Number Theory
An Introduction via the Density of Primes
(Sprache: Englisch)
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...
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Klappentext zu „Number Theory “
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
Inhaltsverzeichnis zu „Number Theory “
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.
Autoren-Porträt von Benjamin Fine, Gerhard Rosenberger
Benjamin Fine, PhD, is Professor of Mathematics at Fairfield University, CT, USA. Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.
Bibliographische Angaben
- Autoren: Benjamin Fine , Gerhard Rosenberger
- 2018, 2. Aufl., XIII, 413 Seiten, 1 farbige Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3319829319
- ISBN-13: 9783319829319
Sprache:
Englisch
Pressezitat
"In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. ... Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students." (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)"The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. ... a good text for an introductory course ... ." (Allen Stenger, MAA Reviews, maa.org, November, 2016)Kommentar zu "Number Theory"
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