Linear algebra is one of the most useful and practical courses in the
mathematics sequence. It is used extensively in computer science (particularly
computer graphics), physics, engineering, and even accounting and finance.
Although its main objects of study -- linear, or "flat" functions -- seem
simple, they also are very powerful tools for understanding
*non*-linear functions. In fact, an important way to investigate a
non-linear function is approximate it (locally) by a linear one. Indeed,
you are already familiar with this process from differential calculus:
the tangent line to a curve is the best linear approximation to the curve
at a point, so studying the tangent line tells you a lot about the curve,
at least near the point of tangency. This same idea is used to understand
the non-linear dynamics of phase spaces in physics, and financial trends in
economics.

You already are familiar with some linear algebra from Math
15. (Remember Gauss-Jordan elimination and matrix inverses?) We
will revisit these here is a wider context, and introduce a number of new
concepts, such as vector space, linear independence, and basis
vectors. We will use matrices to represent an important class of
functions, and will interpret them geometrically. Our final topic,
eigenvectors and eigenvalues, is one of the most useful ones for the
physical sciences.