course information

Mathematics 36               Winter 2003         Tentative Syllabus

Date             Topics                                                                                 Homework

 1-6 Population models Read Chapter 1 and do:  Problem 1 1-8 Interacting populations p. 33:  8, 9  and  Problems 2,3.   Reading: Chapter 3 1-10 Linearizations, classifying equilibria Problems 4,5.   Optional reading for the week: Chapters 3 and 4 of Olinick (on Baker reserve)

Hand in problem 3 on Monday the 13th.

 1-13 Voting theory (Guest lecturer)    Introduction Problems a,b,c,d  and For All Practical Purposes, p.186: 1a,b,c, and one part of d. Reading: Chapter 9 of For All Practical Purposes and chapter 6 of Olinick. 1-15 Voting axioms For All Practical Purposes, p.187: 2,3;  Olinick, p. 192: 9, and p. 193: 19(The voting mechanism, i.e. the function from the set of profiles to group rankings, that you construct does not need to be "reasonable";  and Problem 6. Handout(Voting Axioms) 1-17 Proof of Arrow's theorem These Problems

Problems to be handed in on Wednesday, the 22nd: Problems a,b,c,d ,   Problem 6  and  number 19, page 193 of Olinick.

 1-22 More population modeling Problem 7 1-23 Tournaments  Introduction 1-24 Transitive tournaments Problems 8,9,10

Due Monday the 27th or Wednesday the 29th: Problems 8 and 10

 1-27 Consistency of tournaments Problems 11,12  and: How many transitive and cyclic triples does this tournament (which is also on p. 83 of Roberts) have? 1-29 End tournaments, start games the test 1-31 Values of games Problem 13

Hand in Problem 13 on Monday.

 2-3 Zermelo's theorem Problem 14 2-5 More on voting These problems 2-6 More voting, Discussion of projects none

Due Monday the 10th: 14(a) and one part of 14(b), i.e. either address the case where m and n are both even, or when m is even and n odd, or when m=n=3.  Also, either 1. or 2. of These problems.

 2-10 Back to game theory Problems 15,16 2-12 Problem 17 2-14 Start mixed strategies Problem 18

Hand in Problems 16 and 17 on Monday.

 2-17 Mixed strategies Problems 19, 20 and 21  Wednesday's class should be helpful for 20 and 21, but you might start on these before it.  There is now a Game theory book on reserve by Binmore.  Much of what we've done is in chapter 1, and chapter 6 discusses mixed strategies. 2-19 Start von Neumann's theorem nothing new, just the problems from Monday. 2-21 Proof of von Neumann's theorem Problem 22

Hand in Problems 19 and 21 on Monday.

 2-24 End of von Neumann's theorem and applications Problem 23 2-26 General-sum games test 2-28 Nash bargaining axioms Problems 24, 25(a)

Nothing to hand in on Monday.  Last assignment due on Friday, the 7th.

 3-03 Solving bargaining games Problem 25b,c 3-05 Threat games Problem 25d,e 3-06 (X-hour)

Hand in (under my office door, 312 Bradley) problem 25 anytime Friday.