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Number theory[electronic resource] :an introduction via the density of primes /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	512.7
書名/作者:	Number theory : an introduction via the density of primes // by Benjamin Fine, Gerhard Rosenberger.
作者:	Fine, Benjamin.
其他作者:	Rosenberger, Gerhard.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiii, 413 p. : : ill. (some col.), digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Number theory.
標題:	Mathematics.
標題:	Number Theory.
標題:	Mathematical Logic and Foundations.
標題:	Linear and Multilinear Algebras, Matrix Theory.
標題:	Analysis.
標題:	Applications of Mathematics.
標題:	Data Structures, Cryptology and Information Theory.
ISBN:	9783319438757
ISBN:	9783319438733
摘要、提要註:	Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.
電子資源:	http://dx.doi.org/10.1007/978-3-319-43875-7

Number theory[electronic resource] :an introduction via the density of primes /
Fine, Benjamin.

Number theoryan introduction via the density of primes /[electronic resource] :by Benjamin Fine, Gerhard Rosenberger. - 2nd ed. - Cham :Springer International Publishing :2016. - xiii, 413 p. :ill. (some col.), digital ;24 cm.

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.

ISBN: 9783319438757

Standard No.: 10.1007/978-3-319-43875-7doiSubjects--Topical Terms:

464118
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Number theory[electronic resource] :an introduction via the density of primes /
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