Mathematical Problem Solving
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1. Before each class session begins please try to remember to turn your phones off so as not to cause a disruption during class and do realize that even the sound of a vibrating phone can be disruptive Furthermore cell phones are not permitted at all during exam situations quizzes and tests The Computer Lab Are you mature enough to be in a class that s held ina computer lab Please resist the temptation to constantly check email Facebook ESPN com or other such distractions that sitting at a computer can present Realize that much of what I have to show you in this course are things that I have to show you typically on the overhead screen If you re not paying attention while I m demonstrating something do not expect me to explain it to you once you re done doing your own computer work Tentative Course Schedule Material Intro to the course Single linear equation in one variable An introduction to GameMaker Cartesian Coordinate Systems 1D Mathematics 2D Cartesian Space 3D Cartesian Space Wed 1 3 3D Cartesian Space 9 3 1 4 Odds and Ends Concepts from Geometry Compass and straightedge constructions Wed n a Some Geometry of Pathfinding 9 10 Pathfinding and AI Mon Chp 2 Vectors 9 15 2 1 Mathematical Definition of 2 2 Vector and Other Boring 2 3 Stuff 2 4 Geometric Definition of a Vector Specifying Vectors with Ca2. Making up a missed quiz is highly improbable and is only considered when notice is given prior when possible to the missed quiz there is a valid reason for missing the quiz and the quiz is made up before to the next class session Projects There will be several Projects assigned for a grade mostly taking the form of a program you will complete on the computer using either the GameMaker or the Unity software These Projects are intended for you to demonstrate your understanding of how the mathematical concepts learned in class are incorporated in a video game Realize that these Projects are intended to test your mathematical ability much more so than your programming ability The guidelines templates and demonstrative examples should assist you on how to code the commands for the Projects that are to be completed on the computer For further assistance on the technical aspect of coding in either GameMaker or Unity refer to the respective help libraries the user manual for GameMaker or the Scripting Reference for Unity The points the individual Projects will be worth will vary totaling 100 points by the end of the term For each of these Projects there will be guidelines to follow to ensure that you demonstrate your understanding of the relevant concepts from the course Also though you will always be encouraged to infuse your own creativity into these Projects so don t just follow the guidelines there will be points aw
3. will discuss functions graphs trigonometry probability statistics and logic Particulars for this Section In an effort to explore the mathematics used in the making of video games we will look at the geometry and algebra of 2D and 3D space We will look at the mathematical standards used to describe objects in 2D and 3D space and the positions orientations and trajectories of such objects While the focus of the lessons and assessments will be on the mathematics it is worth noting that a substantial side effect of these lessons is that the student will gain some rudimentary skills in the craft of making their own video games Course Objectives The students will acquire a significant subset of precalculus level mathematical skills hence improving their critical thinking especially with regard to logic abstraction attention to detail and demand for precision Furthermore the students will gain experience in mathematical analysis and consequential creative synthesis into original observations solutions or works of expression Statement of Support for the Mercy Mission This course supports the Mercy Mission by creating students who are intellectually creative This is achieved through fostering critical habits of the mind which support the aspirations for excellence manifested within the academic community In particular the student will achieve this by synthesizing course materials to produce an original applica
4. Math Applications Video Games MATH110 Fall Term 2014 MW 7 05 8 45 Old Main Lab Professor Patrick M Kelly Office 402 Old Main Phone 824 2174 E mail pkelly mercyhurst edu Emailing will always be the best way of contacting me Please feel free to email me any time and I should typically be able to get back to you within a few hours Note Also though if you re emailing me for any reason other than turning in an assignment please do not include an attachment have a rule established in Outlook that will send any email directly to a different folder not my Inbox if the message has an attachment and is coming from a student in this class I keep very current on the emails in my Inbox but I typically won t even look in those other folders until I actually sit down to grade projects If you re trying to email me to ask a question and you would need me to look at your file simply email me an attachment less message first and explain your question and then send a second email with the attached file The second message will go directly to my MathApps folder but the first message will nag at me in my Inbox so that I know to look in my other folder for your file Also Always compress zip your files when you send them to me Office Mondays 1 00 3 00 Hours Wednesdays 1 00 3 00 Fridays 1 00 3 00 Meeting times by appointment may be arranged as well Other Information This course is registered on Blackboa
