Second Step to Mathematical Olympiad Problems

Paperback

Derek Holton 저자(글)

World Scientific · 2011년 01월 01일

책 소개

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.

작가정보

저자(글) Derek Holton

목차

• Foreword	p. vii
  Combinatorics	p. 1
  A Quick Reminder	p. 1
  Partial Fraction	p. 4
  Geometric Progressions	p. 9
  Extending the Binomial Theorem	p. 12
  Recurrence Relations	p. 14
  Generating Functions	p. 20
  Of Rabbits and Postmen	p. 24
  Solutions	p. 29
  Geometry	p. 3
  The Circumcircle	p. 42
  Incircles	p. 46
  Exercises	p. 49
  The 6-Point Circle?	p. 51
  The Euler Line and the Nine Point Circle	p. 56
  Some More Examples	p. 58
  Hints	p. 60
  Solutions	p. 65
  Glossary	p. 84
  Solving Problems	p. 85
  Introduction	p. 85
  A Problem to Solve	p. 85
  Mathematics: What is it?	p. 87
  Back to Six Circles	p. 90
  More on Research Methods	p. 91
  Georg P?ya	p. 98
  Asking Questions	p. 100
  Solutions	p. 102
  Number Theory 2	p. 107
  A Problem	p. 107
  Euler's ?function	p. 110
  Back to Section 4.2	p. 112
  Wilson	p. 115
  Some More Problems	p. 117
  Solutions	p. 118
  Means and Inequalities	p. 133
  Introduction	p. 133
  Rules to Order the Reals By	p. 133
  Means Arithmetic and Geometric	p. 135
  More Means	p. 139
  More Inequalities	p. 141
  A Collection of Problems	p. 146
  Solutions	p. 148
  Combinatorics 3	p. 167
  Introduction	p. 167
  Inclusion-Exclusion	p. 167
  Derangements (Revisited)	p. 172
  Linear Diophantine Equations Again	p. 174
  Non-taking Rooks	p. 176
  The Board of Forbidden Positions	p. 183
  Stirling Numbers	p. 187
  Some Other Numbers	p. 190
  Solutions	p. 195
  Creating Problems	p. 215
  Introduction	p. 215
  Counting	p. 216
  Packing	p. 220
  Intersecting	p. 224
  Chessboards	p. 230
  Squigonometry	p. 233
  The Equations of Squares	p. 236
  Solutions	p. 238
  IMO Problems 2	p. 257
  Introduction	p. 257
  Aus 3	p. 258
  Hel 2	p. 258
  Tur 4	p. 259
  Rom 4	p. 259
  Uss 1	p. 260
  Revue	p. 260
  Hints Aus 3	p. 261
  Hints ?el 2	p. 263
  Hints ?ur 4	p. 264
  Hints ?Rom 4	p. 266
  Hints ?Uss 1	p. 268
  Some More Olympiad Problems	p. 269
  Solutions	p. 272
  Index	p. 295
  Table of Contents provided by Ingram. All Rights Reserved.

기본정보

ISBN	9789814327879 ( 9814327875 )
발행(출시)일자	2011년 01월 01일
쪽수	299쪽
크기	150 * 224 * 18 mm / 476 g
총권수	1권
언어	영어