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Michael Stoff, Director 305 East 23rd St, CLA 2.102, (G3600) Austin, TX 78712-1250 • 512-471-1442

Spring 2007

T C 310 • Modes of Reasoning: The Mathematics of Puzzles

Unique Days Time Location Instructor
43360 TTh
11:00 AM-12:30 PM
RLM 5.112
Rodriguez-Villegas

Course Description

The goal of this class is to explore the relations between the three concepts summarized in its name. We will discuss familiar puzzles (Nim, chinese rings, Peg-solitaire, 15-puzzle, lighs out, Rubiks cube) with an emphasis on understanding their structure; we will see what mathematics and computers can and cannot say about them.

For example, three commonly available commercial puzzles (the chinese rings puzzle, the brain, a sliding puzzle) are clever implementations of the same structure: the Gray code, a method of encoding information originally invented for efficient signal transmission. The puzzles are like a two-way street on a foggy day with our goal at one end. Solving them only requires knowing which direction to go at each step, but how do we manage that?

In the process we will cover from scratch the mathematical concepts of groups, linear algebra over a finite field and the theory of impartial games.

About the Professor

Professor Fernando Rodriguez-Villegas is a mathematician whose main interest is Number Theory. He came to UT after spending several years at Princeton University as a post-doc.

Grading Policy

Weekly Homework: 30%
One Midterm: 30%
Final Project (in lieu of final exam): 40%

Texts

E. Berlekamp, J. Conway and R. Guy, Winning Ways
Class notes.

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