Linear Algebra

Course Description

Vector spaces, linear transformations, matrices, systems of linear equations, bases, projections, rotations, determinants, and inner products. Applications may include differential equations, difference equations, least squares approximations, and models in economics and in biological and physical sciences. MATH 0520 or 0540 is a prerequisite for all 1000-level courses in Mathematics except MATH 1260 or 1610.

The core theme is the essential equivalence of algebra and geometry (envisioned by Descartes) in the simplest case: degree 1. Another feature is the interplay between the concrete (matrices) and the abstract (vector spaces). Students often describe this as their first real math course, in contrast to the formulaic approach of their previous experience.

The topics of this course include matrix algebra, systems of linear equations, row/column operations, equivalence relations, determinants, eigentheory, characteristic polynomials, diagonalization, quadratic forms, vector spaces and linear transformations. We'll also consider a few applications of linear algebra, such as linear differential equations, least squares regression and regular Markov chains. This material will prepare students for further study in computer graphics (projections), linear programming (simplex method) or econometrics (linear models).

Prerequisites: Recommended prerequisite: MATH 0180, 0200, or 0350. May not be taken in addition to MATH 0540.