course information
Mathematics 36
Winter 2003 Tentative
Syllabus
Date
Topics
Homework
16 
Population models 
Read Chapter 1 and do:
Problem 1 
18 
Interacting populations 
p. 33: 8, 9 and
Problems 2,3. Reading: Chapter 3 
110 
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.
113 
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. 
115 
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) 
117 
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.
Due Monday the 27th or Wednesday the
29th: Problems 8 and 10
127 
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? 
129 
End tournaments, start games

the test

131 
Values of games

Problem
13

Hand in
Problem 13 on Monday.
23

Zermelo's theorem

Problem 14

25

More on voting

These
problems

26

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.
Hand in
Problems 16 and 17 on Monday.
217

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.

219

Start von Neumann's theorem

nothing new, just the problems from
Monday.

221

Proof of von Neumann's
theorem

Problem 22

Hand
in Problems 19 and 21 on Monday.
Nothing
to hand in on Monday. Last assignment due on Friday, the
7th.
Hand in (under my office
door, 312 Bradley) problem 25 anytime Friday.