Chapter 1 Groups and Generating Sets
1.1 Binary operations
1.2 Isomorphic binary structures
1.3 Groups
1.4 Subgroups
1.5 Cyclic groups
1.6 Generating sets
1.7 Exercises
Chapter 2 Permutation Groups and Alternating Groups
2.1 Permutation groups
2.2 Alternating groups
2.3 Exercises
Chapter 3 Finitely Generated Abelian Groups and Quotient Groups
3.1 The theorem of Lagrange
3.2 Finitely generated abelian groups
3.3 Properties of homomorphisms
3.4 Quotient groups and isomorphism theorems
3.5 Automorphism groups
3.6 Simple groups
3.7 Exercises
Chapter 4 Rings, Quotient Rings and Ideal Theory
4.1 Basic definitions
4.2 Integral domains
4.3 Noncommutative rings
4.4 Quaternions
4.5 Isomorphism theorems
4.6 Euler's theorem
4.7 Ideal theory
4.8 Exercises
Chapter 5 Unique Factorization Domains
5.1 Basic definitions
5.2 Principal ideal domains
5.3 Euclidean domains
5.4 Polynomial rings over UFDs
5.5 Multiplicative norms
5.6 Exercises
Chapter 6 Extension Fields
6.1 Prime fields and extension fields
6.2 Algebraic and transcendental elements
6.3 Algebraic extensions and algebraic closure
6.4 Finite fields
6.5 Exercises
Appendix A Equivalence Relations and Quotient Set
Appendix B Zorn's Lemma
Appendix C Quotient field
Reference
Index
