Number Theory [electronic resource] : An Introduction via the Density of Primes / by Benjamin Fine, Gerhard Rosenberger.
By: Fine, Benjamin [author.].
Contributor(s): Rosenberger, Gerhard [author.]  SpringerLink (Online service).
Material type: TextPublisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016Edition: 2nd ed. 2016.Description: XIII, 413 p. 12 illus., 1 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319438757.Subject(s): Number theory  Logic, Symbolic and mathematical  Matrix theory  Global analysis (Mathematics)  Mathematics  Data structures (Computer scienc  Number Theory  Mathematical Logic and Foundations  Linear and Multilinear Algebras, Matrix Theory  Analysis  Applications of Mathematics  Data Structures, Cryptology and Information TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 512.7 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB1888 
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 padic Numbers: Hensel's Lemma  References  Index.
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 padic numbers, Hensel's lemma, multiple zetavalues, 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 userfriendly 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 selfstudy 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.
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