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$2ND STEP MATH OLYMPIAD PROB(V7) : Mathematical Olympiad - DEREK HOLTON$

2ND STEP MATH OLYMPIAD PROB(V7)

By: DEREK HOLTON

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Paperback | 14 July 2011

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314 Pages

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15 x 11 x 1.5

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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.

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You Can Find This Book In

Non-Fiction Mathematics Combinatorics & Graph Theory Geometry Number Theory Algebra Bargains Non-Fiction Bargains Science Bargains Academia & Knowledge Bargains

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 Pólya	p. 98
Asking Questions	p. 100
Solutions	p. 102
Number Theory 2	p. 107
A Problem	p. 107
Euler's ø-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 ùHel 2	p. 263
Hints ùTur 4	p. 264
Hints ù Rom 4	p. 266
Hints ù 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.

2ND STEP MATH OLYMPIAD PROB(V7)

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