Learn a new theorem in combinatorics, group theory, or representation
theory and communicate it in written form.
Minimum Requirements
Each student will focus on a different result.
The written document will introduce/motivate, correctly state, and
prove a theorem. It will also include at least one interesting
example, construction, or special case illustrating the theorem. The
article will be as self-contained as possible. The new document must
be typed, be at most eight pages in length (with one inch margins and
a 12pt font), and be available in PDF format.
By design, this assignment is very open-ended. Students are strongly
encouraged to explore examples. Students are also encouraged to
formulate, test, and prove their own conjectures. Here are some
questions that you may want to consider:
What was the original motivation or historical context for your
theorem?
Can you give more than one proof of your theorem?
Does your theorem have any interesting specializations or
important applications?
