Description
Book SynopsisTeaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle.
Table of Contents
- Preliminaries
- Session plans: Introduction
- Checkerboard problems
- Review: Math logic and other problem-solving strategies
- Invariants
- Proof by contradiction
- Decimal number system and problems on digits
- Binary numbers I
- Binary numbers II
- Mathematical dominoes tournament
- Pigeonhole principle
- Geometric pigeonhole principle
- Mathematical Olympiad I
- Combinatorics I. Review
- Combinatorics II. Combinations
- Mathematical auction
- Combinatorics III. Complements. Snake pit game
- Combinatorics IV. Combinatorial conundrum
- Magic squares and related problems
- Double counting, or there is more than one way to cut a cake
- Mathematical Olympiad II
- Divisibility I. Review
- Divisibility II. Relatively prime numbers
- GCF and LCM
- Divisibility III. Mathematical race game
- Mathematical auction
- Divisibility IV. Divisibility by 3 and remainders
- Divisibility V. Divisibility and remainders
- Graph theory I. Graphs and their applications
- Graph theory II. Handshaking theorem
- Graph theory III. Solving problems with graphs
- Mathematical Olympiad III
- Mathematical contests and competitions: Mathematical contests
- Mathematical auction
- Mathematical dominoes
- Mathematical snake pit
- Mathematical race
- Mathematical Olympiad
- Short entertaining math games
- More teaching advice: How to be a great math circle teacher
- What comes next?
- Solutions: Solutions
- Appendix to Session 6
- Bibliography.
