Combinatorial Extremization

Combinatorial Extremization


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Combinatorial Extremization by Yuefeng Feng

In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.

Product Details

ISBN-13: 9789814723169
Publisher: World Scientific / East China Normal Univ Press, China
Publication date: 01/21/2016
Series: Mathematical Olympiad Series , #13
Pages: 200
Sales rank: 903,710
Product dimensions: 6.00(w) x 8.90(h) x 0.70(d)

Table of Contents

Introduction v

Preface vii

Chapter 1 Inequality Control 1

Chapter 2 Repeated Extremum 12

Chapter 3 Partial Adjustment 22

Chapter 4 Exploiting Symmetry 34

Chapter 5 Polishing Transform 42

Chapter 6 Space Estimates 52

Chapter 7 Block Estimates 57

Chapter 8 Guesses and Contradiction 71

Chapter 9 Global Estimates 85

Chapter 10 Parameter Estimates 97

Chapter 11 Counting in Two Ways 111

Chapter 12 Shrinking the Encirclement 126

Chapter 13 Considering Special Cases 138

Solutions to Exercises 159

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