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An illustrated theory of numbers /

American Mathematical Society.

An illustrated theory of numbers /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An illustrated theory of numbers /Martin H. Weissman.
作者:	Weissman, Martin H.,
面頁冊數:	xv, 323 pages :illustrations (chiefly color) ;29 cm.
標題:	Number theory.
ISBN:	9781470434939

An illustrated theory of numbers /
Weissman, Martin H.,1976-

An illustrated theory of numbers /Martin H. Weissman. - xv, 323 pages :illustrations (chiefly color) ;29 cm.

Includes bibliographical references and index.

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.

"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."--Back cover.

ISBN: 9781470434939$69.00

LCCN: 2017003379Subjects--Topical Terms:

189521
Number theory.
Index Terms--Genre/Form:

708244
Textbooks.

LC Class. No.: QA241 / W429 2017

Dewey Class. No.: 512.7

An illustrated theory of numbers /
LDR:02607nam a2200289 a 4500 001 548474
003 OCoLC
005 20180801223412.0
008 190801s2017 riua b 001 0 eng
010 $a 2017003379
020 $a 9781470434939 $c $69.00
020 $a 1470434938
025 6 4 $a cam a2200277 i 4500
035 $a (OCoLC)970396599
035 $a 970396599
040 $a DLC $b eng $e rda $c DLC $d OCLCO $d OCLCF $d OCLCQ $d YDX $d BTCTA $d MNN $d YDX $d OCLCO $d DAC $d LANGC $d OCLCO $d OCL $d CLE $d TOH $d AS $d MATH
042 $a pcc
050 0 0 $a QA241 $b W429 2017
082 0 0 $a 512.7 $2 23
100 1 $a Weissman, Martin H., $d 1976- $e author. $3 827858
245 1 3 $a An illustrated theory of numbers / $c Martin H. Weissman.
264 1 $a Providence, Rhode Island : $b American Mathematical Society, $c [2017]
300 $a xv, 323 pages : $b illustrations (chiefly color) ; $c 29 cm.
336 $a text $b txt $2 rdacontent.
337 $a unmediated $b n $2 rdamedia.
338 $a volume $b nc $2 rdacarrier.
504 $a Includes bibliographical references and index.
505 0 $a 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.
520 $a "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."--Back cover.
650 0 $a Number theory. $3 189521
650 7 $a Number theory $x Elementary number theory $x Multiplicative structure; Euclidean algorithm; greatest common divisors. $2 msc. $3 827859
650 7 $a Number theory $x Elementary number theory $x Congruences; primitive roots; residue systems. $2 msc. $3 827860
650 7 $a Number theory $x Elementary number theory $x Power residues, reciprocity. $2 msc. $3 827861
650 7 $a Number theory $x Elementary number theory $x Primes. $2 msc. $3 827862
650 7 $a Number theory $x Elementary number theory $x Factorization; primality. $2 msc. $3 827863
650 7 $a Number theory $x Diophantine equations $x Linear equations. $2 msc. $3 827864
650 7 $a Number theory $x Diophantine equations $x Quadratic and bilinear equations. $2 msc. $3 827865
650 7 $a Number theory $x Forms and linear algebraic groups $x General binary quadratic forms. $2 msc. $3 827866
650 7 $a Number theory $x Forms and linear algebraic groups $x Class numbers of quadratic and Hermitian forms. $2 msc. $3 827867
650 7 $a MATHEMATICS / Number Theory. $2 bisacsh. $3 827868
655 7 $a Textbooks. $2 fast $3 708244
710 2 $a American Mathematical Society. $3 209262