5. arded for appropriately creative elements included in your Projects Academic Integrity Mercyhurst University believes that academic integrity is a core principle of education According to the Center for Academic Integrity www academicintegrity org academic integrity begins as a commitment to five fundamental values honesty trust fairness respect and responsibility These values begin with the individual and extend to others in the community of learning Academic integrity should not be an issue in this course if we all embrace the values of honesty trust fairness respect and responsibility The danger in a course such as this as is the case with the majority of courses in which you submit projects completed on the computer is to give in to the temptation to share files For any assignment that earns a grade you must do your own work and turn in your own files Attendance You are expected to attend every class session If you do miss a class for any reason it is your responsibility to catch up on what was missed Please do not expect me to re teach the material that was taught on the day you were absent Services Learning Differences In keeping with college policy any student with a disability who needs academic accommodations must call Learning Differences at 824 3017 to arrange a confidential appointment with the Disability Services Director during the first week of classes Cell Phones
6. be assigning the entire exercise set from each chapter I ll specify at the time if there are any exceptions to this In addition I will give you some supplemental problems as Suggested Exercises when the authors exercise set could use some bolstering All Suggested Exercises are your responsibility to do and understand Do what it takes to make sense of how to work through these problems see me email me find extra help online etc Seven Hand in Homework assignments will be given throughout the term as well each worth 10 points toward your final course score It will always be announced in advance what will be due and when for a Hand In Homework assignment i e there will be no surprises so you should be able to put forth the appropriate effort to earn most if not all of the points for these assignments The content of the Hand In Homework assignments will be either identical to some of the Suggested Exercises or will be very similar to them Hand In Homework assignments will be announced well in advance of when each is due Late submissions will not be accepted Quizzes Quizzes will be used as an assessment of your understanding of the material and your progress in the course Quizzes will be held seven times during the term each asa pop quiz To be frank this is intended to determine who is keeping up with the Suggested Exercises Material for the quizzes will come directly from the Suggested Exercises
7. ctively use scientific inquir evaluation issued online t Scientific Reasoning Judg 2 p y uuy all student enrolled in an and reasoning to solve problems and analyze and interpret data relevant course Supporting Learning Outcome Critical Thinking Supporting Learning Outcome Creative Thinking All Core Student Learning Outcomes are assessed on a rotating basis of at least once every three years All assessment documents and information including the scoring rubrics can be found on the Mercyhurst portal and website Please direct questions to the course professor or to the Core Assessment Coordinator coreassessment mercyhurst edu Course Learning Goals and Objectives The following course objectives detail how the specific content of this course will support the above Core Outcomes Acquire a significant subset of precalculus level hence improving critical thinking skills especially with regard to logic abstraction attention to detail and demand for precision Further gain experience in mathematical analysis and consequential creative synthesis into original observations solutions or works of expression
