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Illustrated Theory of Numbers [Kõva köide]

  • Formaat: Hardback, 321 pages, kõrgus x laius: 279x216 mm
  • Ilmumisaeg: 01-May-2017
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470434938
  • ISBN-13: 9781470434939
Teised raamatud teemal:
  • Formaat: Hardback, 321 pages, kõrgus x laius: 279x216 mm
  • Ilmumisaeg: 01-May-2017
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470434938
  • ISBN-13: 9781470434939
Teised raamatud teemal:
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.

Arvustused

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

Seeing Arithmetic
1(22)
I Foundations
23(102)
1 The Euclidean Algorithm
25(22)
2 Prime Factorization
47(28)
3 Rational and Constructible Numbers
75(24)
4 Gaussian and Eisenstein Integers
99(26)
II Modular Arithmetic
125(98)
5 The Modular Worlds
127(26)
6 Modular Dynamics
153(20)
7 Assembling the Modular Worlds
173(20)
8 Quadratic Residues
193(30)
III Quadratic Forms
223(82)
9 The Topograph
225(34)
10 Definite Forms
259(22)
11 Indefinite Forms
281(24)
Index of Theorems 305(4)
Index of Terms 309(4)
Index of Names 313(4)
Bibliography 317
Martin H. Weissman, University of California, Santa Cruz, CA.