Abstract Algebra by Dummit and Foote Content #shorts #mathuniverse28

Abstract Algebra by Dummit and Foote Content #shorts #mathuniverse28

Abstract Algebra by David S. Dummit and Richard M. Foote Third Edition

BOOK CONTENT
PART 1 GROUP THEORY
1. Introduction to Groups
2. Subgroups
3. Quoitent Groups and Homomorphisms
4. Group Actions
5. Direct and Semidirect Products and Abelian Groups
6. Further Topics in Group Theory

PART 2 RING THEORY
7. Introduction to Rings
8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
9. Polynomial Rings

PART 3 MODULES AND VECTOR SPACES
10. Introduction to Module theory
11. Vector Spaces
12. Modules over Principal Ideal Domains

PART4 FIELD THEORY AND GALOIS THEORY
13, Field Theory
14. Galios Theory

PART5 AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY AND HOMOLOGICAL ALGEBRA
15. Commutative Rings and Algebraic Geometry
16. Artinian Rings, discrete Valuation Rings and Dedekind Domains
17. Introduction to Homological Algebra and Group Cohomology

PART 6 INTRODUCTION TO THE REPRESENRARION THEORY OF FINITE GROUPS
18. Representation theory and Character theory
19. Examples and Applications of Character Theory

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