Groups, Matrices, and Vector Spaces

Abstract Linear Algebra, Groups and Rings is an excellent introduction to the theory of groups, rings and fields. To emphasize the importance of a foundation of knowledge in both geometry and algebra, this text includes an introduction to Euclidean Spaces, and a brief treatment of algebraic topics such as matrix algebra, linear systems, vector spaces, linear coding theory, determinants, eigentheory, group theory, ring theory, and field extensions, even covering an introduction to cryptography.§This text has evolved from sets of notes from two different semester-long courses that the author has taught for several years at the University of British Columbia. The first portion of the book is from an undergraduate honors course on abstract linear algebra. The final chapters were developed from a course on the theory of groups and rings for math students. With content from these two courses, this book is ideal as a textbook for a year long course. Additionally, every sub-section of each of chapter ends with practice problems to aid in the understanding of the subject matter.§The readership does not need to have knowledge of calculus, but should have an understanding of mathematical induction and the notion of proof. Advanced undergraduate or graduate students in mathematics, physics, computer science, and engineering will find this book useful and enjoyable. The text can also be used as a supplementary text for various professional applications.