Schaum's Outline of Abstract Algebra
2nd Edition
Published on 16. January 2004
429 pages
978-0-07-143098-2 (ISBN)
Available for download
Description
Tough Test Questions? Missed Lectures? Not Rnough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you - Practice problems with full explanations that reinforce knowledge - Coverage of the most up-to-date developments in your course field - In-depth review of practices and applicationsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.
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Lloyd Jaisingh | Frank Ayres
Schaum's Outline of Abstract Algebra
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12/2003
2nd Edition
Schaum Outline Series
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Persons
Author
Lloyd R. Jaisingh, Ph.D., is Professor of Mathematics at Morehead State University, Morehead, Kentucky. He has taught statistics for the past thirteen years at Morehead State University, and has published several articles in applied statistics as well as books dealing with elementary statistics and the use of technology in the classroom. He has received a number of grants and fellowships, and an award as Outstanding Researcher of the Year at Morehead State.
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide
Content
- Cover Page
- Schaum's Outline of Theory and Problems of ABSTRACT ALGEBRA
- Copyright Page
- Preface
- Contents
- PART I SETS AND RELATIONS
- Chapter 1 Sets
- Introduction
- 1.1 Sets
- 1.2 Equal Sets
- 1.3 Subsets of a Set
- 1.4 Universal Sets
- 1.5 Intersection and Union of Sets
- 1.6 Venn Diagrams
- 1.7 Operations with Sets
- 1.8 The Product Set
- 1.9 Mappings
- 1.10 One-to-One Mappings
- 1.11 One-to-One Mapping of a Set onto Itself
- Solved Problems
- Supplementary Problems
- Chapter 2 Relations and Operations
- Introduction
- 2.1 Relations
- 2.2 Properties of Binary Relations
- 2.3 Equivalence Relations
- 2.4 Equivalence Sets
- 2.5 Ordering in Sets
- 2.6 Operations
- 2.7 Types of Binary Operations
- 2.8 Well-Defined Operations
- 2.9 Isomorphisms
- 2.10 Permutations
- 2.11 Transpositions
- 2.12 Algebraic Systems
- Solved Problems
- Supplementary Problems
- PART II NUMBER SYSTEMS
- Chapter 3 The Natural Numbers
- Introduction
- 3.1 The Peano Postulates
- 3.2 Addition on N
- 3.3 Multiplication on N
- 3.4 Mathematical Induction
- 3.5 The Order Relations
- 3.6 Multiples and Powers
- 3.7 Isomorphic Sets
- Solved Problems
- Supplementary Problems
- Chapter 4 The Integers
- Introduction
- 4.1 Binary Relation ~
- 4.2 Addition and Multiplication on
- 4.3 The Positive Integers
- 4.4 Zero and Negative Integers
- 4.5 The Integers
- 4.6 Order Relations
- 4.7 Subtraction "-"
- 4.8 Absolute Value |a|
- 4.9 Addition and Multiplication on Z
- 4.10 Other Properties of Integers
- Solved Problems
- Supplementary Problems
- Chapter 5 Some Properties of Integers
- Introduction
- 5.1 Divisors
- 5.2 Primes
- 5.3 Greatest Common Divisor
- 5.4 Relatively Prime Integers
- 5.5 Prime Factors
- 5.6 Congruences
- 5.7 The Algebra of Residue Classes
- 5.8 Linear Congruences
- 5.9 Positional Notation for Integers
- Solved Problems
- Supplementary Problems
- Chapter 6 The Rational Numbers
- Introduction
- 6.1 The Rational Numbers
- 6.2 Addition and Multiplication
- 6.3 Subtraction and Division
- 6.4 Replacement
- 6.5 Order Relations
- 6.6 Reduction to Lowest Terms
- 6.7 Decimal Representation
- Solved Problems
- Supplementary Problems
- Chapter 7 The Real Numbers
- Introduction
- 7.1 Dedekind Cuts
- 7.2 Positive Cuts
- 7.3 Multiplicative Inverses
- 7.4 Additive Inverses
- 7.5 Multiplication on
- 7.6 Subtraction and Division
- 7.7 Order Relations
- 7.8 Properties of the Real Numbers
- Solved Problems
- Supplementary Problems
- Chapter 8 The Complex Numbers
- Introduction
- 8.1 Addition and Multiplication on C
- 8.2 Properties of Complex Numbers
