Abstract algebra / edited by Ramesh Chandra Kashyap.

Includes bibliographical references and index.

Sets, relations and mappings -- Applications of integral -- Algebra of complex number -- Abstract function -- Cyclic groups and subgroups -- Linear transformation -- Abstract of permutation groups -- Ring, integral domain and fields -- Laplace transforms -- Vector space, subspace and algebra -- Functions of matrices.

"Algebra is the branch of mathematics that deals with numbers and their relations. Algebra is used throughout of people's daily lives from buying groceries in the store to scientific researches. Algebra is so useful that NASA is using binary numbers to communicate to the possible extraterrestrial lives. So learning algebra is so important because that people's lives are depended on algebra. Designed for undergraduate and postgraduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called variety of groups. This book presents a lucid and unified description of Abstract algebra at a level which can be easily understood by the students who posses reasonable mathematical aptitude and abstract reasoning. The book provides an example oriented, less heavily symbolic approach to abstract algebra and the text emphasizes specifics such as rings, integral domains and field, polynomial rings, vector spaces, matrices and linear transformations etc. the book concludes with the coverage of eigen values and eigen vectors of matrices." -- Back cover