Book description
Algebra is a compulsory paper offered to the undergraduate students of Mathematics. The majority of universities offer the subject as a two /three year paper or in two/three semesters. Algebra I: A Basic Course in Abstract Algebra covers the topic required for a basic course.
Table of contents
 Cover
 Title Page
 Contents
 About the Authors
 Dedication
 Preface

Unit  1
 1. Sets and Relations
 2. Binary Operations

3. Functions
 3.1 Definition and Representation
 3.2 Images and Inverse Images
 3.3 Types of Functions
 3.4 Real Valued Functions
 3.5 Some Functions on the Set of Real Numbers
 3.6 Exercise
 3.7 Inverse of a Function
 3.8 Composition of Functions
 3.9 Solved Problems
 3.10 Exercise
 3.11 Cardinality of a Set
 3.12 Countable Sets
 3.13 Exercise
 3.14 Solved Problems
 3.15 Supplementary Exercise
 3.16 Answers to Exercises
 4. Number System

Unit  2

5. Group: Definition and Examples
 5.1 Definition of Group
 5.2 Exercise
 5.3 Groups of Numbers
 5.4 Exercise
 5.5 Groups of Residues
 5.6 Exercise
 5.7 Groups of Matrices
 5.8 Exercise
 5.9 Groups of Functions
 5.10 Exercise
 5.11 Group of Subsets of a Set
 5.12 Exercise
 5.13 Groups of Symmetries
 5.14 Supplementary Exercise
 5.15 Answers to Exercises
 6. Group: Properties and Characterization

7. Subgroups
 7.1 Criteria for Subgroups
 7.2 Solved Problems
 7.3 Exercise
 7.4 Centralizers, Normalizers and Centre
 7.5 Exercise
 7.6 Order of an Element
 7.7 Solved Problems
 7.8 Exercise
 7.9 Cyclic Subgroups
 7.10 Solved Problems
 7.11 Exercise
 7.12 Lattice of Subgroups
 7.13 Exercise
 7.14 Supplementary Exercises
 7.15 Answers to Exercises

8. Cyclic Groups
 8.1 Definition and Examples
 8.2 Description of Cyclic Groups
 8.3 Exercise
 8.4 Generators of a Cyclic Group
 8.5 Exercise
 8.6 Subgroups of Cyclic Groups
 8.7 Subgroups of Infinite Cyclic Groups
 8.8 Subgroups of Finite Cyclic Groups
 8.9 Number of Generators
 8.10 Exercise
 8.11 Solved Problems
 8.12 Supplementary Exercise
 8.13 Answers to Exercises

5. Group: Definition and Examples
 Unit  3

Unit  4

10 System of Linear Equations
 10.1 Matrix Notation
 10.2 Solving a Linear System
 10.3 Elementary Row Operations (ERO)
 10.4 Solved Problems
 10.5 Exercise
 10.6 Row Reduction and Echelon Forms
 10.7 Exercise
 10.8 Vector Equations
 10.9 Vectors in R2
 10.10 Geometric Descriptions of R2
 10.11 Vectors in Rn
 10.12 Exercise
 10.13 Solutions of Linear Systems
 10.14 Parametric Description of Solution Sets
 10.15 Existence and Uniqueness of Solutions
 10.16 Homogenous System
 10.17 Exercise
 10.18 Solution Sets of Linear Systems
 10.19 Exercise
 10.20 Answers to Exercises

11. Matrices
 11.1 Matrix of Numbers
 11.2 Operations on Matrices
 11.3 Partitioning of Matrices
 11.4 Special Types of Matrices
 11.5 Exercise
 11.6 Inverse of a Matrix
 11.7 Adjoint of a Matrix
 11.8 Negative Integral Powers of a Nonsingular Matrix
 11.9 Inverse of Partitioned Matrices
 11.10 Solved Problems
 11.11 Exercise
 11.12 Orthogonal and Unitary Matrices
 11.13 Length Preserving Mapping
 11.14 Exercise
 11.15 Eigenvalues and Eigenvectors
 11.16 Cayley Hamilton Theorem and Its Applications
 11.17 Solved Problems
 11.18 Exercise
 11.19 Supplementary Exercises
 11.20 Answers to Exercises

12. Matrices and Linear Transformations
 12.1 Introduction to Linear Transformations
 12.2 Exercise
 12.3 Matrix Transformations
 12.4 Surjective and Injective Matrix Transformations
 12.5 Exercise
 12.6 Linear Transformation
 12.7 Exercise
 12.8 The Matrix of a Linear Transformation
 12.9 Exercises
 12.10 Geometric Transformations of R2 and R3
 12.11 Exercises
 12.12 Supplementary Problems
 12.13 Supplementary Exercise
 12.14 Answers to Exercises

10 System of Linear Equations
 Unit  5
 Notes
 Copyright
Product information
 Title: Algebra I: A Basic Course in Abstract Algebra
 Author(s):
 Release date: June 2011
 Publisher(s): Pearson India
 ISBN: 9788131760864
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