Course Description and Outline

Linear algebra is a branch of mathematics that is central to modern mathematics.  It is a study of vector spaces, also called linear spaces, along with linear functions that input one vector and output another. We will learn the theory and computational techniques that have widespread applications in the natural and social sciences, industry, finance, and management and range from finding the solution of a system of linear equations in several unknowns to game theory and Google’s PageRank web search system.

The more general objective of this course is to continue providing you with a deeper understanding and working knowledge of mathematics, while in the process strengthening your analytical skills, increasing your ability to communicate mathematics symbolically and orally, making you comfortable with reading and understanding mathematics on your own, and continuing to develop your appreciation for abstract mathematics. In particular, a strong emphasis will be placed on proofs and proof techniques.

We will cover the first three chapters, as well as selected topics from the fourth and the fifth chapter, of Hefferon’s Linear Algebra, a free textbook. Topics will include vector spaces, subspaces, linear independence, bases, dimension, inner products, linear transformations, matrix representations, range and null spaces, inverses, determinants, and eigenvalues.