Lecture notes on mathematical olympiad courses : for senior section
著者
書誌事項
Lecture notes on mathematical olympiad courses : for senior section
(Mathematical Olympiad series / series editors, Lee Peng Yee, Xiong Bin, v. 8)
World Scientific, c2012
- : set
- v. 1 : pbk
- v. 2 : pbk
大学図書館所蔵 全1件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes index
内容説明・目次
内容説明
Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well.In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.
目次
- Volume 1: Fractional Equations
- Higher Degree Polynomial Equations
- Irrational Equations
- Indicial Functions and Logarithmic Functions
- Trigonometric Functions
- Law of Sines and Law of Cosines
- Manipulations of Trigonometric Expressions
- Extreme Values of Functions and Mean Inequality
- Extreme Value Problems in Trigonometry
- Fundamental Properties of Circles
- Relation of Line and Circle and Relation of Circles
- Cyclic Polygons
- Power of a Point with Respect to a Circle
- Some Important Theorems in Geometry
- Five Centers of a Triangle
- Volume 2: Mathematical Induction
- Arithmetic Progression and Geometric Progression
- Recursive Sequence
- Summation of Series
- Some Fundamental Theorems on Congruence
- Chinese Remainder Theorem and Order of Integer
- Diophantine Equation (III)
- Cauchy - Schwartz Inequality
- Rearrangement Inequality and Jensen' Inequality
- Schur Inequality
- Fractional Inequality
- Variable - Freezing Method
- Some Methods in Counting Numbers (I)
- Some Methods in Counting Numbers (II)
- Introduction to Functional Equations.
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