Judson, Thomas W.

Abstract algebra : theory and applications / Thomas W. Judson. - 2016 edition - xiii, 417 pages : illustrations ; 25 cm.

Includes index.

Includes bibliographical references.

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

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.

9781944325022

93017126


Algebra, Abstract
Álgebra abstracta

QA162 / .J83 2016

512.02 / J932a 2016