Algebra -1 (Basic Course)

This book is designed as a textbook for the Undergraduate students. It meets the curriculum requirements of the Course I.2 Algebra I (DC-I) of the University of Delhi. This book is useful for students of any other University also who would like to study the topics covered in this book. It focuses on the introductory aspects of the course supporting the theory with numerous Examples and Solved Problems. The text starts with equivalence relations and goes on to functions. It explains the Principle of Mathematical Induction and also proves the Fundamental Theorem of Arithmetic. Complex numbers in polar form have also been introduced and the nth roots of unity have been explained in detail. Linear equations linear transformations matrices eigenvalues and eigenvectors and vector spaces have also been covered.A unique feature is the glossary of the terms used in the text and summary of the chapters.The salient features of the book are:-Learning objectives given at the beginning of each chapter.-Concepts illustrated with examples.-Stepwise Proofs of Theorems and Solution of problems.-Emphasis on techniques of problem solving through numerous solved problems.-Graded Exercises.-Concepts reinforced by true/false questions.-Chapter-wise summary for ready reference.-Glossary of the terms used in the text.-Index for ready reference.-Answers to all the exercises and hints to difficult questions.