Publisher's Synopsis
It is known that linear algebra is a useful tool in engineering but, since the middle of this century, abstract linear algebra has also found more and more applications. For instance, finite fields play a prominent role in coding theory and ring theory is the foundation of linear systems over rings. Both linear and abstract algebra should now be in the curriculum of undergraduate engineering students. This introductory book on algebra aims to provide the basic material for such a course. It also constitutes a solid algebraic basis for the non-specialists who wish to become specialists in, for example, coding theory, cryptography and linear systems theory.;The important algebraic structures, such as groups, rings and fields, are introduced and the main contents of linear algebra are included. Many examples are given to illustrate the abstract concepts and the computational methods are emphasized. Finite fields and the canonical forms of the various kinds of matrices over finite fields are treated in some detail.;The book concludes with a chapter on polynomials over finite fields, which uses both the abstract and the linear algebra studied in the previous chapter.;The only prerequisite needed to read this book is high-school mathematics. It is suited to self-tuition. Exercises are given at the end of each chapter.
