Math 419 - Linear Spaces and Matrix Theory (Winter 2021)

Instructor / Office hours

Dr. Iian Smythe (smythe@umich.edu) / Wednesday 10:00am-11:30am on Zoom.

Lecture (remote, synchronous)

TTh 8:30am-10:00am on Zoom.

Textbooks & Resources

All material (including Zoom links, homework, recorded lectures, and lecture notes) will be posted on the course Canvas site.

Required textbook: Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, Wellesley Cambridge Press, 2016.

Course outline

An introduction to linear algebra: the study of spaces of vectors and the transformations that act upon them, as represented by matrices.

We will cover topics from chapters 1-8 in Strang, including systems of linear equations, vector spaces and subspaces, bases and dimension, linear transformations, orthogonality, determinants, eigenvalues and eigenvectors, diagonalization, and the singular value decomposition (SVD). Other topics (difference equations, complex matrices) may be covered as time allows.

Our course will be both theoretical and computational; students will be expected to develop a conceptual understanding and write simple proofs involving the fundamental notions, as well as master algorithms to solve concrete problems. We will have an eye towards the applications of linear algebra in science and engineering, including statistics and data science.

See the course syllabus (PDF, Google Docs) for more detailed information on course format, evaluation, and expectations.