Math 398 - Game & Voting Theory - Course PoliciesOverview | Evaluation | Reading Assignments | Homework | Exams | Notes on Written WorkPresentations and Projects | Grading of Group Assignments | Attendance | Getting Help Hudson River Undergraduate Conference |
Overview
Game theory was originally developed by John von Neumann as a purely mathematical theory, but it began to flourish and gain widespread attention with von Neumann's collaboration with the economist Oskar Morgenstern in the 1940's. Most recently, game theory has been thrust into the public spotlight because of A Beautiful Mind, the book and movie chronicling the life of John Nash. In addition to studying the underlying theory, we will also see applications of game theory to some expected areas (economics and international conflict) and some very unexpected areas (anthropology and evolutionary biology). Voting theory has a slightly longer history, but did not gain prominence until Kenneth Arrow's celebrated Impossibility Theorem in 1951. Most disconcerting to students new to the area are the results that there is no completely ``fair'' voting system and that every voting system can be manipulated through strategic voting. Although these results are bothersome, we will see that they should not come as a surprise. One of the goals of voting theory is to understand why different procedures behave as they do so that we can avoid their pitfalls. In addition to the expected applications to political elections and rankings of sports teams, we will also see applications to computational biology and computer science. This is going to be a really fun semester.Evaluation
Your final grade will be determined by| Reading Assignments | 5% |
| Homework | 30% |
| Two Exams | 30% |
| Comprehensive Takehome Final Exam | 15% |
| Presentations and Projects | 20% |
Reading Assignments
You will have a reading assignment for every class period. I think that the texts are well-written, but that does not mean that the material is easy - it's not. You may need to re-read each section several times, but don't be scared or get discouraged. The reading assignments are intended to help you learn the course material, not be a major obstacle or obstruction. If you feel that the assignments are taking too long, please come see me.Homework
A major emphasis in this course is that you learn how to write precise and complete mathematical arguments. This can be a challenging endeavor and may require several iterations, but the process will not only aid your mathematical development but can also great improve your clarity of thought in other disciplines and areas as well. With this emphasis, your homework should be precise, comprehensible, completely justified, and written in complete sentences. Most of the homework problems will be worth 5 points, and the possible grades will be 5, 4, or No Grade. A few of the problems may be worth 10 points, and the possible grades will be 10, 9, 8, or No Grade. After I have returned the homework, I will allow you one opportunity to rewrite any problem that you have made a serious effort to complete. The maximum that you can receive on a rewrite is 4 (on 5 point problems) or 8 (on 10 point problems). You must turn in your rewrite, along with your original paper, within one week of when I return the homework to the class. An important aspect of your mathematical development is that you learn to discuss mathematics with others and collaborate on problems. The homework assignments will alternate between Individual assignments and Group assignments. On the group homework assignments, you will work in groups of two and turn in one paper. It is extremely important that both of you understand every solution that your group produces. On each assignment, one student will be designated as the primary author who writes-up the solutions, and the role of primary author must alternate between the members of the group. You may discuss the Individual assignments with other students, but each person must turn in a separate paper that represents his/her own work. Homework will usually be due at my office on Fridays at 2:00 pm.Exams
The two exams during the semester will have a closed-book, inclass component, which count for 10-20% of the total grade. The remaining part of the exam will be open-book and takehome. You will have at least five days to complete each takehome exam and at least one week to complete the final exam. I would strongly suggest that you begin these early to leave time to ask me questions about the exam.A Few Notes on Your Homework and Exams
Here are a few guidelines for the presentation of your written work. If you do not follow these, I reserve the right to return your homework ungraded- Your writing must be clear and legible.
- Your solutions should be well-written,
using complete sentences to justify your results where necessary.
A list of answers without explanation is not acceptable. - Here is a good rule of thumb to follow when writing up your
work:
Write your solutions so that you could hand them to another student in the class and she could understand your explanation.
- Do not turn in your first draft of the assignment. You should expect to neatly recopy and organize your work.
- If you write in pen, there should be no scratch-outs.
- Do not turn in paper torn from a spiral notebook with ragged edges.
- I strongly recommend that you turn in all assignments on time. For each 24 hour period that an assignment is late, you will lose 25%.
Presentations and Projects
You will give two group presentations during the semester, one on Game Theory and one on Voting Theory. These will cover topics of your choosing that we have not discussed during class. I will give you more details on my expectations as the times get closer. You will also write a book review on a mathematical book written for a popular audience. There are many possibilities, including A Beautiful Mind, Fermat's Enigma, A Mathematician's Apology, Flatterland, The Man Who Knew Infinity (a biography of Srinivasa Ramanujan), and The Man Who Loved Only Numbers (an account of Paul Erdos). I can help you find a book for this. More information will be forthcoming during the semester.Grading of Group Assignments
Each group assignment will receive a single grade, and the group will determine how the points are allocated to each member. For example, if a group of two receives an 85 on a presentation, then the group will have 2 x 85=170 points to distribute among them. I will be available to mediate this process, if necessary.Class Attendance
Although class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.Getting Help
Please come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.Hudson River Undergraduate Mathematics Conference
The HRUMC will be held on Saturday April 27 at Hamilton College. I would strongly encourage all of you to attend, and you should also consider giving a talk. This is a really nice day to be involved with mathematics with other undergraduates. A good time will be had by all. If you do give a presentation, you will receive an extra 5% on your final grade. Each talk is attended by anywhere from 10 to 50 people, most of whom are other mathematics students from around New England. Before you submit an abstract to give a talk, we will need to discuss your topic and make sure that it is at the appropriate level. I have very high expectations for the quality of these talks so you should expect to devote significant effort to your presentation. I will, of course, work with each of you on your talk. If you decide to attend without giving a talk, you will receive an extra 2% on your final grade.