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Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
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Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
Algebra Textbook - Comprehensive Guide for Students & Teachers | Dover Books on Mathematics | Perfect for Classroom Learning & Self-Study
$5.55
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Description
This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduate-level courses. It employs presentations and proofs that are accessible to students, and it provides numerous concrete examples.Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian groups, transcendental field extensions, representations and characters of finite groups, Galois groups, and additional areas.Based on many years of classroom experience, this self-contained treatment breathes new life into abstract concepts.
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This 1983 algebra book by Larry Charles Grove (1938-2006) progresses systematically through the fundamental categories of algebraic structures (groups, rings, fields, modules and algebras), but without any category theory. So this is a concrete presentation of pure algebra which avoids the high abstractions of category theory. That's exactly how I like it.This book is very concise and brief, and definitely not a comprehensive encyclopedic kind of book because it is so short. But on the positive side, this means that there's very little here that could be called superfluous. It's all core algebra which everyone would be expected to know at this level.Chapter 1 on "Groups" devotes an entire 6-line paragraph to semigroups and monoids. This chapter summarizes the basic definitions and theorems for group theory, including the three Sylow theorems. Chapter 2 likewise presents "Rings", including universal factorization domains. Chapter 3 presents "Fields and Galois theory", including applications to constructibility in classical Euclidean geometry.Chapter 4 on "Modules" includes some material on linear algebra and computations with matrices, and on page 163, at the very end of this chapter, associative algebras are defined, called "R-algebras" here. Then Chapter 5 on "Structure of rings and algebras" gives some theorems for associative algebras. There is nothing about Lie algebras.The big 94-page Chapter 6 on "Further topics" is a bit beyond my level. So I'll say nothing about it. The author explains in the preface that Chapter 6 contains independent optional extra topics.All in all, this is a relatively down-to-Earth concrete book with nothing superfluous, although there are numerous "further topics" in Chapter 6. The coverage is not comprehensive, but it's only intended as a tidy summary at a first-year graduate level of undergraduate algebra which is assumed to have been seen at least at some level in undergraduate years.

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