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Preface to the Third Edition | p. ix |
Suggested Syllabi | p. xiii |
To the Reader | p. xvii |
Number Theory | p. 1 |
Induction | p. 1 |
Binomial Theorem and Complex Numbers | p. 18 |
Greatest Common Divisors | p. 37 |
The Fundamental Theorem of Arithmetic | p. 55 |
Congruences | p. 59 |
Dates and Days | p. 76 |
Groups I | p. 84 |
Some Set Theory | p. 84 |
Functions | p. 87 |
Equivalence Relations | p. 99 |
Permutations | p. 106 |
Groups | p. 125 |
Symmetry | p. 137 |
Subgroups and Lagrange's Theorem | p. 147 |
Homomorphisms | p. 159 |
Quotient Groups | p. 171 |
Group Actions | p. 192 |
Counting with Groups | p. 208 |
Commutative Rings I | p. 217 |
First Properties | p. 217 |
Fields | p. 230 |
Polynomials | p. 235 |
Homomorphisms | p. 243 |
From Numbers to Polynomials | p. 252 |
Euclidean Rings | p. 267 |
Unique Factorization | p. 275 |
Irreducibility | p. 281 |
Quotient Rings and Finite Fields | p. 290 |
A Mathematical Odyssey | p. 305 |
Latin Squares | p. 305 |
Magic Squares | p. 310 |
Design of Experiments | p. 314 |
Projective Planes | p. 316 |
Linear Algebra | p. 320 |
Vector Spaces | p. 320 |
Gaussian Elimination | p. 344 |
Euclidean Constructions | p. 354 |
Linear Transformations | p. 366 |
Eigenvalues | p. 383 |
Codes | p. 399 |
Block Codes | p. 399 |
Linear Codes | p. 406 |
Decoding | p. 423 |
Fields | p. 432 |
Classical Formulas | p. 432 |
Viete's Cubic Formula | p. 444 |
Insolvability of the General Quintic | p. 449 |
Formulas and Solvability by Radicals | p. 459 |
Quadratics | p. 460 |
Cubics | p. 461 |
Quartics | p. 461 |
Translation into Group Theory | p. 462 |
Epilog | p. 471 |
Groups II | p. 475 |
Finite Abelian Groups | p. 475 |
The Sylow Theorems | p. 489 |
Ornamental Symmetry | p. 501 |
Commutative Rings II | p. 518 |
Prime Ideals and Maximal Ideals | p. 518 |
Unique Factorization | p. 525 |
Noetherian Rings | p. 535 |
Varieties | p. 540 |
Generalized Divison Algorithm | p. 558 |
Monomial Orders | p. 559 |
Division Algorithm | p. 565 |
Grobner Bases | p. 570 |
Inequalities | p. 1 |
Pseudocodes | p. 3 |
Hints for Selected Exercises | p. 1 |
Bibliography | p. 1 |
Index | p. 1 |
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