Mathematical Circle Diaries, Year 2
American Mathematical Society (Verlag)
978-1-4704-3718-3 (ISBN)
Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world.
This book, a sequel to Mathematical Circle Diaries, Year 1, teaches 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. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year.
This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Anna Burago, Prime Factor Math Circle, Seattle, WA.
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.
| Erscheinungsdatum | 14.05.2018 |
|---|---|
| Reihe/Serie | MSRI Mathematical Circles Library |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 653 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| ISBN-10 | 1-4704-3718-X / 147043718X |
| ISBN-13 | 978-1-4704-3718-3 / 9781470437183 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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