Now, that might seem like a silly reason to be happy or indeed to write a blog entry, but I've just been realizing some very cool things while sitting here. Basically, at the beginning of the course, my notes where about 80% English, and consisted mostly of little notes in the margins which were my attempts to understand what the professor was saying - though not always just because it was in German. The sidebar notes were mainly due to the fact that there were lots of things that I was mathematically unfamiliar with that were assumed to be common knowledge at the start of the course. That was the main reason for my confusion in Stochastics this semester- the first few weeks, I was so busy learning the background information I needed that I couldn't be learning the stuff they were actually teaching in the course in time with the lessons and homework. At least, it started that way.
I'm sitting here with my cup of tea and just watching the evolution in my notes into almost complete German, with the occasional comment in English on the side (usually something non-Mathy - such as the lyrics to a song that I had stuck in my head, z.B), and I also notice these giant, darkly scribbled question marks and highlighted areas of the notes where I obviously desperately didn't understand the math or steps in question - and it's all so clear to me now. I've learned SO much in this last semester. Unlike most classes in which you simply further your knowledge that has already been growing for a while - for example, you might have already known how to differentiate or integrate, but by the end of another more advanced course, you can differentiate more complicated things, maybe do more tricky integrals than you could before - in these courses, I've learned to do things of which I had absolutely no knowledge before.
Now, in Complex Analysis, this might not be the case - at least, not as much. In that class, we basically did learn how to "do more tricky integrals" and a whole lot more (though by the end of the class, it's gotten to the point that I can't explain what we're doing to a non-math person without seriously sounding like I'm making it all up on the spot... it's a rough time when someone asks you for an example and you have to say "Well, I actually don't know that there are any, but we can prove that they must exist, somewhere"**) - but in Stochastics and Programming? I didn't even know the subject of Stochastics existed before I came here, and computer programming was as foreign to me as riding a unicycle. And it's amazing to be able to see progress like that. I think when we keep taking courses inside our comfort zone, or at least inside our zone of familiarity, it's easy to feel like we're not moving forward.
But now, the main question: will I still feel so inspired and chummy with my courses when I have to take the exams starting in a week and a half? I'll let you know the answer to that when I know it.
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The other mind-boggling thing is just how LITTLE I know in the realm of mathematics. I've had several eye-opening experiences to do with that in the past year - attending the Nebraska Conference for Undergraduate Women in Mathematics, attending the Carleton College Summer Math Program, and just looking through the different courses offered here -- how can such vast worlds of knowledge exist when so few people know that they do? I'm sure Chemistry has just as many facets and paths and eye-opening processes of which I am totally ignorant, and to think that every subject must, every aspect of learning must - that is truly mind-blowing. In fact, it is so mind-blowing that when I truly think and try to understand just how mind-bogglingly-huge the complexities are, I devolve into a classic teenager and just have to say, quite rightly, DUDE. WOW.
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