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A Concrete Introduction to Higher Algebra

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Cover of 'A Concrete Introduction to Higher Algebra'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Numbers
  3. Altmetric Badge
    Chapter 2 Induction; the Binomial Theorem
  4. Altmetric Badge
    Chapter 3 Unique Factorization into Products of Primes
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    Chapter 4 Primes
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    Chapter 5 Bases
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    Chapter 6 Congruences
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    Chapter 7 Congruence Classes
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    Chapter 8 Rings and Fields
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    Chapter 9 Matrices and Vectors
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    Chapter 10 Secret Codes, I
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    Chapter 11 Fermat’s Theorem, I: Abelian Groups
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    Chapter 12 Repeating Decimals, I
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    Chapter 13 Error-correcting Codes, I
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    Chapter 14 The Chinese Remainder Theorem
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    Chapter 15 Secret Codes, II
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    Chapter 16 Polynomials
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    Chapter 17 Unique Factorization
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    Chapter 18 The Fundamental Theorem of Algebra
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    Chapter 19 Irreducible Polynomials in ℝ[ x ]
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    Chapter 20 Partial Fractions
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    Chapter 21 The Derivative of a Polynomial
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    Chapter 22 Sturm’s Algorithm
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    Chapter 23 Factoring in ℚ[ x ], I
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    Chapter 24 Congruences Modulo a Polynomial
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    Chapter 25 Fermat’s Theorem, II
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    Chapter 26 Factoring in ℚ[ x ], II: Lagrange Interpolation
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    Chapter 27 Factoring in ℤ p [ x ]
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    Chapter 28 Factoring in ℚ[ x ], III: mod M
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    Chapter 29 Primitive Elements
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    Chapter 30 Repeating Decimals, II
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    Chapter 31 Testing for Primeness
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    Chapter 32 Fourth Roots of One in ℤ p
  34. Altmetric Badge
    Chapter 33 Telephone Cable Splicing
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    Chapter 34 Factoring in ℚ[ x ], IV: Bad Examples mod p
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    Chapter 35 Congruence Classes Modulo a Polynomial: Simple Field Extensions
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    Chapter 36 Polynomials and Roots
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    Chapter 37 Error-Correcting Codes, II
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    Chapter 38 Isomorphisms, I
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    Chapter 39 Finite Fields are Simple
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    Chapter 40 Latin Squares
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    Chapter 41 Irreducible Polynomials in ℤ p [ x ]
  43. Altmetric Badge
    Chapter 42 Finite Fields
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    Chapter 43 The Discriminant and Stickelberger’s Theorem
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    Chapter 44 Quadratic Residues
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    Chapter 45 Duplicate Bridge Tournaments
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    Chapter 46 Algebraic Number Fields
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    Chapter 47 Isomorphisms, II
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    Chapter 48 Sums of Two Squares
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    Chapter 49 On Unique Factorization
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Title
A Concrete Introduction to Higher Algebra
Published by
Springer US, January 1979
DOI 10.1007/978-1-4684-0065-6
ISBNs
978-1-4684-0067-0, 978-1-4684-0065-6
Authors

Lindsay Childs, Childs, Lindsay

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