Crossroads

All of a sudden, I'm in the second semester of the M.Sc. program here. The classes are getting harder, which is to be expected, and all around me, the folks I have been studying with are going in their own directions.

Here's what I mean. In the Bachelor's program, there's a core set of classes that everyone has to take - you have to prove you've mastered the basics of the three largest areas of mathematics. Here, we call them areas A, B, and C.

A is for Algebra, which includes abstract algebra (groups and rings and things I've explained a bit on this blog before), number theory (questions about finding prime numbers, for example, or figuring out how the primes are distributed ((they're all clumped together at the beginning, 3,5,7 for example - and even for larger numbers, you sometimes get some that are really far apart, but every now and then, some that are right close together, just two apart, like 137 and 139. Can we come up with a theorem about when this happens?), and topology (shapes, shapes, and more shapes. I think I've written about this before, too.).

B is for Analysis, which is what we tend to call calculus in the US. But it's not just integrating and differentiating. In analysis, you also encounter things like manifolds, you do differential geometry, things like that. Remember the post about Hausdorff dimension?

C is for Numerical Analysis and Stochastics (Probability Theory). The second half of this area, probability theory, is something that I have never warmed to. Partially it has to do with a lack of intuition and instinct in this area, and partly with the fact that I've never had close friends who really enjoyed it. Someone can explain to me several times what the probability is that you will pull three queens of different suits out of a deck of cards if you put them back in each time- and within an hour, I will have forgotten the explanation. Numerical Analysis, however, is something that I am starting to discover now. It's all about trying to simulate phenomena that can't necessarily be computed exactly, the way we'd like to in the rest of mathematics. There's many applications in physics, chemistry, biology and other fields.

Footnote: apparently mathematicians aren't good with the alphabet. No, those letters don't match up with the subject names in German, either. I feel it would be less confusing to use 1,2,3.

So, these are the three areas. You have to take introductory lectures in each of those during your Bachelor's - (three courses in A, three in B, and one in Numerical Analysis and one in Stochastics). Then, you have some more open credits where you can choose which fields you want to look into.

In your master's, you are required to take at least six credits (a normal lecture + workshop) in every one of these areas, but that's the only distribution requirement. You also pick an area in which to do your "Vertiefung", or the area on which you wish to focus. This will be a sub-area in A, B, or C. And that's why in the Master's, people are drifting apart. They pick a direction and go and soon, it's hard to understand what they're doing if they have picked a direction different to yours. The basics that you had to take in your Bachelor's help you have a rough understanding of what the others are doing, but the specifics get pretty mysterious.

So, that's a changing dynamic. Another other dynamic? Well, these classes are getting hard. That might seem silly to say as we are talking about a master's program in mathematics, but still. I've noticed a big jump from  last semester to this one. In the meantime, you (as a student) also have a minor in which you take classes and in your Master's, you might very well take classes that are technically for Master's students in that field - even though you only have it as a minor. You notice the gaps in your knowledge.

That's one great thing that mathematics teaches. You know, and I mean know, when you have understood something and when you haven't. Three-dimensional understanding. Inside and out, can explain it and cannot forget it. That's understanding.  It's a beautiful feeling. You want it all the time. And you know there's not enough time to have it in everything you do, especially in your minor.

Don't get me wrong - we have a few people here who really can and do have that level of understanding in every class. It's partly because they put in more time and partly because, frankly, some of them are brilliant. It's easier to detect the brilliant ones later in your studies. At the beginning, when someone seems like they are brilliant, they could just be an asshole pretending.

I'm not one of those folks. I don't mean it in a "poor me" sort of way. I know I am smart and I know I have worked hard to understand what I understand. But I know who those people are and I know I am not one of them. And this semester, I can feel the speed being cranked up in the lectures I attend. In some of them, I can increase my pace and keep going but in some, it's a chore. It's like running on the treadmill at a speed just above the pace you can comfortably keep up. It's not that I'm about to fall off, nor that any one particular moment is unbearable - but it's hard to keep going at this pace. And this semester, I also have a lot of extracurricular things on my plate that are filling my time - and I don't just mean those silly luxuries of food, sleep, and exercise.

And just to sprinkle some spice on the top of this situation, I can feel my interests shifting. At this moment, I'm rather enamored with some classes in area C. Area C! Good grief, what has happened to me? I have been an A-girl since I first stumbled into a Linear Algebra class seven years ago. I feel like I'm having an affair. But I'm sitting in rapt attention in a class on computational fluid dynamics and that is exciting and scary. Because, of course, the next big question after all of these classes and credits are done is: what will your thesis be?

At the moment, I'm torn. I guess we'll just have to see what happens next.