section We will see that many TFX commands have such a form which modify their behaviour slightly Not only will ATEX number your sectional units for you it will compile a table of contents too Just include the command tableofcontents after the begin document command and after the topmatter that should precede it LATEX environments Perhaps the most powerful and convenient concept in the ATFX syntax is that of an environ ment We will see most of the heavy typesetting problems we will encounter can be
228. tween various input and output data files as these can become quite numerous A 2 Directories A group of files is stored in a directory A directory can in turn contain other directories The UNIX file system contains all files on the computer and as such is made up of a hierarchy of directories It can be thought of as an upside down tree of directories Fig A 1 Page 131 Appendix A Quick UNIX reference A 2 Directories Figure A 1 Sample directory tree bin users lib cp ls math staff study lisa bob cs1510 m2130 lab1 lab2 lab3 Page 132 Appendix A Quick UNIX reference A 4 Shell The purpose of directories is to help users organize their files Each user can create any number of subdirectories within their home directory to any depth in the tree If you look at the depicted directory structure you can see that the directory bob contains two first level subdirectories named cs1510 and m2130 and the latter contains three second level subdirectories named lab1 lab2 and lab3 A 3 Pathnames There can be files with the same name in different directories For example there are likely dozens of files by the name lab1 tex on the system created by different students Yet there is a method to identify any file in the file system unambiguously The way do this is to use a pathname
229. ular those included with 2130 sty file Besides the picture environment can be used to create a desired layout of imported graphs or to superimpose graphs and text We do not advocate exclusive usage of any one of these graphing utilities Try to draw pictures and draw your conclusions In all cases you have to write a program which in part generates graphics data and it is up to you to select the utility that will handle a current graphics task best A practice not allowed in this course except with an express permission of the instructor is to import graphics files that are not your own production downloaded from the Internet Also do not use bitmap graphics and image compression formats gif jpg png in particular scanned pictures and digital photos Page 96 Chapter 4 Programming and graphing 4 3 Drawing graphs 4 3 1 Postscript Files Many graphics utilities Maple and Gnuplot for example generate Postscript files which are easily recognized by the ps or eps extension Postscript is a popular graphical format in troduced by Adobe Inc It belongs to the category of vector graphics as opposed to bitmap graphics a typical representative of which is the bmp format Postscript is a parent pretty much alive of the Portable Document Format PDF also designed by Adobe Inc EPS stands for Encapsulated Postscript which is now the best supported format for the inclu sion of graphics into ATEX documents To include an ep
230. umber Applied Mathematics 2130 e Your name and student number Your professor s name e The date of submission A typical title page is shown in Figure 3 2 in Section 3 2 1 where the TX code used to produce it is also given About the title try not to repeat the title of the assignment Devise your own way to describe the topic The title should not be too general For example Solving a Mathematical Model by Means of Computer Programming isn t good although it can be a title of choice for an introductory lecture in a Math Modeling course While being short the title should reflect particulars of the work For example Two methods for evaluating the volume of a pyramid is much better than just Pyramids Word play subtle humor puns these may work but make sure you show a good taste Some variants are totally inappropriate like Mathematics Supporting Global Warming Put Behind in place of Supporting and the title becomes acceptable A perfectly normal if not at all fancy version is Mathematical Modeling of 2 3 3 Table of contents The Table of contents is generated automatically by ATEX from the headings of your sections Some extra commands are needed in order to include the References and Appendix sections The details are given in Sect 3 2 2 A safe practice in the first assignment at least is to adhere to the suggested standard plan and headings Then as your experience grows you can vary the paper structure
231. umbers the math mode ensures that the negative sign will have an appropriate length While easy in its syntax this command requires some experience and judgement as to where one should put the label if say the label is referring to the point at the top right corner of a square Try it for yourself Try to label a simple square ABCD and you will need to adjust the values of x and y several times before the labels finally look nice In the scaledpicture environment this is made easy There is one general command and several short forms The great advantage is that they refer to the point that is being labelled say a b The general command angleput deg scale a b label the default scale number is 1 Page 118 Chapter 4 Programming and graphing 4 4 The ATEX picture environment Short forms 1 cput a b label deg 0 scale 0 centred on the point In the next eight commands scale 1 2 eput a b label deg 0 east of the point 3 nput a b label deg 90 north of the point 4 wput a b label deg 180 west of the point 5 sput a b label deg 90 south of the point 6 neput a b label deg 45 northeast of the point 7 nwput a b label deg 135 northwest of the point 8 swput a b label deg 135 southwest of the point 9 seput a b label deg 45 southeast of the point In the scaledpicture environment the font size i
232. underbrace 75 underline 75 usepackage 25 41 verb 25 26 verbatim environment 25 26 31 54 vskip 27 vspace 27 vspace 27 Page 160 Personal notes Page 161
