First Course in Abstract Algebra

✍ Scribed by Richard E. Johnson

• Publisher: Prentice-Hall
• Year: 1965
• Tongue: English
• Leaves: 270
• Edition: 7th printing
• Category: Library

✦ Table of Contents

Title
Preface
Contents
I. Basic Concepts
1. Sets and elements
2. Mappings and operations
3. Relations
II. The Real Number System
4. The natural numbers
5. The integers
6. The rational numbers
7. The real numbers
III. Integral Domains and Fields
8. Integral domains
9. The integers modulo k
10. The characteristic
11. Fields
12. The quotient field of an integral domain
IV. Polynomial Domains
13. The polynomial domain of an integral domain
14. The polynomial domain of a field
V. The Complex Number Field
15. The field of polynomials modulo a given prime
16. The complex number field
17. The polynomial domain C[x]
VI. Groups
18. Permutation groups
19. Abstract groups
20. The symmetric group Pn
21. Cosets of a subgroup in a group
22. Invariant subgroups and quotient groups
VII. Vector Spaces
23. Definition and elementary properties of a vector space
24. Linear independence in a vector space
25. Bases of vector spaces
26. Algebra of subspaces of a vector space
VIII. Linear Transformations and Matrices
27. Elementary properties of linear transformations
28. The algebra of linear transformations
29. The algebra of matrices
30. Further properties of matrices
IX. Linear Equations and Determinants
31. Systems of linear equations
32. Determinants
33. Further properties of determinants
34. On solving a system of linear equations
X. Other Algebraic Systems
35. Linear algebras
36. Rings
37. Boolean algebras
Index