Schaum's Outline of Abstract Algebra

Schaum's Outline of Abstract Algebra

by Deborah C. Arangno, Arangno

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Overview

Schaum's Outline of Abstract Algebra by Deborah C. Arangno, Arangno

Master abstract algebra with this simple-to-use guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams. Students love SchaumOs Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides.
Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, this book helps you: Brush up before tests; Find answers fast; Study quickly and more effectively. Get the big picture without spending hours pouring over lengthy texts. Use with these courses: Abstract Algebra o Modern Algebra o Linear Algebra and Matrix Theory o Homological Algebra o Group Theory o Ring Theory. SchaumOs Outlines give you the information your teachers expect you to know in a handy and succinct formatNwithout overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, SchaumOs lets you study at your own pace and reminds you of all the important facts you need to rememberNfast! And SchaumOs are so complete, theyOre perfect for preparing for graduate or professional exams. Inside, you will find: Clear explanations and examples of all the principal concepts you need in abstract algebra;
Classical topics, key theorems, and definitions, with insights on how the structures interrelate; Hundreds of practice problems with answers explained; A comprehensive glossary of symbols, notations and terms. If you want top grades and a thorough understanding of abstract algebra, this powerful study tool is the best tutor you can have!
Chapters include: Rudiments o Groups o Rings o Modules o Vector Spaces o Introduction to Matrices o Polynomials o Introduction to Galois Theory.

Product Details

ISBN-13: 9780070069954
Publisher: McGraw-Hill Companies, The
Publication date: 01/28/2003
Edition description: Older Edition
Pages: 256
Product dimensions: 8.22(w) x 10.92(h) x 0.46(d)

Table of Contents

INTRODUCTION xi
CHAPTER 1 RUDIMENTS
1(50)
1.1 Sets
1(8)
Classical Problems: Sets
7(2)
Supplemental Exercises: Sets
9(1)
1.2 Mappings
9(10)
Classical Problems: Mappings
15(3)
Supplemental Exercises: Mappings
18(1)
1.3 Relations and Operations
19(10)
Classical Problems: Relations and Operations
24(4)
Supplemental Exercises: Relations and Operations
28(1)
1.4 Number Systems
29(22)
1.4.1 The Natural Numbers
29(2)
1.4.2 The Integers
31(5)
1.4.3 The Rational Numbers
36(1)
1.4.4 The Reals
37(1)
1.4.5 The Complex Numbers
38(1)
Classical Problems: Number Systems
39(10)
Supplemental Exercises: Number Systems
49(2)
CHAPTER 2 GROUPS
51(42)
2.1 Introduction to Groups
51(12)
Classical Problems: Groups and Subgroups
57(6)
2.2 Working With Groups
63(16)
Classical Problems: Working With Groups
69(10)
2.3 More on Group Structure
79(11)
Classical Problems: More on Group Structure
81(9)
2.4 Supplemental Exercises: Groups
90(3)
CHAPTER 3 RINGS
93(38)
3.1 Basic Ring Structure
93(9)
Classical Problems: Basic Ring Structure
96(6)
3.2 Ring Substructures
102(8)
Classical Problems: Ring Substructures
104(6)
3.3 Specialized Rings
110(10)
Classical Problems: Specialized Rings
113(7)
3.4 Working With Rings
120(8)
Classical Problems: Working With Rings
122(6)
3.5 Notes on Rings
128(1)
3.6 Supplemental Exercises: Rings
129(2)
CHAPTER 4 R-MODULES
131(14)
4.1 Introduction to R-Modules
131(4)
4.2 Notes on Modules
135(5)
4.3 Classical Problems: R-Modules
140(4)
4.4 Supplemental Exercises: R-Modules
144(1)
CHAPTER 5 VECTOR SPACES
145(14)
5.1 Introduction to Vector Spaces
145(6)
5.2 Notes on Vector Spaces
151(1)
5.3 Classical Problems: Vector Spaces
152(6)
5.4 Supplemental Exercises: Vector Spaces
158(1)
CHAPTER 6 INTRODUCTION TO MATRICES
159(29)
6.1 Basic Linear Algebra
159(17)
6.1.1 Basic Structures
159(8)
6.1.2 Notes: Basic Linear Algebra
167(2)
Classical Problems: Matrices
169(7)
6.2 Matrices in Solving Systems of Equations
176(10)
6.2.1 Introduction
176(4)
6.2.2 Examples
180(1)
Classical Problems: Applying Matrices in Solving Systems of Equations
181(5)
6.3 Supplemental Exercises: Matrices
186(2)
CHAPTER 7 POLYNOMIALS
188(10)
7.1 Definitions
188(4)
7.2 Background and Notes: Polynomials
192(1)
7.3 Classical Problems: Polynomials
193(3)
7.4 Supplemental Exercises: Polynomials
196(2)
CHAPTER 8 INTRODUCTION TO GALOIS THEORY
198(17)
8.1 Definitions
198(4)
8.2 Theorems
202(1)
8.3 Background and Notes: Galois Theory
203(3)
8.4 Classical Problems: Extension Fields
206(3)
8.5 Supplemental Exercises: Galois Theory
209(6)
GLOSSARY 215(2)
BIOGRAPHICAL SKETCHES 217(4)
BIBLIOGRAPHY 221(2)
INDEX 223

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Schaum's Outline of Abstract Algebra 4.5 out of 5 based on 0 ratings. 2 reviews.
Guest More than 1 year ago
a completely new insight into the relationships among the structures of algebra, how they are interconnected. This printing is terribly marred by typos, but you have to pick carefully, and you will discover a brilliant perspective!
Bruno2011 More than 1 year ago
What surprises me more than that I could finally understand abstract mathematics because of this brilliant book, was that they would let it go out of print! Yes, there are lots of typos, but the publisher had a work of genius on their hands why wouldn't they bother to correct some printing mistakes?