233. ure to type them in pairs Corresponding to the alternatives and that we had for the math shift character we may use and as the display math shift sequences One can also use the environment begin displaymath end displaymath which is equivalent to and is suitable for use with long displayed expressions If you wish ATEX to number your equations for you you can use the environment begin equation end equation which is the same as the displaymath environment except that an equation number will be generated It is poor style to have a displayed expression either begin a paragraph or be a paragraph by itself This can be avoided if you agree to never leave a blank line in your input file before a math display We will see later how to typeset an expression that is to span multiple lines For now let us look at an example of displaying an expression For each a for which the Lebesgue set L_a f neq emptyset we define We could have used begin displaymath here cal B _a f L_fatr f r gt 0 and end displaymath here and these are easily seen to be completely regular which produces For each a for which the Lebesgue set La f 4 we define Ba f La r f r gt 0 and these are easily seen to be completely regular That illustrates how to display an expression but also shows that we have got a lot more to learn about mathematical typesetting Before we have a look
234. verfoot underheadoverfoot The package 2130 sty also contains enhanced graphics command which significantly extend a graphical facility provided by the standard TFX as described in Section 4 4 3 Other useful packages that you will likely need to include in your documents are graphicx to enable import of EPS graphics see Section 4 3 1 and amssymb to enable mathematical symbols like R and various special characters like Besides usepackage command s the preamble may contain your own definitions For example this is a convenient shorthand for an useful but long TAT X s keyword see p 28 newcommand ds displaystyle User defined commands may have parameters for example newcommand pair 214 1 2 Now the command pair A12 b34 produces A12 b34 3 1 2 Comments The percent sign is the commentary symbol in ATfxX Everything that follows it is ignored till the end of line There are two exceptions First the percent sign itself can be printed with command and as a part of this command it does not begin a commentary Second the percent sign within the verbatim environment or verb command has no controlling effect If there is a need to disable rather long parts of a document from processing while deleting them is undesirable the following construction can be used iffalse No matter how many lines or pages everything here will be ignored by LaTeX fi Finally you may put the line end document
235. which should be typeset as a single special symbol because they will clash with each if this is not done Have a look at these words flight flagstaff chaff fixation and compare them with these flight flagstaff chaff fixation See the difference In the first set I let ATX run as it usually does In the second I overruled it somewhat and stopped it from creating ligatures Notice how the fl ff and fi combinations are different in the two sets in the former they form a single symbol a ligature and in the latter they are comprised of two disjoint symbols There are other combinations that yield ligatures but we do not have to bother remembering any of them because ATFX will take care of these too Notice too that TFX has been taught how to hyphenate the majority of words It will hyphenate a word if it feels that the overall quality of the paragraph will be improved For long words it has been taught several potential hyphenation positions TAT X also goes to a lot of trouble to try to choose pleasing page breaks It avoids widows which are single lines of a paragraph occurring by themselves at either the bottom of a page where it would have to be the first line of a paragraph or at the top of a page where it would have to be the last It also vertically justifies your page so that all pages have exactly the same height no matter what appears on them As testimony to the success of the pagebreakin
236. worksheet mw If there is a certain data file with hidden not told to the reader data which your report depends on it too should be included Before issuing the submit command make sure your current directory is the parent directory of the directory containing the files to be submitted For example if your Assignment 1 files are located in A1 math2130 a1 use the command cd A1 to change into the A1 directory before running the submit command Actual submission for Assignment 1 for a course called math2130 2 math2130 section number 2 is done by typing the following in the command line from the parent directory of the directory math2130 a1 containing your submission submit submit math2130 2 al MMIX Department of Mathematics and Statistics Memorial University of Newfoundland September 4 2009 Chapter 5 Local system particulars 5 2 Laboratory computers on campus Assignment 2 will have a submission ID of a2 and so on Students of section 3 should replace math2130 2 into math2130 3 You will be asked to enter your password Students who wonder why the word submit is repeated twice can compare the above com mand with the one that an instructor would use to retrieve your submissions submit retrieve math2130 2 al If you are not sure of the course or assignment ID to use with the submit command you may type at the shell window prompt submit list to get a list of courses and dates on which there are assignm
237. xport LM_LICENSE_FILE 28002 noether After that you should be able to use Maple The command xmaple invokes Maple 11 the most recent version currently available in the lab in the standard mode The command xmaple cw invokes Maple 11 in the Classic Worksheet mode The command xmaple 9 invokes Maple 9 Maple can be invoked in a non graphical command line mode by the maple command The session opens quickly This mode is particularly advantageous if you connect to Maple from your home computer and do not need graphics To end the session type quit 5 3 5 Miscellaneous 1 Gnuplot is invoked by the gnuplot command 2 XFig is invoked by the xfig command 3 To convert a ps file into eps file many UNIX systems have a command pstoeps or ps2eps Windows based versions of GhostView have an EPS convertor under File menu Unfortunately these options are not available on the LabNET machines Here is a con version method which is a little ugly but it works Suppose fig1 ps is the name of the original Postscript file a Type the command es u SDEVICE bbox fig1 ps b Among the output that appears on the screen find and select by mouse a line that looks like this BoundingBox 20 118 575 673 c Open the file fig1 eps in a text editor say in Kile The first line will look like this PS Adobe 2 0 Page 128 Chapter 5 Local system particulars 5 3 Software Change it into PS Adobe 3 0 EPSF 3 0 Paste the selected

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