# Group Theory Tonight at BU

Just a reminder:

This evening at 17 o’clock, or shortly thereafter, we will be meeting in Boston University mathematics territory to discuss group theory. Ben will be leading the discussion, poking us to consider the various transformations of the type

$$f: \mathbb{R}^2 \rightarrow \mathbb{R}^2.$$

What are the different structures of interest which these mappings can preserve? What types of maps preserve distances, angles, areas, orientation (chirality), or topological properties? Notes for past group-theory sessions are available in PDF format, or as a gzipped tarball for those who wish to play with the original LaTeX source.

# Are We Covering the Wrong Subjects?

Uh-oh. It looks like the time Ben has spent teaching groups, semigroups and monoids might have all been for naught. Just look at what Dr. Ray has to say:

Cubicism, Not group theory.
If ignorant of the almighty
Time Cube Creation Truth,
you deserve to be killed.

Killing you is not immoral –
but justified to save life on
Earth for future generations.

# First Session on Group Theory

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.