# Prof Life

## WMC REU, day 2

My group decided to meet daily at 10 am for the first week, which gives me plenty of time each morning to do some research work (that’s when my brain is at its freshest).  I started at 7:30 at The Gov Cup where I made some progress on merging several drafts of The Paper.  Some ideas for streamlining some of the mathematics also occurred to me.  Why use cases if you can help it, right?  When I reached the point where I would need a new a hard copy of The Paper, I turned to outlining a different paper. (This one is work from the past year with my senior research fellow.)  It was hard to shift gears that quickly between projects, though, and I was disappointed with my work on the outline.

During the meeting with my REU students, we talked about how the research reading went.  This discussion led us to create a list of terms that we should define.  We started with one they all knew as a baseline (“ring”) and ramped up to a special kind of ring (“standard graded k-algebra”, where k is any field).  The classic example of a standard graded k-algebra is a polynomial ring over k where each variable has degree 1.  We also defined “module,” “graded module,” “Hilbert function,” and we did some examples.  The research project possibilities all include working with a quotient of a polynomial ring by a homogeneous regular sequence (also known as a “complete intersection”).   Thus, I focused my examples on quotients of the polynomial ring by homogeneous ideals.  We started to talk a bit about free resolutions and Betti tables, too.  Based on our morning session, I assigned some homework.

By afternoon, my triple latte had worn off, so I spent some time on the general bureaucratic professor stuff I alluded to yesterday. I’m about to start my third year at Hamilton College, and that means I have to start putting together my reappointment materials.  Instead of creating any of these materials, I made a list.  Then I made a more precise list.  Then I added due dates.  Then I decided that it’s summer, so that was enough for one day.  Back to the fun stuff!

To round out the work day, I read a bit ahead of where my students were in their research papers with an eye toward what we might talk about next time (free resolutions, Betti diagrams), and I prepared a few examples to clarify some definitions (I hope!).

## Greetings from the Willamette Mathematics Consortium

Today marks the first day of the WMC REU. I never went to a formal REU as an undergraduate, so I’m a first-timer just like many of the students. My first task today finding a suitable coffee shop for my summer caffeinated home base. (I settled on The Governor’s Cup, which sports an exposed brick wall, generously-sized table tops, and coffee that’s roasted in-house).

Although I’d corresponded with my three research students via email, it was a treat to meet them in person. All nine of the students seem like good people, in fact, and so do the other research mentors. It’s rare to find a group where there isn’t a single unlikeable person (which leads me to wonder if, in reality, I’m the unlikable one? Nah…).

Besides having found a coffee shop that will inevitably see many hours of work on my part, I have an office in the mathematics “hearth” at Willamette. I haven’t had much experience visiting places for long enough to have an office; I find myself distracted by trying to calculate the number of math books I have in common with the usual owner. In my professional opinion, it’s a big number. We also have several climbing guides in common. What is it about math and climbers? (One of the REU students is a climber, too.)

In my first meeting with my group, we talked about the basics — scheduling, their goals for the summer, my goals for the summer, project possibilities, and, of course, homework. Since the homework required starting to read research papers, we talked about how to do that.

They had plenty to do for the day, so we broke and I spent the afternoon working on revising a paper that I’m writing with my graduate advisors. If I can get the paper out of my hands by next week, I’ll be a jubilant mathematician. After a productive session, I outlined some of my other summer goals. I’ve got other research work to do, and some general administrative professor “stuff” that I have been, well, lazy about getting done. While I feel well-prepared for my role as an REU mentor, I would like to wrangle some resources together in case they’re helpful.

It’s been a fun day!

## What the wha? Bernoulli’s theorem, applied.1

Today, as part of the AGAM camp, the girls had a mini course on aerodynamics. And then we flew in tiny airplanes.

I wish I could say that this post was going to contain some math, but really, I’m just going to post pictures.

I got to steer the plane, to everyone’s dismay.

But despite my lack off subtlety and grace, no high schoolers were harmed this evening. And now, I think I’ll look into flight schools!

## All Girls/All Math

All Girls/All Math 2014

This week, I’m teaching one of the parallel “Codes and Cryptography” classes at the All Girls/All Math camp at University of Nebraska-Lincoln. It’s so much fun to be in a room full of budding mathematicians from all over the country, and it reminds me of what it felt like to love the idea of math before getting too deep into any particular specialization.

I’ve made a few resources for the class, which I’ll drop in this post as the week continues.

Obviously, the rock climbing links come first…:
Rock climbing and teaching math

And here are some relevant math links:

The Bletchley Circle on PBS:
http://www.pbs.org/program/bletchley-circle/

A quick review of the symmetric cryptography systems we talked about on Day 1:
http://animoto.com/play/x7rvb7VPhZZWbFKdzH3J0g

Here’s an article about a new kind of space race — the race to bounce perfectly secret codes off low-orbit satellites using quantum cryptography:
http://www.technologyreview.com/view/528671/the-space-based-quantum-cryptography-race/

For encrypting and decrypting messages, you can play with the web apps at http://www.cryptoclub.org.

And after the jump, there’s an except lifted from a blog post by Cathy O’Neil at mathbabe.org:

## Undercover at an Algebraic Combinatorics Conference

Before I went to graduate school and became a commutative algebraist, I did a little work in graph theory. It was fun! I proved theorems! My mentor/coauthor Josh Laison provided a wonderful introduction to the fun inherent in doing research.

Well, roughly a decade later, I found myself at an Algebraic Combinatorics conference in honor of Chris Godsil’s 65th birthday (whose book with Royle was my introduction to Algebraic Graph Theory almost *exactly* 10 years ago). It’s exciting to see that some of the work we did is still relevant.

It’s also a lovely drive to get to U. Waterloo from Hamilton College. In fact, on the way home, I spent a night camping on Nairne Island at the Upper Canada Migratory Bird Sanctuary. It was the maiden voyage for my new solo tent, and I had plenty of math to think about in the peace and quiet!

Sometimes when I say I’m going to work at a coffee shop, I realize that it sounds like I’m changing careers. But today is the first time I’ve been mistaken for an actual employee at an actual coffee shop. My latest, greatest thought was just interrupted by someone earnestly claiming to be one of my customers. I was very confused until we both realized what was happening.

I guess I’m a natural. Good to know there are options if I don’t like being a math prof!