First Post

Well, I got to this a little later than everyone else, but hey, I'm not enrolled in the course! I'm just going to learn everything you're going to learn and not get credit for it. Tah Dah!

My name is David Gross. I am a senior Mathematics Major at HMC and I have a Humanities concentration in Literature. I am taking this class because I would really like to learn some higher mathematics my last semester at Mudd, even if I don't have room in my schedule for it. I took Fields and Waves from Sahakian and learned a lot at the time, but can't quite use tensor notation fluidly (a.k.a. I may have done poorly or less than my best during that course). As such I feel this would be another way to robustify my skills.

My favorite equation...that's tricky. Here's one of my favorites though. Check out this dimensionless ODE:

dx/d&tau = rx(1- x/k) - x^2/(1+x^2)

You can think about x as the percentage amount that a population of bugs is over a critical amount at which birds start preying on them. You can think of r as the growth rate of the bugs and you can think of k as the carrying capacity of the bugs in whatever environment then live in.

What's interesting about it? In the two dimensional parameter space, (r,k)-space, there is a region where the bugs go into refuge, and there is a region where there is a bug outbreak. However, there is also a bistable region where both stable states can exist. This is because the parameter space is the projection of a cusp of a catastrophe surface, and seasonal changes in the predation parameters, carrying capacity, and growth rate (which happen) can lead to a hysteresis loop (like it does). Hooray!

Here's a fact: My favorite cheeses are Bleu Cheeses, even though my mom hates them!