Author Description

This book prepares the reader to cope with abstract mathematics, specifically abstract algebra. It can serve as a text for prospective mathematics majors, as well as for those students taking or preparing to take a first course in abstract algebra, or those in applied fields who need experience in dealing with abstract mathematical ideas. Learning any area of abstract mathematics involves writing formal proofs, but it is equally important to think intuitively about the subject and to express ideas clearly and cogently. The author aids intuition by keeping proofs short and as informal as possible, using concrete examples which illustrate all the features of the general case, and by giving heuristic arguments when a formal development would take too long. The text can serve as a model on how to write mathematics for an audience with limited experience in formalism and abstraction. Ash introduces several expository innovations in A Primer of Abstract Mathematics. He presents an entirely informal development of set theory that gives students the basic results that they will need in algebra. The chapter which presents the theory of linear operators introduces the Jordan canonical Form right at the beginning, with a proof of existence at the end of the chapter. - Publisher.