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Preface | p. ix |
Sets | p. 1 |
Operations on Sets | p. 1 |
Exercise Set 1.1 | p. 6 |
Set Mappings | p. 8 |
Exercise Set 1.2 | p. 19 |
Products of Mappings | p. 20 |
Exercise Set 1.3 | p. 26 |
Some Properties of Integers | p. 28 |
Exercise Set 1.4 | p. 39 |
Matrices and Determinants | p. 41 |
Operations on Matrices | p. 41 |
Exercise Set 2.1 | p. 52 |
Permutations of Finite Sets | p. 54 |
Exercise Set 2.2 | p. 64 |
Determinants of Matrices | p. 66 |
Exercise Set 2.3 | p. 77 |
Computing Determinants | p. 79 |
Exercise Set 2.4 | p. 91 |
Properties of the Product of Matrices | p. 93 |
Exercise Set 2.5 | p. 103 |
Fields | p. 105 |
Binary Algebraic Operations | p. 105 |
Exercise Set 3.1 | p. 118 |
Basic Properties of Fields | p. 119 |
Exercise Set 3.2 | p. 129 |
The Field of Complex Numbers | p. 130 |
Exercise Set 3.3 | p. 144 |
Vector Spaces | p. 145 |
Vector Spaces | p. 146 |
Exercise Set 4.1 | p. 158 |
Dimension | p. 159 |
Exercise Set 4.2 | p. 172 |
The Rank of a Matrix | p. 174 |
Exercise Set 4.3 | p. 181 |
Quotient Spaces | p. 182 |
Exercise Set 4.4 | p. 186 |
Linear Mappings | p. 187 |
Linear Mappings | p. 187 |
Exercise Set 5.1 | p. 199 |
Matrices of Linear Mappings | p. 200 |
Exercise Set 5.2 | p. 207 |
Systems of Linear Equations | p. 209 |
Exercise Set 5.3 | p. 215 |
Eigenvectors and Eigenvalues | p. 217 |
Exercise Set 5.4 | p. 223 |
Bilinear Forms | p. 226 |
Bilinear Forms | p. 226 |
Exercise Set 6.1 | p. 234 |
Classical Forms | p. 235 |
Exercise Set 6.2 | p. 247 |
Symmetric Forms over R | p. 250 |
Exercise Set 6.3 | p. 257 |
Euclidean Spaces | p. 259 |
Exercise Set 6.4 | p. 269 |
Rings | p. 272 |
Rings, Subrings, and Examples | p. 272 |
Exercise Set 7.1 | p. 287 |
Equivalence Relations | p. 288 |
Exercise Set 7.2 | p. 295 |
Ideals and Quotient Rings | p. 297 |
Exercise Set 7.3 | p. 303 |
Homomorphisms of Rings | p. 303 |
Exercise Set 7.4 | p. 313 |
Rings of Polynomials and Formal Power Series | p. 315 |
Exercise Set 7.5 | p. 327 |
Rings of Multivariable Polynomials | p. 328 |
Exercise Set 7.6 | p. 336 |
Groups | p. 338 |
Groups and Subgroups | p. 338 |
Exercise Set 8.1 | p. 348 |
Examples of Groups and Subgroups | p. 349 |
Exercise Set 8.2 | p. 358 |
Cosets | p. 359 |
Exercise Set 8.3 | p. 364 |
Normal Subgroups and Factor Groups | p. 365 |
Exercise Set 8.4 | p. 374 |
Homomorphisms of Groups | p. 375 |
Exercise Set 8.5 | p. 382 |
Arithmetic Properties of Rings | p. 384 |
Extending Arithmetic to Commutative Rings | p. 384 |
Exercise Set 9.1 | p. 399 |
Euclidean Rings | p. 400 |
Exercise Set 9.2 | p. 404 |
Irreducible Polynomials | p. 406 |
Exercise Set 9.3 | p. 415 |
Arithmetic Functions | p. 416 |
Exercise Set 9.4 | p. 429 |
Congruences | p. 430 |
Exercise Set 9.5 | p. 446 |
The Real Number System | p. 448 |
The Natural Numbers | p. 448 |
The Integers | p. 458 |
The Rationals | p. 468 |
The Real Numbers | p. 477 |
Answers to Selected Exercises | p. 489 |
Index | p. 513 |
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