Engineering Education

I haven't told you where I go to school yet, and I'll keep that under wraps for a bit, though it wouldn't be hard to guess, I think. For the most part, our profs are amazing. They are really helpful, always available, and knowledgeable as well. This school is supposed to the best. The #1. Too often for my taste though, I find examples of substandard work in progress.
The other day, I was in my economics class, Managerial Economics. My professor (whom I really enjoy) assigned us a Lagrangian maximization problem. As a math major, this shouldn't be a big deal. Unfortunately, I consider myself to be lacking in the general knowledge of mathematics. Even though I should have learned Lagrangians long ago in Calculus 1, 2, or 3 (before my freshman year), I don't remember how to do them. I think most people don't, but as a math major, I feel like I'm sort of obligated to remember this type of thing.
This Lagrangian maximization was a bit special though, because it had an inequality constraint. After searching the internet up and down, old calculus assignments, asking a math professor, and asking my Econ professor, I finally discovered one way to solve such a problem.

To maximize (or minimize, of course) the function f(q) with a constraint such as q <= 300, you could add a "slack" variable in. Now my first intuition was to add a variable like 's', to make the inequality an equality like this: q+s = 300. Although you would expect this to work, when you take the partial derivatives, you will discover that the Lagrangian multiplier effectively disappears! The solution, it turns out, is to add s^2, rather than s. Mathematically, it makes no difference of all, of course. But when you take the partial of f with respect to s, now you get 2*s*lambda, instead of just lambda. Since this problem is now a nightmare to solve by hand, you need a good friend like Maple to do it for you. As a math major and an engineer, I am always trying to figure out WHY things work. It drives me completely insane that I have NO idea why you have to add an s^2 rather than s, since it should make no mathematical difference. But no one has been able to explain it to me, and no internet site had a satisfactory explanation. So I must accept it for now. The irritating part of this problem is that my Econ prof had no idea how to solve the Lagrangian maximization with the inequality. His solution was to "assume it was an equality". This means that you are assuming about 100 things about the function and its partial derivatives which may or may not be true. What if the constraint isn't binding (the global maximum is less than 300)? What if f(q) isn't parabolic? It's completely ridiculous to make such a rash assumption. I am appalled that such an invalid assumption is being made. It offends me as a student, as a math major, as an econ major, and as a inquisitive human being. You make wild assumptions in high school. Now it's time to play ball. You face all of your worst mathematical nightmares like a big boy and solve them.

You'll figure out soon enough that I'm pretty smart. I really don't like to brag about it, and I didn't even accept that I was smarter than most people here for a long time. I'm finally coming to grips with it though. I thought that by coming to "the best" that I would be mentally stimulated, but that isn't the case to an astonishingly large extent. Some days I am disappointed in my college, and its #1 rating. My roommate and I often wonder if it really is the best. And we are demoralized at the thought that it really might be. Could this be the best that the world has to offer? MIT wouldn't have me, though I don't know why. I suppose I don't play enough sports or something. I'm a CS major for crying out loud. I'm not supposed to play sports, that would make me weird ;-).


I was walking around the campus lake today, and I spied a very large turtle. It wasn't the largest turtle I've ever seen. It wasn't a snapping turtle, it was just the standard Speed Lake turtle, except monstrous. It was at least three times the size of the next largest turtle I've ever seen in the lake. He didn't mind me much, he wasn't even looking at me. I've always wondered how turtles grow inside their shells, and I do believe I've discovered the answer! This largish turtle was "shedding" the outer layer of his shell. I could see parts where the outer layer was gone, and there was dark, new shell underneath. The rest of it was all dried out and falling off.