Linear Algebra: The Mathematics of Matrices and Vector Spaces

Intermediate—Fall

An introduction to both the algebra and geometry of vector spaces and matrices, this course explores various mathematical concepts and tools used commonly in advanced mathematics, computer science, physics, chemistry, and economics. Developing systematic methods of solving systems of linear equations is the underlying theme, and applications of the theory will be emphasized. Topics of exploration include Gaussian elimination, determinants, linear transformations, linear independence, bases, eigenvectors, and eigenvalues. Applications will be pursued in the realms of game theory, optimization and linear programming, network/graph theory, and medical imaging, among others. Conference time will be allocated to exploring additional applications of linear algebra or exploring another branch of mathematics. This seminar is intended for students interested in advanced mathematics, computer science, the physical sciences, and/or economics. Prerequisite: prior study of Calculus or Discrete Mathematics.