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Introduction to Math Olympiad Problems

Michael A. Radin
Chapman and Hall/CRC
Publication Date: 
Number of Pages: 
Problem Book
[Reviewed by
Russel Jay Hendel
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This book has two principal goals: Preparing students for typical problems they will face in i) Olympiad-style events, and ii) future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory, and Abstract Algebra. For each topic, the book introduces the topic with a remarkably easy pace and then proceeds to provide numerous practice problems to ensure mastery of the necessary skills. Traditional book solutions to exercises and a bibliography are provided. Therefore, this book targets i) advanced high school students preparing for Math Olympiad competitions, ii) college students taking relevant courses who want supplementary explanations and extra practice, iii) college instructors of relevant courses who want supplementary reference material for their courses.
The book expounds on four main areas, induction, graph theory, number theory, and geometry.  
For induction, the book presents in proper sequential order, exercises on recognizing patterns and sequences, formulating recursive sequences, solving recursive sequences, and inductive proofs. The sections on recognizing patterns and sequences comprehensively include linear, quadratic, geometric, factorial, alternating, and piecewise sequences. Both numeric and geometric patterns are explored. As already indicated, this is excellent reference material for a university discrete mathematics course.
For graph theory, the book presents in proper sequential order, the components of graphs (vertices, edges, degrees), and traditional graph classes, cyclic graphs, complete graphs, bi-partite graphs, and lattice graphs. The semi-regular cases and cycles including Hamiltonian cycles are also covered.
For number theory, the book presents prime factorizations including a discussion of the Euler Phi Function, and treats problems on consecutive integers, perfect squares, and ending digits of integers. There is also a chapter on Pascal’s triangle which presents the binomial expansion and discusses horizontally oriented identities and diagonally oriented identities.
The chapter on Geometry covers the topics of area, perimeter, proportions, and special triangles including isosceles, 30-60-90, 45-45-90, and right triangles.


About the reviewer. Russell Jay Hendel, RHendel@Towson.Edu, holds a Ph.D. in theoretical mathematics and an Associateship from the Society of Actuaries. He teaches at Towson University. His interests include discrete number theory, graph theory, applications of technology to education, problem writing, theory of pedagogy, actuarial science, and the interaction between mathematics, art, and poetry.