[PDF] Mathematics Via Problems: Part 1: Algebra (MSRI Mathematical Circles Library) Free Download

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This book is a translation from Russian of Part I of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. The other two parts, Geometry and Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The author tries to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into the sophisticated world of topics such as group theory, Galois theory, and so on, thus building a bridge (by showing that there is no gap) between standard high school exercises and more intricate and abstract concepts in mathematics. Definitions and/or references for material that is not standard in the school curriculum are included. However, many topics in the book are difficult when you start learning them from scratch. To help with this, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions The book is based on classes taught by the author at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. 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

 

Table of contents :

Foreword
Problems, exercises, circles, and olympiads
Chapter 1. Divisibility
Chapter 2. Multiplication modulo p
Chapter 3. Polynomials and complex numbers
Chapter 4. Permutations
Chapter 5. Inequalities
Chapter 6. Sequences and limits
Chapter 7. Functions
Chapter 8. Solving algebraic equations
Solutions

Product information

Publisher‏:‎American Mathematical Society (February 11, 2021)
Language‏:‎English
Paperback‏:‎196 pages
ISBN-10‏:‎1470448785
ISBN-13‏:‎978-1470448783
Item Weight‏:‎14.1 ounces
Dimensions‏:‎7.09 x 0.67 x 10.04 inches
1470448785

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