Description: This course prepares a student for research in the mathematical sciences on a specific topic. Each section is dedicated to a different topic. Current topics include eigenvalues, model reduction, combinatorial optimization, optimization algorithms, scientific computing, and numerical analysis. The topics may vary each semester. This course covers the same lecture material as CAAM 499, but fosters greater theoretical sphistication through more challenging problem sets or projects.
FALL 2014:
We will introduce and study the most common Matrix Groups, prove the fundamental results of Representation Theory for Finite Groups and apply these findings to basic questions in Quantum Mechanics and network design in Theoretical Mechanics and Theoretical Computer Science. In particular, we will
1) characterize the full electronic spectrum of the buckyball,
2) construct a large class of Buckminister Fuller's tensegrities, and
3) construct expanders (large graphs that remain well connected and yet have relatively few edges).
Recommended Prerequisite: One course in Linear Algebra.
Cross-list: CAAM 499. Repeatable for Credit.