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OverviewThis text-based on the author's popular courses at Pomona College-provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results. Full Product DetailsAuthor: Shahriar ShahriariPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 1.360kg ISBN: 9781470428495ISBN 10: 1470428490 Pages: 675 Publication Date: 30 September 2017 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents(Mostly finite) group theory: Four basic examples Groups: The basics The alternating groups Group actions A subgroup acts on the group: Cosets and Lagrange's theorem A group acts on itself: Counting and the conjugation of action Acting on subsets, cosets, and subgroups: The Sylow theorems Counting the number of orbits The lattice of subgroups Acting on its subgroups: Normal subgroups and quotient groups Group homomorphisms Using Sylow theorems to analyze finite groups Direct and semidirect products Solvable and nilpotent groups (Mostly commutative) ring theory: Rings Homomorphisms, ideals, and quotient rings Field of fractions and localization Factorization, EDs, PIDs, and UFDs Polynomial rings Gaussian integers and (a little) number theory Field and Galois theory: Introducing field theory and Galois theory Field extensions Straightedge and compass constructions Splitting fields and Galois groups Galois, normal, and separable extensions Fundamental theorem of Galois theory Finite fields and cyclotomic extensions Radical extensions, solvable groups, and the quintic Hints for selected problems Short answers for selected problems Complete solutions for selected (odd-numbered) problems Bibliography IndexReviewsWritten with great care and clarity, Shahriari's Algebra in Action provides an excellent introduction to abstract algebra. I have used the book twice to teach abstract algebra class at Reed College, and it's a perfect fit. The book is sophisticated yet readable, and packed with examples and exercises. Group actions appear early on, serving to motivate and unify many of the important concepts in group theory. The book also includes plenty of material on rings and fields, including the basics of Galois theory. - Jamie Pommersheim, Reed College The structure of the text Algebra in Action lets students see what groups really do right from the very beginning. In the very first chapter, the author introduces a rich selection of examples, the dihedral groups, the symmetric group, the integers modulo n, and matrix groups, that students can see 'in action' before the presentation of the formal definitions of groups and group actions in chapter 2 where the theoretical foundations are introduced. Students return to these examples again and again as the formal theory unfolds, seeing how the theory lets them study all groups at once...It is one of the few texts at the undergraduate level that supports the incorporation of group actions at an early stage in the course. - Jessica Sidman, Mount Holyoke College It is rigorous, well-written, ample in terms of problems and solutions provided, and sufficiently advanced for its target audience. - Jason M. Graham, MAA Reviews Author InformationShahriar Shahriari, Pomona College, Claremont, CA. Tab Content 6Author Website:Countries AvailableAll regions |
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