Subtitle: Algorithmic Algebraic 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 algebraic combinatorics, and the powerful theory of symmetric functions. This is a beautiful subject for its own sake, and approaching it from the standpoint of computer algebra will make it crystal clear.
In addition to the actual, very important content, students will master the methodology of computer-generated and computer-assisted research that is so crucial for their future.
There are no prerequisites (in particular, no prior knowledge of Maple, or any programming experience, is assumed). Also, no overlap with previous years.