國立高雄大學圖資館 |

Language: English

Back

Number theoryan introduction via the...

Fine, Benjamin.

Number theoryan introduction via the density of primes /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Number theoryby Benjamin Fine, Gerhard Rosenberger.
Reminder of title:	an introduction via the density of primes /
Author:	Fine, Benjamin.
other author:	Rosenberger, Gerhard.
Published:	Cham :Springer International Publishing :2016.
Description:	xiii, 413 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Number theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-43875-7
ISBN:	9783319438757$q(electronic bk.)

Number theoryan 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$q(electronic bk.)

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

189521
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Number theoryan introduction via the density of primes /
LDR:02742nmm a2200313 a 4500 001 497585
003 DE-He213
005 20160919145705.0
006 m d
007 cr nn 008maaau
008 170420s2016 gw s 0 eng d
020 $a 9783319438757$q(electronic bk.)
020 $a 9783319438733$q(paper)
024 7 $a 10.1007/978-3-319-43875-7 $2 doi
035 $a 978-3-319-43875-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .F495 2016
100 1 $a Fine, Benjamin. $3 760311
245 1 0 $a Number theory $h [electronic resource] : $b an introduction via the density of primes / $c by Benjamin Fine, Gerhard Rosenberger.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2016.
300 $a xiii, 413 p. : $b ill. (some col.), digital ; $c 24 cm.
520 $a 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.
650 0 $a Number theory. $3 189521
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Mathematical Logic and Foundations. $3 274479
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
650 2 4 $a Analysis. $3 273775
650 2 4 $a Applications of Mathematics. $3 273744
650 2 4 $a Data Structures, Cryptology and Information Theory. $3 273993
700 1 $a Rosenberger, Gerhard. $3 544945
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-43875-7
950 $a Mathematics and Statistics (Springer-11649)