Matrices and polynomials are important areas of
algebra. Each topic is rich with
structure, properties, and applications.
The two topics are also closely connected, with knowledge of
and contributing to understanding of the other.
In this course we will survey several topics that involve
aspects of both matrices and polynomials, including companion matrices,
permutation matrices, circulant matrices, difference equations,
numbers, cubic and quartic polynomials, diagonalization and
The intended audience for this course includes advanced undergraduate mathematics majors, beginning masters students in mathematics, and anyone with an interest in polynomials, matrices, and their mathematical applications. Students should have completed a course in linear algebra, and at least one course emphasizing reading, understanding, and writing proofs of mathematical theorems. At American University, Math 310 Linear Algebra and Math 403/603 Foundations of Mathematics are such courses.