Elements of Abstract and Linear Algebra

HAL (Le Centre pour la Communication Scientifique Directe), 2021

This text is intended for a one-or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

2015

The tone and level of mathematical sophistication of these two chapters is considerably different in these two chapters from those in the others. Much more background is expected from the reader interested in these sections.

The principal change from the first edition is the addition of a new chapter on linear programming. While linear programming is one of the most widely used and successful applications of linear algebra, it rarely appears in a text such as this. In the new Chapter Ten the theoretical basis of the simplex algorithm is carefully explained and its geometrical interpretation is stressed.

ii This is a supplement to Abstract Algebra, Second Edition

Begin the abstract here, typewritten and double-spaced. A thesis abstract should consist of 350 words or less including the heading. A page and one-half is approximately 350 words.)

Linear Algebra and its Applications, 1992

This two volume set of texts is designed to provide material for a course of up to one full year at the undergraduate level. It requires as a prerequisite some knowledge of calculus and complex numbers, but little mathematical