Introduction To Abstract And Linear Algebra

Introduction to Abstract and Linear Algebra

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.

Introduction to Abstract and Linear Algebra

Linear Algebra

Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.