An Illustrated Theory of Numbers

Name: An Illustrated Theory of Numbers
Price: 206 AUD
Availability: OutOfStock
ISBN: 9781470469474

Updated Edition

Martin H. Weissman

$206

Hardback

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English

American Mathematical Society
22 February 2026

Number theory

Series: Monograph Books

An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.

Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers.

Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject. In this updated edition, you will find a new chapter which brings the reader from undergraduate calculus into analytic number theory. A new section adds a second proof of quadratic reciprocity due to Gauss and Eisenstein. Hundreds of minor edits correct and improve the original edition.

By: Martin H. Weissman
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 279mm, Width: 216mm,
ISBN: 9781470469474
ISBN 10: 1470469472
Series: Monograph Books
Pages: 359
Publication Date: 22 February 2026
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Martin H. Weissman, University of California, Santa Cruz, CA