Course Syllabus

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The Mathematics of Decision and Beauty

Instructor: Will Orrick
email: worrick@indiana.edu
Office: Swain East 207
Office Hours: TBA

Associate Instructor: Daniel Condon
email: dmcondon@indiana.edu
Office: 1103 Atwater Avenue
Office hours: Monday 2:30 - 3:30, Wednesday 1:15-2:15, Friday 1:15-2:15.

Course Description

Math 106 is an exploration of mathematical structure in art, music, and decision-making. It aims to reveal some of the hidden abstract relationships that animate human experiences and activities like symmetry, perspective drawing, voting systems, packing, scheduling, and musical rhythm. During Spring 2017, we plan to cover:

  • Game Theory
    • What is a game?– Best response and optimal strategies
    • Nash’s equilibrium
    • Pure and mixed strategies
  • Geometry and Art
    • The problem: How do we see 3 dimensions with a 2D retina?
    •  Coordinates in 2- and 3-dimensions
    •  Parallel projection and overlapping cues
    •  The geometry of sight-lines and the heuristics of perspective
    •  Ratios and similar triangles
    •  Quantitative perspective drawing
  • Graph theory
    • Intro to graphs and vocabulary (edges, vertices, valence, etc)
    • Modeling: Euler and Hamiltonian circuits, minimum-cost spanning trees, traveling salesman problem, critical path analysis and order requirement graphs
    • Measures of complexity and basic solution algorithms
    • scheduling tasks
    • bin packing problems
  • Symmetry
    • Symmetries: reflections, rotations, translations
    • Symmetry groups and their symbolic representations
    • Wallpaper groups and crystallographic groups
    • Classification of the seven frieze patterns
  • Music
    • Pitches, scales, and the temperament problem
    • The math of rhythm and polyrhythm
    • The combinatorics of composition in melody and time
  • Social Choice (Voting)
    • Voting systems
    • Strategic voting
    • Fairness principles
    • Arrow's theorem

Unlike most math courses, coverage of each topic will be largely self-contained, so that difficulty in one area shouldn’t impede a student’s potential to excel in others. The course meets daily and will emphasize group- and activity-based learning. For this reason, attendance is expected (see below). Specific General Education learning outcomes are listed at the end of this syllabus.

Attendance

Class meetings are fundamental to the curriculum of this course, and your participation in daily class activities is important not just for your own learning, but for your fellow students as well. Attendance is therefore expected, and students are responsible for everything discussed in class, including changes to the schedule or course syllabus.

Calculators

Students should have a basic scientific calculator like the TI-30. Use of more sophisticated devices (e.g., with text memory) are not permitted on quizzes or tests.

Assignments

Students will submit written or online homework assignments daily. We will try to return homework submitted in class at the next class meeting.

Exams

There will be 5 exams during the semester, one at the end of each unit. The final exam will be two hours long and cumulative.

  1. Game Theory: Wednesday, January 25
  2. Geometry and Art:
  3. Graph Theory and Symmetry:
  4. Voting:
  5. Music: 
  6. Final Exam: Wednesday,  May 3, 12:30PM - 2:30 PM

Missed exams

Making up exams will not be allowed barring truly exceptional circumstances. If you know you will miss an exam due to conditions not under your control, you must notify the instructor during the first week
of class to discuss options.

Grading

The six exams and the homework will be weighted as follows.

  • Semester exams: 12% each
  • Final exam: 20%
  • Quizzes and Activities: 8%
  • Homework: 12%


Letter grades will be assigned using the table below unless the instructor
decides, based on experience and judgement, to use a more lenient curve.

  • A+: 98 - 100
  • A: 92 - 98
  • A-: 90 - 92
  • B+: 88 - 90
  • B: 82 - 88
  • etc.

Summary of Class Policies:

  • Only approved calculators can be used on exams.
  • Smartphones, tablets, or devices of that nature must not be visible—much less used—during exams.
  • Make-ups for unexcused absences from exams and quizzes will not be given. If you must miss an exam or class day due to documented illness or an allowed official IU activity, you must inform the instructor either prior to the absence or (in the case of illness only) earlier the same day. In the latter case, students must visit the Health Center or their personal physician for documentation to obtain any credit.
  • Students who miss class for any reason remain responsible for the material covered on that day.
  • There is no extra credit available in this class.
  • Students with conflicts between course requirements (e.g. exams) and religious observances must contact their instructor during the first week of the term and follow the procedures outlined by campus
    policy, available at: www.indiana.edu/∼bfc/docs/policies/ReligiousObservances09.pdf

Learning Outcomes

The official Gen Ed learning outcomes for M106 are listed below (as required by the document at
http://gened.indiana.edu/Students/outcomes.html)

