- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Contents
Contents; Preface; 1. A refresher on the integers; 2. A first look at groups; 3. Groups acting on sets; 4. Basics on rings-mostly commutative; 5. Primes and unique factorization; 6. Algebraic field extensions; 7. Applications of galois theory; 8. Modules over principal ideal domains; 9. Division algorithms; Appendix A: Infinite sets.
