抽象代数基础教程版 第3版 英文PDF电子书下载

Chapter 1 Number Theory 1

Section 1.1 Induction 1

Section 1.2 Binomial Theorem and Complex Numbers 18

Section 1.3 Greatest Common Divisors 37

Section 1.4 The Fundamental Theorem of Arithmetic 55

Section 1.5 Congruences 59

Section 1.6 Dates and Days 76

Chapter 2 Groups Ⅰ 84

Section 2.1 Some Set Theory 84

Functions 87

Equivalence Relations 99

Section 2.2 Permutations 106

Section 2.3 Groups 125

Symmetry 137

Section 2.4 Subgroups and Lagrange's Theorem 147

Section 2.5 Homomorphisms 159

Section 2.6 Quotient Groups 171

Section 2.7 Group Actions 192

Section 2.8 Counting with Groups 208

Chapter 3 Commutative Rings Ⅰ 217

Section 3.1 First Properties 217

Section 3.2 Fields 230

Section 3.3 Polynomials 235

Section 3.4 Homomorphisms 243

Section 3.5 From Numbers to Polynomials 252

Euclidean Rings 267

Section 3.6 Unique Factorization 275

Section 3.7 Irreducibility 281

Section 3.8 Quotient Rings and Finite Fields 290

Section 3.9 A Mathematical Odyssey 305

Latin Squares 305

Magic Squares 310

Design of Experiments 314

Proiective Planes 316

Chapter 4 Linear Algebra 320

Section 4.1 Vector Spaces 320

Gaussian Elimination 344

Section 4.2 Euclidean Constructions 354

Section 4.3 Linear Transformations 366

Section 4.4 Eigenvalues 383

Section 4.5 Codes 399

Block Codes 399

Linear Codes 406

Decoding 423

Chapter 5 Fields 432

Section 5.1 Classical Formulas 432

Viète's Cubic Formula 444

Section 5.2 Insolvability of the General Quintic 449

Formulas and Solvability by Radicals 459

Quadratics 460

Cubics 461

Quartics 461

Translation into Group Theory 462

Section 5.3 Epilog 471

Chapter 6 Groups Ⅱ 475

Section 6.1 Finite Abelian Groups 475

Section 6.2 The Sylow Theorems 489

Section 6.3 Ornamental Symmetry 501

Chapter 7 Commutative Rings Ⅱ 518

Section 7.1 Prime Ideals and Maximal Ideals 518

Section 7.2 Unique Factorization 525

Section 7.3 Noetherian Rings 535

Section 7.4 Varieties 540

Section 7.5 Generalized Divison Algorithm 558

Monomial Orders 559

Division Algorithm 565

Section 7.6 Gr？bner Bases 570