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| Introduction | |
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| Classical Algebra | |
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| Modern Algebra | |
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| Binary Operations | |
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| Algebraic Structures | |
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| Extending Number Systems | |
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| Boolean Algebras | |
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| Algebra of Sets | |
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| Number of Elements in a Set | |
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| Boolean Algebras | |
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| Switching Circuits | |
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| Posets and Lattices | |
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| Normal Forms and Simplification of Circuits | |
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| Transistor Gates | |
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| Representation Theorem | |
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| Exercises | |
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| Groups | |
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| Groups and Symmetries | |
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| Subgroups | |
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| Cyclic Groups and Dihedral Groups | |
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| Morphisms | |
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| Permutation Groups | |
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| Even and Odd Permutations | |
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| Cayley's Representation Theorem | |
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| Exercises | |
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| Quotient Groups | |
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| Equivalence Relations | |
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| Cosets and Lagrange's Theorem | |
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| Normal Subgroups and Quotient Groups | |
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| Morphism Theorem | |
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| Direct Products | |
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| Groups of Low Order | |
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| Action of a Group on a Set | |
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| Exercises | |
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| Symmetry Groups in Three Dimensions | |
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| Translations and the Euclidean Group | |
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| Matrix Groups | |
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| Finite Groups in Two Dimensions | |
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| Proper Rotations of Regular Solids | |
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| Finite Rotation Groups in Three Dimensions | |
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| Crystallographic Groups | |
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| Exercises | |
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| Polya-Burnside Method of Enumeration | |
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| Burnside's Theorem | |
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| Necklace Problems | |
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| Coloring Polyhedra | |
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| Counting Switching Circuits | |
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| Exercises | |
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| Monoids and Machines | |
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| Monoids and Semigroups | |
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| Finite-State Machines | |
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| Quotient Monoids and the Monoid of a Machine | |
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| Exercises | |
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| Rings and Fields | |
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| Rings | |
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| Integral Domains and Fields | |
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| Subrings and Morphisms of Rings | |
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| New Rings from Old | |
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| Field of Fractions | |
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| Convolution Fractions | |
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| Exercises | |
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| Polynomial and Euclidean Rings | |
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| Division Algorithm | |
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| Euclidean Algorithm | |
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| Unique Factorization | |
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| Factoring Real and Complex Polynomials | |
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| Factoring Rational and Integral Polynomials | |
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| Factoring Polynomials over Finite Fields | |
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| Linear Congruences and the Chinese Remainder Theorem | |
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| Exercises | |
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| Quotient Rings | |
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| Ideals and Quotient Rings | |
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| Computations in Quotient Rings | |
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| Morphism Theorem | |
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| Quotient Polynomial Rings that are Fields | |
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| Exercises | |
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| Field Extensions | |
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| Field Extensions | |
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| Algebraic Numbers | |
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| Galois Fields | |
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| Primitive Elements | |
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| Exercises | |
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| Latin Squares | |
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| Latin Squares | |
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| Orthogonal Latin Squares | |
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| Finite Geometries | |
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| Magic Squares | |
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| Exercises | |
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| Geometrical Constructions | |
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| Constructible Numbers | |
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| Duplicating the Cube | |
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| Trisecting an Angle | |
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| Squaring the Circle | |
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| Constructing Regular Polygons | |
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| A Nonconstructible Number of Degree Four | |
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| Exercises | |
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| Error-Correcting Codes | |
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| The Coding Problem | |
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| Simple Codes | |
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| Polynomial Representation | |
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| Matrix Representation | |
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| Error Correcting and Decoding | |
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| BCH Codes | |
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| Exercises | |
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| Bibliography and References | |
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| Answers to the Odd-Numbered Exercises | |
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| Glossary of Symbols | |
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| Index | |