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Whereas many partial solutions and sketches for the odd-numbered
exercises appear in the book, the Student Solutions Manual, written
by the author, has comprehensive solutions for all odd-numbered
exercises and large number of even-numbered exercises. This Manual
also offers many alternative solutions to those appearing in the
text. These will provide the student with a better understanding of
the material. This is the only available student solutions manual
prepared by the author of Contemporary Abstract Algebra, Tenth
Edition and is designed to supplement that text. Table of Contents
Integers and Equivalence Relations 0. Preliminaries Groups1.
Introduction to Groups 2. Groups 3. Finite Groups; Subgroups 4.
Cyclic Groups 5. Permutation Groups 6. Isomorphisms 7. Cosets and
Lagrange's Theorem 8. External Direct Products 9. Normal Subgroups
and Factor Groups 10. Group Homomorphisms 11. Fundamental Theorem
of Finite Abelian Groups Rings12. Introduction to Rings 13.
Integral Domains 14. Ideals and Factor Rings 15. Ring Homomorphisms
16. Polynomial Rings 17. Factorization of Polynomials 18.
Divisibility in Integral Domains Fields Fields19. Extension Fields
20. Algebraic Extensions 21. Finite Fields 22. Geometric
Constructions Special Topics23. Sylow Theorems 24. Finite Simple
Groups 25. Generators and Relations 26. Symmetry Groups 27.
Symmetry and Counting 28. Cayley Digraphs of Groups 29.
Introduction to Algebraic Coding Theory 30. An Introduction to
Galois Theory 31. Cyclotomic Extensions Biography Joseph A. Gallian
earned his PhD from Notre Dame. In addition to receiving numerous
national awards for his teaching and exposition, he has served
terms as the Second Vice President, and the President of the MAA.
He has served on 40 national committees, chairing ten of them. He
has published over 100 articles and authored six books. Numerous
articles about his work have appeared in the national news outlets,
including the New York Times, the Washington Post, the Boston
Globe, and Newsweek, among many others.
This is an eclectic compendium of the essays solicited for the 2010
Mathematics Awareness Month Web page on the theme of 'Mathematics
and Sports'. In keeping with the goal of promoting mathematics
awareness to a broad audience, all of the articles are accessible
to university-level mathematics students and many are accessible to
the general public. The book is divided into sections by the kind
of sports. The section on American football includes an article
that evaluates a method for reducing the advantage of the winner to
a coin flip in an NFL overtime game; the section on track and field
examines the ultimate limit on how fast a human can run 100 metres;
the section on baseball includes an article on the likelihood of
streaks; the section on golf has an article that describes the
double-pendulum model of a golf swing and an article on modelling
Tiger Woods' career.
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