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 humor 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.
Author(s): Richard P. Stanley
Series: Miscellaneous Books
Publisher: American Mathematical Society
Year: 2020
Language: English
Pages: 189
Tags: Problem Solving
Preface
Chapter 1. The First Day
Chapter 2. Polynomials
Chapter 3. Base Mathematics
Chapter 4. A Mysterious Visitor
Chapter 5. Set Theory
Chapter 6. Two Triangles
Chapter 7. Independence Day
Chapter 8. Independence Aftermath
Chapter 9. Amanda
Chapter 10. An Aesthetical Error
Chapter 11. Miraculous Cancellation
Chapter 12. Probability Theory
Chapter 13. Geometry
Chapter 14. Hodgepodge
Chapter 15. Self-referential Mathematics
Chapter 16. All Good Things Must Come to an End
Notes
1. First Day
2. Polynomials
3. Base Mathematics
4. A Mysterious Visitor
5. Set Theory
6. Two Triangles
7. Independence Day
8. Independence Aftermath
9. Amanda
10. An Aesthetical Error
11. Miraculous Cancellation
12. Probability Theory
13. Geometry
14. Hodgepodge
15. Self-Referential Mathematics
16. All Good Things Must Come to an End
Bibliography
Index
