Combinatorial Extremization: In Mathematical Olympiad And Competitions
Combinatorial Extremization: In Mathematical Olympiad And Competitions

Author: Yuefeng Feng

Publisher: World Scientific Publishing Company

Published: 2016-02-17

Total Pages: 230

ISBN-13: 9814723185

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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.

102 Combinatorial Problems
102 Combinatorial Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 125

ISBN-13: 0817682228

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"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

A First Step To Mathematical Olympiad Problems
A First Step To Mathematical Olympiad Problems

Author: Derek Allan Holton

Publisher: World Scientific Publishing Company

Published: 2009-07-30

Total Pages: 292

ISBN-13: 9814365254

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See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.

Geometric Inequalities: In Mathematical Olympiad And Competitions
Geometric Inequalities: In Mathematical Olympiad And Competitions

Author: Gangsong Leng

Publisher: World Scientific Publishing Company

Published: 2015-10-21

Total Pages: 145

ISBN-13: 9814696501

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In China, lots of excellent maths students take an active interest 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 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 Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.

Sequences And Mathematical Induction:in Mathematical Olympiad And Competitions (2nd Edition)
Sequences And Mathematical Induction:in Mathematical Olympiad And Competitions (2nd Edition)

Author: Zhi-gang Feng

Publisher: World Scientific

Published: 2019-10-08

Total Pages: 224

ISBN-13: 9811211051

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In China, lots of excellent maths students 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 senior coaches of China's IMO National Team, he is the headmaster of Shanghai senior high school which is one of the best high schools of China. In the past decade, the students of this school have won the IMO gold medals almost every year.The author attempts to use some common characteristics of sequence and mathematical induction to fundamentally connect Math Olympiad problems to particular branches of mathematics. In doing so, the author hopes to reveal the beauty and joy involved with math exploration and at the same time, attempts to arouse readers' interest of learning math and invigorate their courage to challenge themselves with difficult problems.

Probability And Expectation: In Mathematical Olympiad And Competitions
Probability And Expectation: In Mathematical Olympiad And Competitions

Author: Zun Shan

Publisher: World Scientific Publishing Company

Published: 2016-07-14

Total Pages: 207

ISBN-13: 9813141514

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In China, lots of excellent students who are good at maths take 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 senior 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. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.

Solving Problems in Geometry
Solving Problems in Geometry

Author: Kim Hoo Hang

Publisher: World Scientific Publishing Company

Published: 2017

Total Pages: 250

ISBN-13: 9789814583749

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This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.

A Second Step to Mathematical Olympiad Problems
A Second Step to Mathematical Olympiad Problems

Author: Derek Allan Holton

Publisher: World Scientific

Published: 2011

Total Pages: 312

ISBN-13: 9814327875

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The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the booklets originally produced to guide students intending to contend for placement on their country's IMO team. See also A First Step to Mathematical Olympiad Problems which was published in 2009. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A Second Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.

Principles and Techniques in Combinatorics
Principles and Techniques in Combinatorics

Author: Chuan-Chong Chen

Publisher: World Scientific

Published: 1992

Total Pages: 314

ISBN-13: 9789810211394

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A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.