Yesterday evening, we had our first seminar session on the group theory track, led by Ben Allen. We covered the definition of groups, semigroups and monoids, and we developed several examples by transforming a pentagon. After a brief interlude on discrete topology and â€” no snickers, please â€” pointless topology, Ben introduced the concept of generators and posed several homework questions intended to lead us into the study of Lie groups and Lie algebras.
Notes are available in PDF format, or as a gzipped tarball for those who wish to play with the original LaTeX source. Likewise, the current notes for the entropy and information-theory seminar track (the Friday sessions) are available in both PDF and tarball flavors.
Our next session will be Friday afternoon at NECSI, where we will continue discussing Claude Shannon’s classic paper, A/The Mathematical Theory of Communication (1948). The following Monday, Eric will treat us to the grand canonical ensemble.