This course will present a number of combinatorial games and puzzles, focusing on those for which there exist mathematical techniques for solving them. (Links to previous instantiations of the course below suggest the kinds of topics we'll be covering.)

Time and Place: Tuesday Thursday 1:30-2:50 in WEH 5312

Grading will be fairly informal, and based on homework assignments and class participtation, and class presentation.

- Homework 1, Due February 3
- Homework 2, Due February 22

One of the books we'll be using is *Lessons in Play* by Albert, Nowakowski, and Wolff.

- Jan 11, Jan 13, Jan 18, Jan 20

Frieze notes Combinatorial Games

more Frieze notes Combinatorial Games

Part 1 of Ferguson

Frieze notes Subtraction Games - Jan 25, Jan 27, Feb 1

Combinatorial Game Theory from Lessons In Play (Chapters 0 through 6)

Sleator's notes on games that are numbers

Mathworld Article

Wikipedia on Surreal Numbers - Feb 3

Frieze notes Maker-Breaker Games

Maker/Breaker Games, a paper by Chvatal and Erdos - Feb 8, Feb 10
Frieze notes on Cops and Robbers

A Game of Cops and Robbers (paper by Aigner and Fromme)

Variations on Cops and Robbers (paper by Frieze, Krivelevich and Loh)

Noga Alon Weighs in on Cops and Robbers - Feb 15, Feb 17

Chapters 5 and 6 from Lessons in Play - Feb 22: Lisa: Angel And Devil
- Feb 24: Mine Sweeper
- Mar 1, Mar 3: John: Dundee and the Problem of Coincidences

John Dickerson's Lecture Slides

Lajos Takacs, The Problem of Coincidences

Mcfadyen's Review of*Book on Games of Chance*by Gerolamo Cardano

A History of Probability and Statistics and their Applications before 1750

How to Play Dundee - Mar 15: Emily: Welter's Game
- Mar 17: Sam: Green Hackenbush

A Short Guide to Hackenbush

Green Hackenbush from Winning Ways

Notes by A. N. Walker - Mar 22: Brian K: Game Chromatic Number The Map Coloring Game
- Mar 24: Amin: Richman Games
- Mar 29: David Bergman: King and Devil (Chapter 19 of Winning Ways)
- Mar 31: Brian M: Peg Solitaire (Chapter 23 of Winning Ways)
- Apr 5: Marla: Sylver Coinage (Chapter 18 of Winning Ways)
- Apr 7: Klaus Suttner Lights out and Related Puzzles:

Linear Cellular Automata and the Garden-of-Eden

Sigma-Automata and Chebyshev-polynomials

Decomposition of Additive Cellular Automata

Lecture Notes - Apr 12: Frieze Patterns

Conway, Coxeter, Mathematical Gazette Jun., 1973

Lighter Side of Mathematics, 1994

- Coin Weighing Problems:notes, coins2, coincompet.pdf, maacoins.pdf
- Game Chromatic Numbers
- Dundee
- On Numbers and Endgames, Noam Elkies
- Impartial Misere Games

- Combinatorial Game Programs by D. Sleator: Game.java, Simplify.java, Domineering.java, Topple.java
- Game Theory is a book by Tom Ferguson
- Mathematical Games Course, 2005
- Mathematical Games Course, 2001
- David Epstein's Combinatorial Game Theory page
- Thane Plambeck's pages studies Misere games
- The Combinatorial Games Suite is a free interactive system for analyzing combinatorial games, written in Java.

Danny Sleator Last modified: Mon Apr 11 16:22:58 2011