Basic algebra : along with a companion volume Advanced algebra

書誌事項

Basic algebra : along with a companion volume Advanced algebra

Anthony W. Knapp

(Cornerstones)

Birkhäuser, c2006

  • : set

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注記

Includes bibliographical references (p. 697-698) and indexes

内容説明・目次

巻冊次

ISBN 9780817632489

内容説明

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

目次

Preliminaries about the Integers, Polynomials, and Matrices.- Vector Spaces over ?, ?, and ?.- Inner-Product Spaces.- Groups and Group Actions.- Theory of a Single Linear Transformation.- Multilinear Algebra.- Advanced Group Theory.- Commutative Rings and Their Modules.- Fields and Galois Theory.- Modules over Noncommutative Rings.
巻冊次

: set ISBN 9780817645335

内容説明

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development. Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry. The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with separate sections giving hints or complete solutions for most of the problems.

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詳細情報

  • NII書誌ID(NCID)
    BA79783153
  • ISBN
    • 0817645330
    • 9780817632489
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Boston
  • ページ数/冊数
    xxii, 717 p.
  • 大きさ
    25 cm
  • 親書誌ID
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