- 8.3 Subtraction and Division on C
- 8.4 Trigonometric Representation
- 8.5 Roots
- 8.6 Primitive Roots of Unity
- Solved Problems
- Supplementary Problems
- PART III GROUPS, RINGS AND FIELDS
- Chapter 9 Groups
- Introduction
- 9.1 Groups
- 9.2 Simple Properties of Groups
- 9.3 Subgroups
- 9.4 Cyclic Groups
- 9.5 Permutation Groups
- 9.6 Homomorphisms
- 9.7 Isomorphisms
- 9.8 Cosets
- 9.9 Invariant Subgroups
- 9.10 Quotient Groups
- 9.11 Product of Subgroups
- 9.12 Composition Series
- Solved Problems
- Supplementary Problems
- Chapter 10 Further Topics on Group Theory
- Introduction
- 10.1 Cauchy's Theorem for Groups
- 10.2 Groups of Order 2p and p2
- 10.3 The Sylow Theorems
- 10.4 Galois Group
- Solved Problems
- Supplementary Problems
- Chapter 11 Rings
- Introduction
- 11.1 Rings
- 11.2 Properties of Rings
- 11.3 Subrings
- 11.4 Types of Rings
- 11.5 Characteristic
- 11.6 Divisors of Zero
- 11.7 Homomorphisms and Isomorphisms
- 11.8 Ideals
- 11.9 Principal Ideals
- 11.10 Prime and Maximal Ideals
- 11.11 Quotient Rings
- 11.12 Euclidean Rings
- Solved Problems
- Supplementary Problems
- Chapter 12 Integral Domains, Division Rings, Fields
- Introduction
- 12.1 Integral Domains
- 12.2 Unit, Associate, Divisor
- 12.3 Subdomains
- 12.4 Ordered Integral Domains
- 12.5 Division Algorithm
- 12.6 Unique Factorization
- 12.7 Division Rings
- 12.8 Fields
- Solved Problems
- Supplementary Problems
- Chapter 13 Polynomials
- Introduction
- 13.1 Polynomial Forms
- 13.2 Monic Polynomials
- 13.3 Division
- 13.4 Commutative Polynomial Rings with Unity
- 13.5 Substitution Process
- 13.6 The Polynomial Domain [x]
- 13.7 Prime Polynomials
- 13.8 The Polynomial Domain C[x]
- 13.9 Greatest Common Divisor
- 13.10 Properties of the Polynomial Domain [x]
- Solved Problems
- Supplementary Problems
- Chapter 14 Vector Spaces
- Introduction
- 14.1 Vector Spaces
- 14.2 Subspace of a Vector Space
- 14.3 Linear Dependence
- 14.4 Bases of a Vector Space
- 14.5 Subspaces of a Vector Space
- 14.6 Vector Spaces Over R
- 14.7 Linear Transformations
- 14.8 The Algebra of Linear Transformations
- Solved Problems
- Supplementary Problems
- Chapter 15 Matrices
- Introduction
- 15.1 Matrices
- 15.2 Square Matrices
- 15.3 Total Matrix Algebra
- 15.4 A Matrix of Order m × n
- 15.5 Solutions of a System of Linear Equations
- 15.6 Elementary Transformations on a Matrix
- 15.7 Upper Triangular, Lower Triangular, and Diagonal Matrices
- 15.8 A Canonical Form
- 15.9 Elementary Column Transformations
- 15.10 Elementary Matrices
- 15.11 Inverses of Elementary Matrices
- 15.12 The Inverse of a Non-Singular Matrix
- 15.13 Minimum Polynomial of a Square Matrix
- 15.14 Systems of Linear Equations
- 15.15 Systems of Non-Homogeneous Linear Equations
- 15.16 Systems of Homogeneous Linear Equations
- 15.17 Determinant of a Square Matrix
- 15.18 Properties of Determinants
- 15.19 Evaluation of Determinants
- Solved Problems
- Supplementary Problems
- Chapter 16 Matrix Polynomials
- Introduction
- 16.1 Matrices with Polynomial Elements
- 16.2 Elementary Transformations
- 16.3 Normal Form of a ?-Matrix
- 16.4 Polynomials with Matrix Coefficients
- 16.5 Division Algorithm
- 16.6 The Characteristic Roots and Vectors of a Matrix
- 16.7 Similar Matrices
- 16.8 Real Symmetric Matrices
- 16.9 Orthogonal Matrices
- 16.10 Conics and Quadric Surfaces
- Solved Problems
- Supplementary Problems
- Chapter 17 Linear Algebras
- Introduction
- 17.1 Linear Algebra
- 17.2 An Isomorphism
- Solved Problems
- Supplementary Problems
- Chapter 18 Boolean Algebras
- Introduction
- 18.1 Boolean Algebra
- 18.2 Boolean Functions
- 18.3 Normal Forms
- 18.4 Changing the Form of a Boolean Function
- 18.5 Order Relation in a Boolean Algebra
- 18.6 Algebra of Electrical Networks
- 18.7 Simplification of Networks
- Solved Problems
- Supplementary Problems
- INDEX