8. es Wed 7 3 3D Polar Space 11 19 7 4 Using Polar Coordinates to Specify Vectors Mon 11 24 Wed 11 26 Thanksgiving Break no classes Mon Chp 8 Rotation in Three Dimensions 12 1 8 1 What Exactly is Orientation 8 2 Matrix Form 8 3 Euler Angles Wed 8 4 Axis Angle and Exponential 12 3 8 5 Map Representations 8 6 Quaternions 8 7 Comparison of Methods Converting between Representations oR Reading Day no classes Fri 12 12 Final 1 at Exam Everything 6 00 MATH 110 Math Applications Video Games Fall 2014 Patrick M Kelly Assistant Professor of Mathematics and Computer Systems pkelly mercyhurst edu math mercyhurst edu pkelly This course has been approved for the Mercyhurst University Core and fulfills a requirement in Core Area V The following explicates the Core Learning Outcomes that are associated with this course and how they will be assessed as part of the Core requirements Core Learning Outcomes and Assessment Strategies The table below highlights the Student Learning Outcomes associated with every course in Core Area V Scientific Quantitative and Critical Reasoning Primary Learning Learning Objective Associated Assessment Outcome DDN Use mathematical concepts to make logically sound decisions Quantitative conceptual Quantitative and judgments and or predictions effe
9. rd an academic software package set up on one of Mercyhurst s servers You may access information about the course via Blackboard at any time from any computer Please check that the e mail address listed for you on Blackboard most likely your Mercyhurst account is the account that you use regularly please change it on Blackboard if this is not the case Text 3D Math Primer for Graphics and Game Development second edition by Fletcher Dunn and Ian Parberry CRC Press Publishing ISBN 978 1 56881 723 1 http www crcpress com product isbn 9781568817231 Needs A compass and a ruler or other straightedge Mathematics Applications Courses Description Through the analysis of a single area of mathematical application such as art music or politics we will see how fundamental and traditionally studied mathematical elements are found in the underlying structure of problems solutions relationships and works of expression and creativity Once familiar with the mathematical building blocks of a certain area of application the students will then synthesize these into an original contribution of their own which may be a mathematical description of a phenomenon a solution to a problem a work of art etc depending upon the particular area of application Students will find a number of ways to be successful in the class including through presentation homework and quizzes projects and examination Specifically we
10. rtesian Coordinates Vectors versus Points Wed 2 5 Negating a Vector 9 17 2 6 Vector Multiplication by a 2 7 Scalar 2 8 Vector Addition and 2 9 Subtraction Vector Magnitude Length Unit Vectors The Distance Formula Vector Dot Product Vector Cross Product Vector Cross Product Linear Algebra Identities Chapters 1 and 2 and geometry material Wed Chp 3 Multiple Coordinate Spaces 10 1 3 1 Why Bother with Multiple 3 2 Coordinate Systems Some Useful Coordinate Spaces Mon 3 3 Basis Vectors and Coordinate 10 6 Space Transformations Wed Midterm Break no class 10 8 Mon 3 4 Nested Coordinate Systems 10 13 3 5 In Defense of Upright Space Introduction to Matrices Mathematical Definition of Matrix Geometric Interpretation of Matrix Wed Chp 5 10 22 5 1 5 2 5 3 The Bigger Picture of Linear Algebra Matrices and Linear Transformations Rotation Scale Orthographic Projection Mon 5 4 Reflection 10 27 5 5 Shearing Combining Transformations Classes of Transformations Chapters 3 4 and 5 More On Matrices Determinant of a Matrix Inverse of a Matrix Orthogonal Matrices 11 10 6 4 4 x 4 Homogeneous Matrices 4 x 4 Matrices and Perspective Projection Polar Coordinate Systems 2D Polar Space Why Would Anybody Use Polar Coordinat
11. tion Statement of Core Curriculum Fulfillment MATH110 is a course in the Scientific Quantitative amp Critical Reasoning category of the Core Curriculum of Mercyhurst University Evidence of this course s alignment with the proper Core student learning outcomes is provided as the last page of this syllabus Grading Your final course grade will be compiled from several factors Seven homework assignments seven quizzes two in class exams an assorted amount of projects and the cumulative final exam will all be considered for the course grade calculation The point distribution amongst these factors will be as follows Seven Hand in Homework assignments 10 points each 70 points Seven Quizzes 20 points each 140 points Exam 1 100 points Exam 2 100 points Projects 100 points Final Exam 140 points Total 650 points Course grades will be determined using the following scale A 608 650 points 93 5 100 B 582 607 points 89 5 93 4 B 543 581 points 83 5 89 4 C 504 542 points 77 5 83 4 C 452 503 points 69 5 77 4 D 419 451 points 64 5 69 4 D 387 418 points 59 5 64 3 F 0 386 points 0 59 4 Homework Suggested Exercises Hand In Homework Homework in a mathematics class is a must Our authors have an exercise set at the end of each chapter designed to test your understanding of the mathematical concepts covered in that chapter As Suggested Exercises I will typically
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