I'll be teaching Math 172, Combinatorics, in the Fall.
Here's a blurb about the course:
- How many different 8-bead pearl necklaces can be made
using black and white pearls?
- If 50 people each bring one gift to a Christmas party and
exchange them at random, what is the chance that no one ends up with
their own gift?
- Are there any 3-dimensional shapes with exactly 10 faces,
18 edges, and 10 vertices?
- Given a network of roads, what is the shortest way from my
house to my Aunt Susie’s?
- How should I encode music onto a CD so that, even if it
gets a scratch, I can still play it?
These are the sorts of questions we will look at in this class.
In combinatorics, we examine discrete objects and do things like count
them, construct them, and find algorithms to analyze them. We
will definitely cover some enumeration and graph theory, and then we
will sample a few topics which might include generating functions,
polyhedral geometry, coding theory, and combinatorial games.
The catalog says that Math 55 (Discrete Math) is a prerequisite for
this course, but it is NOT at all necessary to have taken that. A
great thing about combinatorics is that we can start from scratch and
still cover interesting subjects. All you need to have is the
maturity and readiness for an upper-division proof-oriented course.
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