A Concrete Introduction to Higher Algebra

Editors:

ISBN: 978-0-387-74527-5 (Print) 978-0-387-74725-5 (Online)

Table of contents (27 chapters)

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  1. Front Matter

    Pages i-xiv

  2. Numbers

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      Book Chapter

      Pages 3-7

      Numbers

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      Book Chapter

      Pages 9-25

      Induction

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      Book Chapter

      Pages 27-52

      Euclid's Algorithm

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      Book Chapter

      Pages 53-70

      Unique Factorization

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      Book Chapter

      Pages 71-89

      Congruence

  3. Congruence classes and rings

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      Book Chapter

      Pages 93-121

      Congruence Classes

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      Book Chapter

      Pages 123-146

      Rings and Fields

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      Book Chapter

      Pages 147-167

      Matrices and Codes

  4. Congruences and Groups

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      Book Chapter

      Pages 171-200

      Fermat's and Euler's Theorems

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      Book Chapter

      Pages 201-221

      Applications of Euler's Theorem

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      Book Chapter

      Pages 223-252

      Groups

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      Book Chapter

      Pages 253-281

      The Chinese Remainder Theorem

  5. Polynomials

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      Book Chapter

      Pages 285-293

      Polynomials

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      Book Chapter

      Pages 295-306

      Unique Factorization

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      Book Chapter

      Pages 307-338

      The Fundamental Theorem of Algebra

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      Book Chapter

      Pages 339-353

      Polynomials in ℚ[x]

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      Book Chapter

      Pages 355-371

      Congruences and the Chinese Remainder Theorem

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      Book Chapter

      Pages 373-383

      Fast Polynomial Multiplication

  6. Primitive Roots

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      Book Chapter

      Pages 387-412

      Cyclic Groups and Cryptography

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      Book Chapter

      Pages 413-431

      Carmichael Numbers

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