Blog: Confessions of a Mathematician

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).

Well. Phew. The first year is over! I have so much to reflect on, but instead, here’s some new stuff on the horizon: Next year, I’ll be on the Honor Court. First real committee work, and I hope that it will let me see some of the best students at Hamilton upholding the (student-driven) ideals of the college. I’ll teach Modern Algebra for the first time, and I’m unspeakably excited.

New Comic Book Day Pull-List: ‘Numbercruncher’ Reviewed

The following NPR story starts with an anecdote about Kepler. Apparently, he was trying to find himself a wife, and he had 11 candidates, but he was too thorough in interviewing them (read: slow!), and they all got impatient and rejected him. Damn. Turns out, if you have limited options, the best strategy for a good match (though maybe not the best match) is to interview 1/e (~36.8%) of your candidates without offering the “job” to any of them.

Man’s mind, once stretched by a new idea, never regains its original dimensions.

— Oliver Wendell Holmes

When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?

— Enrico Bombieri

As you probably know, I wear my heart on my sleeve:

Well, I took the golden opportunity (ha!) to bring the golden ratio into Calc 2 this week, using it (and its little pal ) to find a closed formula for the -th term of the Fibonacci sequence.

The ubiquitous Fibonacci sequence! It’s something you may have encountered out in the wild. You know, it goes a little like this:

so

And let’s say for some reason, you need to cook up . I hope you have some time on your hands if you’re planning to add all the way up to that. Instead, wouldn’t it be nice if we had a simple formula that we could use — i.e., a formula that was not recursive — to figure out the -th Fibonacci number?

Luckily, such a formula exists, and there are lots of ways to find it. In this post, we’ll find it using power series. Read on, brave blogosphere traveler.

As you might imagine, starting a “real” job entails a certain amount of stress. Suddenly, your support network of graduate student friends is dispersed across the country, and you’re one of a handful of junior faculty across a smattering of disciplines. So, you have to find new outlets for your stress. Aside from climbing at the rock wall a few times a week, I’ve found that it’s incredibly helpful to have a creative outlet. This brings me to…