Introduction to number theory

書誌事項

Introduction to number theory

Daniel E. Flath

(AMS chelsea publishing, [384])

American Mathematical Society, 2018

  • : hbk

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注記

Originally published: New York : Wiley, 1989

Bibliography: p. 204-205

Includes indexes

内容説明・目次

内容説明

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the $p - q$ symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled $\Delta = b^2 - 4ac$. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.

目次

Prime numbers and unique factorization Sums of two squares Quadratic reciprocity Indefinite forms The class group and genera $\Delta=b^2-4ac^*$ Tables Errata to ``Introduction to number theory'' Bibliography Subject index Notation index

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詳細情報

  • NII書誌ID(NCID)
    BB27061142
  • ISBN
    • 9781470446949
  • LCCN
    88010638
  • 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
    Providence, Rhode Island
  • ページ数/冊数
    xii, 212 p.
  • 大きさ
    27 cm
  • 分類
  • 件名
  • 親書誌ID
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