02118pam a2200289 a 45000010008000000030008000080050017000160060019000330080041000520100017000930200018001100400030001280410008001580500021001660820027001871000022002142450069002362500017003052640056003223000047003785000020004255040041004455050563004865200733010496500022017826500024018043468657EC-UrYT20200625170243.0s||||gr|||| 00| 00930317s1994 maua b 001 0 eng a 93017126 a9781944325022 aEC-UrYTcEC-UrYTdEC-UrYT aeng00aQA162b.J83 201604a512.02223bJ932a 20161 aJudson, Thomas W.10aAbstract algebra :btheory and applications /cThomas W. Judson. a2016 edition34aAnn Arbor, MI : bOrthogonal Publishing L3C,c2016. axiii, 417 pages :billustrations ;c25 cm. aIncludes index. aIncludes bibliographical references.2 a1. 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 Theory3 aThis 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.24aAlgebra, Abstract24aÁlgebra abstracta