Conversational Problem Solving

ISBN-13: 9781470456351

Richard P. Stanley

Opis

This book features mathematical problems and results that would be of interest to all mathematicians, but especially undergraduates (and even high school students) who participate in mathematical competitions such as the International Math Olympiads and Putnam Competition. The format is a dialogue between a professor and eight students in a summer problem solving camp and allows for a conversational approach to the problems as well as some mathematical humour and a few nonmathematical digressions. The problems have been selected for their entertainment value, elegance, trickiness, and unexpectedness, and have a wide range of difficulty, from trivial to horrendous. They range over a wide variety of topics including combinatorics, algebra, probability, geometry, and set theory. Most of the problems have not appeared before in a problem or expository format. A Notes section at the end of the book gives historical information and references.

Spis treści

• The first day
• Polynomials Base
• mathematics
• A mysterious visitor
• Set theory
• Triangles
• Independence day
• Independence aftermath
• Amanda
• An aesthetical error
• Miraculous cancellation
• Probability theory
• Geometry
• Hodegepodge
• Self-referential mathematics
• All good things must come to an end
• Bibliography
• Index.