{"product_id":"algebra-in-action-9781470428495","title":"Algebra in Action","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Written with great care and clarity, Shahriari's \u003cem\u003eAlgebra in Action\u003c\/em\u003e 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\u003cbr\u003e\u003cbr\u003e“The structure of the text \u003cem\u003eAlgebra in Action\u003c\/em\u003e 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\u003cbr\u003e\u003cbr\u003e“It is rigorous, well-written, ample in terms of problems and solutions provided, and sufficiently advanced for its target audience.” — Jason M. Graham, \u003cem\u003eMAA Reviews\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003e(Mostly finite) group theory: Four basic examples\u003c\/li\u003e\n\u003cli\u003e Groups: The basics\u003c\/li\u003e\n\u003cli\u003e The alternating groups\u003c\/li\u003e\n\u003cli\u003e Group actions\u003c\/li\u003e\n\u003cli\u003e A subgroup acts on the group: Cosets and Lagrange's theorem\u003c\/li\u003e\n\u003cli\u003e A group acts on itself: Counting and the conjugation of action\u003c\/li\u003e\n\u003cli\u003e Acting on subsets, cosets, and subgroups: The Sylow theorems\u003c\/li\u003e\n\u003cli\u003e Counting the number of orbits\u003c\/li\u003e\n\u003cli\u003e The lattice of subgroups\u003c\/li\u003e\n\u003cli\u003e Acting on its subgroups: Normal subgroups and quotient groups\u003c\/li\u003e\n\u003cli\u003e Group homomorphisms\u003c\/li\u003e\n\u003cli\u003e Using Sylow theorems to analyze finite groups\u003c\/li\u003e\n\u003cli\u003e Direct and semidirect products\u003c\/li\u003e\n\u003cli\u003e Solvable and nilpotent groups\u003c\/li\u003e\n\u003cli\u003e (Mostly commutative) ring theory: Rings\u003c\/li\u003e\n\u003cli\u003e Homomorphisms, ideals, and quotient rings\u003c\/li\u003e\n\u003cli\u003e Field of fractions and localization\u003c\/li\u003e\n\u003cli\u003e Factorization, EDs, PIDs, and UFDs\u003c\/li\u003e\n\u003cli\u003e Polynomial rings\u003c\/li\u003e\n\u003cli\u003e Gaussian integers and (a little) number theory\u003c\/li\u003e\n\u003cli\u003e Field and Galois theory: Introducing field theory and Galois theory\u003c\/li\u003e\n\u003cli\u003e Field extensions\u003c\/li\u003e\n\u003cli\u003e Straightedge and compass constructions\u003c\/li\u003e\n\u003cli\u003e Splitting fields and Galois groups\u003c\/li\u003e\n\u003cli\u003e Galois, normal, and separable extensions\u003c\/li\u003e\n\u003cli\u003e Fundamental theorem of Galois theory\u003c\/li\u003e\n\u003cli\u003e Finite fields and cyclotomic extensions\u003c\/li\u003e\n\u003cli\u003e Radical extensions, solvable groups, and the quintic\u003c\/li\u003e\n\u003cli\u003e Hints for selected problems\u003c\/li\u003e\n\u003cli\u003e Short answers for selected problems\u003c\/li\u003e\n\u003cli\u003e Complete solutions for selected (odd-numbered) problems\u003c\/li\u003e\n\u003cli\u003e Bibliography\u003c\/li\u003e\n\u003cli\u003e Index\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041319457111,"sku":"9781470428495","price":79.2,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470428495.jpg?v=1740182266","url":"https:\/\/bookcurl.com\/products\/algebra-in-action-9781470428495","provider":"Book Curl","version":"1.0","type":"link"}