Abstract algebra : theory and applications / Thomas W. Judson.Material type: TextLanguage: English Copyright date: Ann Arbor, MI : Orthogonal Publishing L3C, 2016Edition: 2016 editionDescription: xiii, 417 pages : illustrations ; 25 cmISBN: 9781944325022Subject(s): Algebra, Abstract | Álgebra abstractaDDC classification: 512.02 LOC classification: QA162 | .J83 2016
|Item type||Current library||Call number||Copy number||Status||Date due||Barcode||Item holds|
|Libro académico||Biblioteca del Campus||512.02 J932a 2016 (Browse shelf (Opens below))||Ej. 1||Available||005715|
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.