First Step To Mathematical Olympiad Problems, A

by Derek Holton

“This book continues the tradition making national and international mathematical competition problems available to a wider audience and is bound to appeal to anyone interested in mathematical problem solving. The reviewer recommends this book to all students curious about elementary mathematics and how to learn it through solving problems. Teachers would find this book to be a welcome resource for organizing their activities at a high level.” Zentralblatt MATH 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 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.

Genres: Mathematics

292 pages, Paperback

First published January 1, 2009

Reviews

[Boros Smarrt · Rating 5 out of 5]

I want to read this book so much .

[Liquidlasagna · Rating 2 out of 5]

I would be a lot happier if this book was written in the 1960s with a far better fonts and illustrations, and a less informal writing style.

Honestly those old 1960s IBM Selectric math books were easier on the eyes.
Though in some volumes, the exercises are in a pleasant font, but not the main text...

I just wish for better clarity in the explanations, and much better fonts and diagrams

With a lot less white space and a smaller more readable font, you'd get much more print on a page, with quicker comprehension.

If these things were dirt cheap, i might hesitantly recommend them, but i think there's nicer looking and better written stuff out there.

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MAA Review

Derek Holton is well known for his teaching and for his success in creating mathematics competition preparation programs in New Zealand. In 1996, he was presented with the Paul Erdös Award by the World Federation of National Mathematics Competitions for his contributions to mathematical enrichment in his country.

The book under review is an amalgamation of the first 8 of 15 booklets originally produced to prepare students to compete for the six positions on New Zealand’s International Mathematical Olympiad (IMO) team.

The material covers discrete mathematics (sophisticated counting, the pigeonhole principle, basic graph theory), number theory (divisibility, Fermat’s Little Theorem, arithmetic progressions), plane geometry (squares, rectangles/parallelograms, triangles, circles), and a chapter on Cartesian geometry, including conics.

The final chapter consists of six problems posed for the IMO by various countries and some related exercises. Solutions are provided for all problems and exercises.

Late in the book, there is a chapter on proof, focusing on proofs by contradiction and mathematical induction.

At first, the position of this discussion seemed odd, coming after several chapters of problems for which readers are asked to provide proofs.

However, this discussion is an overview of the reasons that proof is necessary and it makes the student aware that there are set patterns of proof.

The problems in this book are, in general, kinder and gentler than those in several other competition preparation manuals―for example, the Olympiad-level collection by Andreescu and Gelca or that of A. Gardiner.

On the other hand, so is the exposition. Holton seems to be assuming a lower level of student background than many authors of such preparation material.

Leavened with historical comments and humor (humour), Holton’s treatment is colloquial and could be used for general classroom enrichment as well as for competition preparation. I recommend Holton’s book as an introduction to problem solving and the construction of proofs and I look forward to the next volume in this Mathematical Olympiad Series.

[Thailand Bkk]

marked it as to-read

[Tiza Ayu]

i wan to read this book ..please open