  • Ability to solve simple scaling problems by using relative sizes in perspective to calculate actual sizes in 3D space
  • Ability to use perspective drawing techniques to create realistic 2D images of simple 3D geometric objects
  • Ability to solve simple scheduling problems
  • Ability to use graphs (e.g., trees) for modeling relationships within a data set
  • Ability to identify pure- and mixed-strategy Nash equilibria
  • Ability to use payoff matrices to model simple conflict dynamics, find best responses, dominant strategies, and Nash equilibria.
  • Ability to explain the difference between Pythagorean tuning vs. even temperament
  • Given one pitch frequency, ability to find others at perfect intervals above or below it, and can determine tonal intervals between given pitch frequencies


General Education


This course may be used to satisfy either the campus General Education Mathematical Modeling requirement, or the campus General Education Natural and Mathematical Sciences requirement, but not both simultaneously.  Mathematical Modeling courses provide rigorous instruction in fundamental mathematical concepts and skills presented in the context of real-world applications. The modeling skills provide analytical methods for approaching problems students encounter in their future endeavors.


Learning Outcomes addressed in Math-M 106 include but are not limited to

  1. Create mathematical models of empirical or theoretical phenomena in domains such as the physical, natural, or social sciences;
  2. Create variables and other abstractions to solve college-level mathematical problems in conjunction with previously-learned fundamental mathematical skills such as algebra;
  3. Draw inferences from models using college-level mathematical techniques including problem solving, quantitative reasoning, and exploration using multiple representations such as equations, tables, and graphs.

A passing grade in an approved course is required to show proficiency in mathematical modeling under the General Education curriculum.

Natural and Mathematical Sciences


Learning Outcomes addressed in Math-M 106 include but are not limited to

  1. model and understand the physical and natural world;
  2. the ability to solve problems;
  3. analytical and/or quantitative skills.

 

Academic Integrity


As a student at IU, you are expected to adhere to the standards and policies detailed in the Code of Student Rights, Responsibilities, and Conduct (Code). When you submit an assignment with your name on it, you are signifying that the work contained therein is yours, unless otherwise cited or referenced. Any ideas or materials taken from another source for either written or oral use must be fully acknowledged. All suspected violations of the Code will be reported to the Dean of Students and handled according to University policies. Sanctions for academic misconduct may include a failing grade on the assignment, reduction in your final course grade, and a failing grade in the course, among other possibilities. If you are unsure about the expectations for completing an assignment or taking a test or exam, be sure to seek clarification beforehand.

Note Selling: Several commercial services have approached students regarding selling class notes/study guides to their classmates. Selling the instructor’s notes/study guides in this course is not permitted. Violations of this policy will be reported to the Dean of Students as academic misconduct (violation of course rules). Sanctions for academic misconduct may include a failing grade on the assignment for which the notes/study guides are being sold, a reduction in your final course grade, or a failing grade in the course, among other possibilities.


Additionally, you should know that selling a faculty member’s notes/study guides individually or on behalf of one of these services using IU email, or via Canvas may also constitute a violation of IU information technology and IU intellectual property policies and additional consequences may result.

Disability Services

Every attempt will be made to accommodate qualified students with disabilities (e.g. mental health, learning, chronic health, physical, hearing, vision neurological, etc.) You must have established your eligibility for support services through the appropriate office that services students with disabilities. Note that services are confidential, may take time to put into place and are not retroactive; Captions and alternate media for print materials may take three or more weeks to get produced.  Please contact Disability Services for Students at http://disabilityservices.indiana.edu  or 812-855-7578 as soon as possible if accommodations are needed.  The office is located on the third floor, west tower, of the Wells Library, Room W302.  Walk-ins are welcome 8 AM to 5 PM, Monday through Friday.  You can also locate a variety of campus resources for students and visitors that need assistance at:  http://www.iu.edu/~ada/index.shtml

Sexual Misconduct

As your instructor, one of my responsibilities is to help create a safe learning environment on our campus. Title IX and our own Sexual Misconduct policy prohibit sexual misconduct.  If you have experienced sexual misconduct, or know someone who has, the University can help.

If you are seeking help and would like to speak to someone confidentially, support resources for individuals who have experienced sexual assault are available 24-hours a day. Call (812) 855-8900.  More information about available resources can be found here:  http://stopsexualviolence.iu.edu/help/index.html 

It is also important that you know that federal regulations and University policy require me to promptly convey any information about potential sexual misconduct known to me to our campus’ Deputy Title IX Coordinator or IU’s Title IX Coordinator.  In that event, they will work with a small number of others on campus to ensure that appropriate measures are taken and resources are made available to the student who may have been harmed.  Protecting a student’s privacy is of utmost concern, and all involved will only share information with those that need to know to ensure the University can respond and assist. 

I encourage you to visit stopsexualviolence.iu.edu to learn more.

Course Summary:

Course Summary
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