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Category : Mathematics

Table of contents:

PART I: INTEGERS AND EQUIVALENCE RELATIONS.
Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises.
PART I!: GROUPS.
1. Introduction to Groups.
2. Groups.
3. Finite Groups; Subgroups.
4. Cyclic Groups.
5. Permutation Groups.
6. Isomorphisms.
7. Cosets and Lagrange’s Theorem.
8. External Direct Products.
9. Normal Subgroups and Factor Groups.
10. Group Homomorphisms.
11. Fundamental Theorem of Finite Abelian Groups.
PART III: RINGS.
12. Introduction to Rings.
13. Integral Domains.
14. Ideals and Factor Rings.
15. Ring Homomorphisms.
16. Polynomial Rings.
17. Factorization of Polynomials.
18. Divisibility in Integral Domains.
PART IV: FIELDS.
19. Vector Spaces.
20. Extension Fields.
21. Algebraic Extensions.
22. Finite Fields.
23. Geometric Constructions.
PART V: SPECIAL TOPICS.
24. Sylow Theorems.
25. Finite Simple Groups.
26. Generators and Relations.
27. Symmetry Groups.
28. Frieze Groups and Crystallographic Groups..
29. Symmetry and Counting.
30. Cayley Digraphs of Groups.
31. Introduction to Algebraic Coding Theory.
33. Cyclotomic Extensions.

Product Detail:

Language: English
ISBN-10: 1305657969
ISBN-13: 978-1305657960
ISBN-13: 9781305657960

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