
Numerical range and pseudospectra of operators
I would like to do a reading with some students about the numerical range and pseudospectra of operators. We will start by looking at matrices, and if time we will then see how what we have learned about matrices may apply to infinitedimensional operators. By the end of this reading students will learn about the…

The Unified Transform Method for solving partial differential equations
Fokas at Cambridge discovered the unified transform method (UTM) for solving initialboundary value problems. The method is more general than the traditional classical methods of Fourier and Laplace, and not more complicated to use. We will discuss the method, applying it to a variety of problems, including some that cannot be solved using the classical…

Topics in Number Theory
I’ll assign readings that include examples as well as concepts and ask the students to supply proofs, for instance to find proofs by induction of the formula for the sum of the first n squares, or for Fibonacci numbers in terms of the nth power of a matrix. I’ll have them study concrete number theory…

Dynamics Done with Your Bare Hands
Exploring the basics of some important examples of dynamical systems, following the book “Dynamics Done with your Bare Hands”