Abstract Algebra: Theory and Applications by Thomas W Judson
About this book :-
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. 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, with enough material for a semester-long course. The second-half is suitable for a second semester and presents important topics rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
This text is covers the traditional theoretical aspects of groups, rings, and fields. It also includes many exercises and real-world applications, such as cryptography and coding theory. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included. It also uses SageMath, a free software, to help students visualize and solve problems.
Book Detail :-
Title:
Abstract Algebra: Theory and Applications by Thomas W 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 Author :-
The author
Thomas W Judson
is a math professor at Stephen F. Austin State University. He become well known because of his textbook Abstract Algebra: Theory and Applications.
Book Contents :-
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
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
22. Finite Fields
23. Galois Theory
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