Number Theory: An Introduction via the Density of Primes
Autor Benjamin Fine, Gerhard Rosenbergeren Limba Engleză Hardback – 26 sep 2016
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.
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (1) | 463.77 lei 6-8 săpt. | |
| Springer International Publishing – 13 iun 2018 | 463.77 lei 6-8 săpt. | |
| Hardback (1) | 393.41 lei 3-5 săpt. | +46.91 lei 7-13 zile |
| Springer International Publishing – 26 sep 2016 | 393.41 lei 3-5 săpt. | +46.91 lei 7-13 zile |
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Specificații
ISBN-13: 9783319438733
ISBN-10: 3319438735
Pagini: 484
Ilustrații: XIII, 413 p. 12 illus., 1 illus. in color.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.95 kg
Ediția:2nd ed. 2016
Editura: Springer International Publishing
Colecția Birkhäuser
Locul publicării:Cham, Switzerland
ISBN-10: 3319438735
Pagini: 484
Ilustrații: XIII, 413 p. 12 illus., 1 illus. in color.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.95 kg
Ediția:2nd ed. 2016
Editura: Springer International Publishing
Colecția Birkhäuser
Locul publicării:Cham, Switzerland
Cuprins
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.
Recenzii
“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)Notă biografică
Benjamin Fine, PhD, is Professor of Mathematics at Fairfield University, CT, USA.
Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.
Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.
Textul de pe ultima copertă
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.
Caracteristici
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: sn.pub/extras
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: sn.pub/extras