Blog: Confessions of a Mathematician

Hooray, hooray! I have printing privileges! This development will seriously help with the paper writing. I envy all of the digital natives out there who don’t have to print a document to proofread it. Alas. That’s the way I learned, and my efforts to edit on-screen yield pretty poor results. Upshot: this is a game-changer. My REU students and I talked about one of my favorite mathematical topics (today, in the context of rings and modules): how do you tell how big something is?

Yikes. These past two days have not been particularly productive, research-wise — I think I made negative progress. Indeed, on Wednesday, I met all sorts of challenges that made everything harder than it needed to be. For example, I realized that I forgot to pack my cable for my external hard drive, rendering my collection of digital math textbooks inaccessible for now. This oversight is less of an issue for my research and more of an issue for assigning well-crafted problems to help my REU students learn the necessary background material.

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?

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.

Outrage Over Government’s Animal Experiments Leads To USDA Review http://n.pr/1BY5Y4q Some of the outrageous experiments in here seem even more offensive if you believe (as I do) that we have enough information to make a fairly good predictive model for some of these “empiric” questions. I find it morally objectionable that the government didn’t hire someone to sit down and do some math before condemning all these animals to horrific deaths.

Legend had it that, during the invasion, Archimedes was so engrossed in the study of a geometric figure in the sand that he failed to respond to the questioning of a Roman soldier. As a result, he was speared to death. After reading this, Sophie Germain concluded that if somebody could be so consumed by a geometric problem that it could lead to their death, then mathematics must be the most captivating subject in the world.

The argument I’ve always heard for why leaves or branches grow by rotating around a stem/trunk one golden angle at a time is that this is an optimal mutation. I’ve even heard this as an explanation for why clovers typically have three leaves. I’m not sure I understand how the thinking applies, since it seems to be about getting the most sunlight without completely overshadowing earlier growth, and this clearly isn’t a factor for a single clover.

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.

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…:

Bouldering vs. Top-Roping (vs. Lead-Climbing)

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:

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.