Linear Algebra

Course Overview

Linear algebra is arguably the most theoretically well understood and most widely applied subject in all of undergraduate mathematics. Calculation and theory go hand-in-hand in this course. The topics covered will include the following standard concepts: solving systems of linear equations, matrices and linear transformations, image and kernel of a linear transformation, vector spaces, coordinates relative to different bases, determinants, eigenvalues and eigenvectors, orthogonal projections, the Gram-Schmidt algorithm, and least-squares approximation. Applications to physics, chemistry, and other sciences will be included throughout the course. The geometric interpretation of results will be emphasized.

Homework and other assessments will include a mixture of concrete computations and proofs of elementary theoretical results. The utility of computers in finding solutions to linear systems cannot be denied. However, at least initially such calculations will be done by hand, not just because they build character, but because they build intuition.

The coverage and pacing of topics in this semester-long class are similar to that of a true college course. As such, this course is intended for students with a proven record of accomplishment and interest in mathematics.