Abstract algebra
theory and applications
Judson, Thomas W.
creator
text
bibliography
mau
1994
2016 edition
monographic
eng
xiii, 417 pages : illustrations ; 25 cm.
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.
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
Thomas W. Judson.
Includes index.
Includes bibliographical references.
Algebra, Abstract
Álgebra abstracta
QA162 .J83 2016
512.02 J932a 2016
9781944325022
93017126
EC-UrYT
930317
20200625170243.0
3468657