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Algebra in action : a course in groups, rings, and fields

Author: Shahriar Shahriari
Publisher: Providence, Rhode Island : American Mathematical Society, [2017] ©2017
Series: Pure and applied undergraduate texts, 27.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This 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  Read more...
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Genre/Form: Textbooks
Electronic books
Additional Physical Format: Print version:
Shahriari, Shahriar.
Algebra in action.
Providence, Rhode Island : American Mathematical Society, [2017]
(DLC) 2016036490
(OCoLC)956583840
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Shahriar Shahriari
ISBN: 9781470436612 1470436612
OCLC Number: 1004354489
Description: 1 online resource (xvii, 675 pages).
Contents: 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 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 --
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 --
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.
Series Title: Pure and applied undergraduate texts, 27.
Responsibility: Shahriar Shahriari.

Abstract:

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.  Read more...

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