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A Primer for Mathematics Competitions

Alexander Zawaira and Gavin Hitchcock
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Henry Ricardo
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I like this book as an introduction to problem solving and as a source for general high school classroom enrichment. In the Preface, the authors state that the aim of this book is “not to equip you for the Himalayan heights of the IMO (International Mathematical Olympiad) but for the intermediate challenge of national Olympiads — say, of Welsh mountains, and moderately challenging Swiss Alps, North American Rockies, Peruvian Andes, South African Drakensberg, etc.” The book originated in preparations for various African competitions; and, with respect to the quoted intent and its overall level, the book under review is very much like A First Step to Mathematical Olympiad Problems by Derek Holton.

The fairly standard topics (‘toolchests’) in this primer (see the Table of Contents) are handled with more than customary thoroughness. There are historical remarks, derivations of theorems and formulas, and connections with other tools. A typical chapter or section starts with motivating ‘appetizer’ problems, followed by exposition of theory, worked out examples, the solution to the appetizer problem, and a good selection of problems (with solutions) related to the subject matter of the chapter. Many of these end-of-chapter problems are multiple-choice. Although more topics are covered to a greater extent than in Holton’s book, the book under review provides no actual IMO problems. The book’s last two pages provide further resources for those interested in mathematical competitions, including a number of useful web sites.

Henry Ricardo ( has retired from Medgar Evers College (CUNY), but continues to serve as Governor of the Metropolitan NY Section of the MAA. He is the author of A Modern Introduction to Differential Equations (Second Edition). His linear algebra text was published in October 2009 by CRC Press.


1. Geometry 
2. Algebraic Inequalities and Induction 
3. Diophantine Equations 
4. Number Theory 
5. Trigonometry 
6. Sequences and Series 
7. Binomial Theorem 
8. Combinatorics 
9. Miscellaneous Problems and Solutions