Benjamin Fine: Number Theory | Taschenbuch

Cover: 9783319829319 | Number Theory | An Introduction via the Density of Primes | Buch

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Sprache: Englisch

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Beschreibung

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.

Key topics and features include:

Über den Autor

Benjamin Fine, PhD, is Professor of Mathematics at Fairfield University, CT, USA.
Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.

Zusammenfassung

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

One of the few books to include the AKS algorithm that shows that primality testing is one of polynomial time

Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers

Includes supplementary material: [...]

Inhaltsverzeichnis

Introduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- The Fields Q_
p
of
p
-adic Numbers: Hensel's Lemma.- References.- Index.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiii 413 S. 11 s/w Illustr. 1 farbige Illustr. 413 p. 12 illus. 1 illus. in color.
ISBN-13:	9783319829319
ISBN-10:	3319829319
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Fine, Benjamin Rosenberger, Gerhard
Auflage:	Softcover reprint of the original 2nd edition 2016
Hersteller:	Birkhäuser Palgrave Macmillan Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 24 mm
Von/Mit:	Benjamin Fine (u. a.)
Erscheinungsdatum:	14.06.2018
Gewicht:	0,645 kg