Author: Vijay K Khanna

Brand: Vikas

Edition: 6TH Latest Edition 2025 - 2026

Binding: paperback

Number Of Pages: 800

Release Date: 26-08-2025

Details: The book has been designed for undergraduate and postgraduate students of Mathematics and it can also be used by those preparing for various competitive examinations. The text starts with an introduction to results from Sets and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. Of late, Number theory has been becoming a part of Algebra syllabus and thus sufficient relevant material on the subject has been covered especially in the present edition. This includes besides others the phi, greatest integer and möbius functions, primitive roots, Euler and Wilson theorems. The topics under Groups include subgroups, normal subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian rings. Topics in Fields include algebraic extensions, normal and separable extensions, splitting fields, algebraically closed fields, Galois extensions and construction by ruler and compass. The portion on linear algebra deals with Vector spaces, linear transformations, eigen spaces, diagonalizable operators, inner product spaces etc. The theory has been strongly supported by numerous examples and worked out problems. There is also plenty of scope for the readers to try and solve problems on their own. New In the Sixth Edition: ✍ A full section on operators in inner product spaces. ✍ Complete survey of finite groups of order up to 15 and Wedderburn theorem on finite division rings. ✍ Addition of around one hundred new worked-out problems and examples. ✍ Alternate and simpler proofs of some results. ✍ A new section on quick recall of various useful results at the end of the book to facilitate the reader to get instant answers to tricky questions. Table of Contents: Preface to the Sixth Edition Preface to the First Edition Glossary of Symbols 1. Sets and Number Theory 2. Groups. 3. Normal Subgroups, Homomorphisms, Permutation Groups 4. Automorphisms and Conjugate Elements 5. Sylow Theorems and Direct Products 6. Group Actions, Solvable and Nilpotent Groups 7. Rings 8. Homomorphisms and Embedding of Rings 9. Euclidean and Factorization Domains 10. Vector Spaces 11. Linear Transformations 12. Eigen Values and Eigen Vectors 13. Inner Product Spaces 14. Fields 15. More on Fields Appendix: Quick Recall Index Useful for: The book has been designed for undergraduate and postgraduate students of Mathematics and it can also be used by those preparing for various competitive examinations.

EAN: 9789359305271

Package Dimensions: 9.3 x 6.5 x 1.3 inches

Languages: English