Overview

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.

Full Product Details

Author:   Anna Burago
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.653kg
ISBN:  

9781470437183

ISBN 10:   147043718
Pages:   351
Publication Date:   30 August 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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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.

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Author Information

Anna Burago, Prime Factor Math Circle, Seattle, WA.

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