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 each illuminating and contributing to understanding of the other.  In this course we will survey several topics that involve significant aspects of both matrices and polynomials, including companion matrices, permutation matrices, circulant matrices, difference equations, Fibonacci numbers, cubic and quartic polynomials, diagonalization and Jordan form, minimal polynomials, the Cayley Hamilton theorem. 

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.