An illustrated theory of numbers
 Responsibility
 Martin H. Weissman.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Copyright notice
 ©2017
 Physical description
 xv, 323 pages ; 29 cm
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA241 .W354 2017  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Weissman, Martin H., 1976 author.
 Contributor
 American Mathematical Society.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Seeing arithmeticFoundations: The Euclidean algorithmPrime factorizationRational and constructible numbersGaussian and Eisenstein integersModular arithmetic: The modular worldsModular dynamicsAssembling the modular worldsQuadratic residuesQuadratic forms: The topographDefinite formsIndefinite formsIndex of theoremsIndex of termsIndex of namesBibliography.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["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 cuttingedge 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.", {"source"=>"(source: Nielsen Book Data)"}, "9781470434939", "20171009"]
Subjects
 Subject
 Number theory.
 Number theory.
 Number theory > Elementary number theory > Multiplicative structure; Euclidean algorithm; greatest common divisors.
 Number theory > Elementary number theory > Congruences; primitive roots; residue systems.
 Number theory > Elementary number theory > Power residues, reciprocity.
 Number theory > Elementary number theory > Primes.
 Number theory > Elementary number theory > Factorization; primality.
 Number theory > Diophantine equations > Linear equations.
 Number theory > Diophantine equations > Quadratic and bilinear equations.
 Number theory > Forms and linear algebraic groups > General binary quadratic forms.
 Number theory > Forms and linear algebraic groups > Class numbers of quadratic and Hermitian forms.
Bibliographic information
 Publication date
 2017
 Copyright date
 2017
 ISBN
 9781470434939 hardcover
 1470434938 hardcover