In China, lots of excellent math students takes an active part in various math 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.
Author(s): Zhigang Feng
Series: Mathematical Olympiad Series 16
Publisher: World Scientific
Year: 2019
Language: English
Pages: 219
Title
Copyright
Introduction
Preface
Acknowledgment
Notations
Table of Contents
CHAPTER 1 Knowledge and Technique
1 The First Form of Mathematical Induction
2 The Second Form of Mathematical Induction
3 Well-ordering Principle and Infinite Descent
4 General Terms and Summation of Sequences
5 Arithmetic Sequences and Geometric Sequences
6 Higher-order Arithmetic Sequences and the Method of Differences
7 Recursive Sequences
8 Periodic Sequences
Exercise Set 1
CHAPTER 2 Selected Topical Discussions
9 The Fibonacci Sequence
10 Several Proofs of AM-GM Inequality
11 Choosing a Proper Span
12 Choosing the Appropriate Object for Induction
13 Make Appropriate Changes to the Propositions
14 Guessing Before Proving
15 Problems Regarding Existence with Sequences
Exercise Set 2
Solutions to Exercises
Solutions to Exercise Set 1
Solutions to Exercise Set 2
Bibliography
