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A Concise Introduction to the Theory of Numbers

Alan Baker
Cambridge University Press
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Allen Stenger
, on

This book is indeed concise, as it manages to cover all the ideas of elementary number theory in a mere 91 pages. The proofs are also concise, leaving out many details, and this is likely to distress students. There are exercises at the end of each chapter; these are mostly straightforward applications of the ideas in the chapter.

The book can also be described as austere, as it sticks strictly to the central ideas of the subject, without any of the interesting digressions that thicker books include. As such it is less likely to inspire a love of the subject than are more discursive books such as Hardy & Wright’s An Introduction to the Theory of Numbers and Niven & Zuckerman’s An Introduction to the Theory of Numbers.

The coverage is not well-balanced, with nearly two-thirds of the book being devoted to diophantine equations and diophantine approximation. A recent concise but less austere book with broader coverage is Underwood Dudley’s 2009 A Guide to Elementary Number Theory.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at, a math help site that fosters inquiry learning.

 Preface; Introduction; 1. Divisibility; 2. Arithmetical functions; 3. Congruences; 4. Quadratic residues; 5. Quadratic forms; 6. Diophantine approximation; 7. Quadratic fields; 8. Diophantine equations.