Abstract Algebra: Theory and Applications by Thomas Judson
Abstract Algebra: Theory and Applications - Table of Contents
- Part I: Foundations & Group Theory
- 1. Preliminaries
- 2. The Integers
- 3. Groups
- 4. Cyclic Groups
- 5. Permutation Groups
- 6. Cosets and Lagrange’s Theorem
- 7. Introduction to Cryptography
- 8. Algebraic Coding Theory
- 9. Isomorphisms
- 10. Normal Subgroups and Factor Groups
- 11. Homomorphisms
- 12. Matrix Groups and Symmetry
- Part II: Rings, Fields & Galois Theory
- 13. The Structure of Groups
- 14. Group Actions
- 15. The Sylow Theorems
- 16. Rings
- 17. Polynomials
- 18. Integral Domains
- 19. Lattices and Boolean Algebras
- 20. Vector Spaces
- 21. Fields and Galois Theory
- 22. Finite Fields
- 23. Galois Theory
What You Will Learn in Abstract Algebra: Theory and Applications
Abstract Algebra: Theory and Applications is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. As a definitive abstract algebra theory and applications textbook, its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems, providing enough material for a semester-long course.
The second half of this judson abstract algebra guide is suitable for a second semester and presents important topics like rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory. This text covers the traditional theoretical aspects of groups, rings, and fields, while helping students learn abstract algebra concepts step-by-step. It also includes real-world applications such as cryptography and coding theory, utilizing SageMath software to help readers master advanced mathematical structure concepts through computational, conceptual, and theoretical exercises, making it an ideal free abstract algebra textbook for beginners.
Book Details & Specifications
Title:
Abstract Algebra: Theory and Applications by Thomas Judson
Publisher:
Virginia Commonwealth University
Year:
2012
Pages:
386
Type:
PDF
Language:
English
ISBN-10 #:
0982406223
ISBN-13 #:
978-0982406229
License:
GNU
Amazon:
Amazon
About the Author: Thomas W Judson
The author Thomas W Judson
is a math professor at Stephen F. Austin State University. He became well known globally because of his definitive abstract algebra theory and applications textbook, which stands out as an exceptional free abstract algebra textbook for beginners and advanced learners alike.
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