About the Authors
Preface to the Fourth Edition
Preface to the First Edition
1. Preliminaries
1.1 Sets
1.2 Relations
1.3 Congruous Relation
1.4 Functions
1.5 Binary Operations
2. Integers
2.1 Divisibility
2.2 Mathematical Induction
2.3 Prime Numbers
2.4 Linear Diophantine Equations
2.5 Arithmetic Functions
2.6 More on Congruence
3. Groups
3.1 Elementary Properties
4. Permutation Groups
4.1 Permutation Group
5. Subgroups
5.1 Subgroups
5.2 Cyclic Groups
5.3 Cosets and Lagrange’s Theorem
5.4 Normal Subgroups and Quotient Groups
6. Homomorphisms of Groups
6.1 Homomorphisms
6.2 Isomorphism Theorems
7. Direct Product of Groups
7.1 Direct Product
8. Symmetry
8.1 Isometry
8.2 Four Isometries of the Plane
8.3 Group of Symmetries
9. Finite Abelian Groups
9.1 Finite Abelian Groups
10. Sylow Theorems
10.1 Group Actions
10.2 Class Equation and Cauchy’s Theorem
10.3 Sylow Theorems
11. Simple Groups
11.1 Simple Groups
12. Rings
12.1 Elementary Properties
12.2 Integral Domains, Division Rings and Fields
12.3 Subrings and Subfields
13. Ideals and Homomorphisms of Rings
13.1 Ideals and Quotient Rings
13.2 Homomorphisms
13.3 Maximal ideals and Prime ideals
13.4 Regular Rings
13.5 Embedding of Rings
14. Factorization in Integer Domains
14.1 Factorization Domain
14.2 Euclidean Domain
15. Polynomial Rings
15.1 Ring of Polynomials
15.2 Irreducibility of Polynomials
Appendices
Bibliography
Answers
Index