Learning modern algebra : from early attempts to prove Fermat's last theorem

書誌事項

Learning modern algebra : from early attempts to prove Fermat's last theorem

Al Cuoco and Joseph J. Rotman

(MAA textbooks)

Mathematical Association of America, c2013

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注記

Includes bibliographical references (p. 449-450) and index

内容説明・目次

内容説明

Much of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.

目次

  • Preface
  • Some features of this book
  • A note to students
  • A note to instructors
  • Notation
  • 1. Early number theory
  • 2. Induction
  • 3. Renaissance
  • 4. Modular arithmetic
  • 5. Abstract algebra
  • 6. Arithmetic of polynomials
  • 7. Quotients, fields, and classical problems
  • 8. Cyclotomic integers
  • 9. Epilogue
  • References
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BB17655173
  • ISBN
    • 9781939512017
  • LCCN
    2013940990
  • 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
    Washington, D.C.
  • ページ数/冊数
    xix, 459 p.
  • 大きさ
    28 cm
  • 分類
  • 件名
  • 親書誌ID
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