Abstract Algebra

Description

The end of the 19th and the beginning of the 20th century saw a tremendous shift in the methodology of mathematics. Abstract algebra emerged around the start of the 20th century, under the name Modern algebra. Its study was part of the drive for more intellectual rigour in mathematics. Initially, the assumptions in classical algebra, on which the whole of mathematics depend, took the form of axiomatic systems. No longer satisfied with establishing properties of concrete objects, mathematicians started to turn their attention to general theory. Formal definitions of certain algebraic structures began to emerge in the 19th century. The results about various groups of permutations came to be seen as instances of general theorems that concern a common notion of an abstract group. Questions of structure and classification of various mathematical objects came to forefront.
This book presents a lucid and unified description of Abstract algebra at a level which can be easily understood by the students who possess reasonable mathematical aptitude and abstract reasoning. 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 and goes on to cover Groups, Rings, Fields and Linear Algebra concluding with the coverage of Eigen values and Eigen vectors of matrices.