3 Review(s)

Contemporary Abstract Algebra is a great tool for teachers and researchers of the subject as it provides detailed explanations of important concepts related to the subject. Summary Of The Book The study of algebraic structures like modules, groups, fields and rings is known as abstract algebra. Contemporary Abstract Algebra is well-structured and divided into five sections. The first section deals with Integers and Equivalence Relations, and makes readers aware of the basic features of the concepts. The book then goes on to describe different types of groups such as permutation, finite, and cyclic groups. It also provides thorough explanations of theorems. The concept of rings is presented to readers. It covers all the important aspects like factorization of polynomials, integral domains, divisibility in integral domains, and ring homomorphisms. An abstract algebra manual would be incomplete without discussing fields. Comprehensive descriptions of finite and extension fields, geometric constructions, and vector spaces are included. Important algebraic theories and concepts such as Galois theory, Sylow theorem, and cyclotomic extensions are presented in Contemporary Abstract Algebra. The group of orthogonal transformations of R' is thoroughly explained along with Jordan's classification of its finite subgroups. Apart from theory, the book focuses on training students on how to apply these theorems. It features several exercises and examples which deal with the roots of algebra in number theory. These useful exercises also lay an emphasis on theory of equations and geometry. The accurate solutions to certain questions are also part of the book. This edition even has another unique feature. It contains an index of famous mathematicians from history, which becomes a rich source of information for students. About Joseph A. Gallian Joseph A. Gallian is a celebrated mathematician and author. He has also penned For All Practical Purposes, Principles and Practices of Mathematics, and Mathematics and Sports. He was born in Pennsylvania, USA, in 1942. He studied at the University of Notre Dame, earning his Ph.D. He is a mathematics professor at the University of Minnesota Duluth. For over two decades, he even taught a humanities subject titled, The Lives and Music of the Beatles. The Mathematical Association of America presented him with the Haimo Award for teaching. He was also bestowed with the Allendoerfer and Evans awards, amongst many other accolades.