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Discrete Mathematics and Its Applications #9: Algebraic Number Theory, Second Edition

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Discrete Mathematics and Its Applications #9: Algebraic Number Theory, Second Edition Cover

 

Synopses & Reviews

Publisher Comments:

Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and class groups in the third chapter. Applications are now collected in chapter four and at the end of chapter five, where primality testing is highlighted as an application of the Kronecker?Weber theorem. In chapter five, the sections on ideal decomposition in number fields have been more evenly distributed. The final chapter continues to cover reciprocity laws.

New to the Second Edition

  • Reorganization of all chapters
  • More complete and involved treatment of Galois theory
  • A study of binary quadratic forms and a comparison of the ideal and form class groups
  • More comprehensive section on Pollard's cubic factoring algorithm
  • More detailed explanations of proofs, with less reliance on exercises, to provide a sound understanding of challenging material

The book includes mini-biographies of notable mathematicians, convenient cross-referencing, a comprehensive index, and numerous exercises. The appendices present an overview of all the concepts used in the main text, an overview of sequences and series, the Greek alphabet with English transliteration, and a table of Latin phrases and their English equivalents.

Suitable for a one-semester course, this accessible, self-contained text offers broad, in-depth coverage of numerous applications. Readers are lead at a measured pace through the topics to enable a clear understanding of the pinnacles of algebraic number theory.

Synopsis:

"The second edition of this popular book features coverage of L-functions and function fields to provide a more modern view of the field. This edition also introduces class groups for both binary and quadratic forms, making it much easier to prove the finiteness of the class number of both groups via an isomorphism. In addition, the text provides new results on the relationship between quadratic residue symbols and fundamental units of real quadratic fields in conjunction with prime representation. Along with reorganizing and shortening chapters for an easier presentation of material, the author includes updated problem sets and additional examples"--

Product Details

ISBN:
9781439845981
Author:
Mollin, Richard A.
Publisher:
CRC Press
Subject:
Operating Systems - General
Subject:
Number Theory
Subject:
Combinatorics
Edition Description:
New
Series:
Discrete Mathematics and Its Applications
Series Volume:
9
Publication Date:
20110131
Binding:
Hardcover
Language:
English
Pages:
420

Related Subjects

Computers and Internet » Operating Systems » General
Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory

Discrete Mathematics and Its Applications #9: Algebraic Number Theory, Second Edition New Hardcover
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Product details 420 pages CRC Press - English 9781439845981 Reviews:
"Synopsis" by , "The second edition of this popular book features coverage of L-functions and function fields to provide a more modern view of the field. This edition also introduces class groups for both binary and quadratic forms, making it much easier to prove the finiteness of the class number of both groups via an isomorphism. In addition, the text provides new results on the relationship between quadratic residue symbols and fundamental units of real quadratic fields in conjunction with prime representation. Along with reorganizing and shortening chapters for an easier presentation of material, the author includes updated problem sets and additional examples"--
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