A Concrete Introduction to Higher Algebra

Table of Contents

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   Book Overview
2. Altmetric Badge
   Chapter 1 Numbers
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   Chapter 2 Induction
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   Chapter 3 Euclid’s Algorithm
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   Chapter 4 Unique Factorization
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   Chapter 5 Congruences
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   Chapter 6 Congruence Classes
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   Chapter 7 Applications of Congruences
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   Chapter 8 Rings and Fields
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    Chapter 9 Fermat’s and Euler’s Theorems
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    Chapter 10 Applications of Fermat’s and Euler’s Theorems
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    Chapter 11 On Groups
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    Chapter 12 The Chinese Remainder Theorem
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    Chapter 13 Matrices and Codes
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    Chapter 14 Polynomials
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    Chapter 15 Unique Factorization
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    Chapter 16 The Fundamental Theorem of Algebra
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    Chapter 17 Derivatives
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    Chapter 18 Factoring in ℚ[ x ], I
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    Chapter 19 The Binomial Theorem in Characteristic p
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    Chapter 20 Congruences and the Chinese Remainder Theorem
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    Chapter 21 Applications of the Chinese Remainder Theorem
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    Chapter 22 Factoring in F p [ x ] and in ℤ[ x ]
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    Chapter 23 Primitive Roots
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    Chapter 24 Cyclic Groups and Primitive Roots
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    Chapter 25 Pseudoprimes
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    Chapter 26 Roots of Unity in ℤ/ m ℤ
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    Chapter 27 Quadratic Residues
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    Chapter 28 Congruence Classes Modulo a Polynomial
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    Chapter 29 Some Applications of Finite Fields
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    Chapter 30 Classifying Finite Fields