A Textbook Of B Sc Mathematics Abstract Algebra

A Textbook of B.Sc. Mathematics Abstract Algebra

This "Textbook of B.Sc Mathematics" for the students studying third year first semester in all universities of Telangana state was first published in the year 1988 and has undergone several editions and many reprints.

This book has been thoroughly revised according to the syllabus of 1st year's 2nd semester students of all universities in Andhra Pradesh. The revised syllabus is being adopted by all the universities in Andhra Pradesh, following Common Core Syllabus 2015-16 (revised in 2016) based on CBCS. This book strictly covers the new curriculum for 1st year, 2nd semester of the theory as well as practical.

"A Textbook of B.Sc. Mathematics [Abstract Algebra] Volume III (Andhra Pradesh)" strictly covers the new curriculum for Semester III (2nd year, 1st semester). It covers types of Groups, Sub-Groups, Homomorphism, Permutations, Cyclic groups, and basic properties of Rings with reference to the revised syllabus with Highlighted topics and theorems included for making the book more comprehensive and co-curricular activities are provided at the end of the book to supplement the curriculum.

Algebra >Functions And Relations >Congruence Of Integers >Some Special Types Of Matrices >Elementary Operations And Inverse Of A Matrix >Linear Dependance Of Vectors >Rank Of A Matrix >Linear Equations >Characteristic Roots Of Vectors >Theory Of Equations

This Textbook of B.Sc. Mathematics for the students studying second year in all universities of Andhra Pradesh was first published in the year 1988 and has undergone several editions and many reprints. The revised syllabus is being adopted by all the universities in Andhra Pradesh, following Common Core model curriculum from the academic year 2015 - 2016 based on CBCS (Choice Based Credit System). This book strictly covers the new curriculum for Semester III (2nd year, 1st semester).

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

The book caters to the 1st semester students of BSc (Hons) Mathematics of Indian universities. It has been written strictly in accordance with the CBCS syllabus of the UGC. The book teaches the concepts and techniques of basic algebra with a focus on explaining definitions and theorems, and creating proofs. The theory is supported by numerous examples and plenty of worked-out problems. Its strict logical organization has been designed to help the reader to develop confidence in the subject. By introducing various interesting applications of algebra the book also aims at creating a broad and solid foundation for the study of advanced mathematics.The contents covered in the book are equivalence relations, functions, cardinality, congruence-modulo, mathematical induction and De Moivre's theorem. Further, some basic topics of linear algebra like vectors and matrices, linear equations, Gauss elimination, subspace and its dimension, rank-nullity theorem, linear trans-formations and their relations to matrices, and eigenvalues and eigenvectors are also covered. Since practice makes the man perfect, there are a good number of problems that stretch the thinking power of the learner. The problems are graded from easy to those involving higher order thinking. By its virtue the book inculcates that mathe-matical maturity which students need in their current and future courses to grow up into mathematicians of substance.