An Illustrated Theory of Numbers

Author:   Martin H. Weissman
Publisher:   American Mathematical Society
ISBN:  

9781470434939


Pages:   321
Publication Date:   30 August 2017
Format:   Hardback
Availability:   In Print   Availability explained
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An Illustrated Theory of Numbers


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Overview

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, and to all mathematicians seeking a fresh perspective on an ancient subject.

Full Product Details

Author:   Martin H. Weissman
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470434939


ISBN 10:   1470434938
Pages:   321
Publication Date:   30 August 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Seeing arithmetic Foundations: The Euclidean algorithm Prime factorization Rational and constructible numbers Gaussian and Eisenstein integers Modular arithmetic: The modular worlds Modular dynamics Assembling the modular worlds Quadratic residues Quadratic forms: The topograph Definite forms Indefinite forms Index of theorems Index of terms Index of names Bibliography.

Reviews

This is a meticulously written and stunningly laid-out book influenced not only by the classical masters of number theory like Fermat, Euler, and Gauss, but also by the work of Edward Tufte on data visualization. Assuming little beyond basic high school mathematics, the author covers a tremendous amount of territory, including topics like Ford circles, Conway's topographs, and Zolotarev's lemma which are rarely seen in introductory courses. All of this is done with a visual and literary flair which very few math books even strive for, let alone accomplish . - Matthew Baker, Georgia Institute of Technology Weissman's book represents a totally fresh approach to a venerable subject. Its choice of topics, superb exposition and beautiful layout will appeal to professional mathematicians as well as to students at all levels. - Kenneth A. Ribet, University of California, Berkeley


"This is a meticulously written and stunningly laid-out book influenced not only by the classical masters of number theory like Fermat, Euler, and Gauss, but also by the work of Edward Tufte on data visualization. Assuming little beyond basic high school mathematics, the author covers a tremendous amount of territory, including topics like Ford circles, Conway's topographs, and Zolotarev's lemma which are rarely seen in introductory courses. All of this is done with a visual and literary flair which very few math books even strive for, let alone accomplish."" — Matthew Baker, Georgia Institute of Technology """"Weissman's book represents a totally fresh approach to a venerable subject. Its choice of topics, superb exposition and beautiful layout will appeal to professional mathematicians as well as to students at all levels."" — Kenneth A. Ribet, University of California, Berkeley"


Author Information

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

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