Automated Enumerative Combinatorics
Experimental Mathematics used to be considered an oxymoron, but the future of mathematics is in that direction. In addition to learning the philosophy and methodology of this budding field, students will become computer-algebra wizards, and that should be very helpful in whatever mathematical specialty they are doing (or will do) research in.
We will first learn Maple, and how to program with it. This semester we will learn, from an experimental mathematics point of view, algorithmic enumerative and algebraic combinatorics. The final projects may lead to published papers. People who already took previous editions are welcome to take it again, since except for the basics, there is very little overlap with previous editions.