In any case, I still have a few moments to take a deep breath and do things that I want. Therefore, what have I been up to? My last post is sometime in mid September, since then so many things have happened.
- I am applying for graduate school in the US. It is as much fun as it sounds. So far it involves an incredible amount of bureaucracy, writing and browsing, but the situation has been good so far. I got the Fulbright scholarship, which means that there is somebody doing most of the bureaucracy for me (applying to six universities on my behalf, five of which I would have happily applied to myself) and offering to pay for my first year of studies in the US. The results of my standardized tests have also been good (and now follows a detailed description of the tests I've taken):
- I've demonstrated I can speak some English with my TOEFL test. That's just a normal English test involving some reading, some writing, some speaking and some listening. Nothing too ambitious, less absurd tricky grammar questions (compared to CAE&CPE), the format of the questions was easy to get used to, so if someone chooses to "train" for the test, it's more about improving English than just standardized useless questions. Surprisingly the only thing I cannot do very well is to speak about familiar topics. Well, perhaps I am turning into an introvert. Who knows.
- I've almost aced my GRE General score, if you don't look at the results of my essays. Those would have been superhard for me even in Czech. This test is a longish one, with some random English part, Math part and the aforementioned tricky essays. The Math part was easy to train for and also lots of fun, because the questions were just high school mathematics, occasionally sprinkled with questions resembling very simple Olympiad math reasoning. It was precisely what I liked: questions that were doable with hard work and preparation, but if one had the luxury of time, one could save lots of time just finding a smart solution. And the English part was fun, part of it was about reasoning about the text and careful reading, but a huge chunk was just these funny questions with 1-3 blanks and lots of choices for beautiful random English words: the task is to get a general feeling of the message of the sentence and then choose a combination of words that together make the most sense; typically all the words could be used to fill the blank, but only one combination would give a meaningful sentence. I like that a lot.
- And finally GRE Subject math, which is just a speed test in calculus. There are many past tests available and good books for review questions, so practice makes perfect I guess. Funnily enough, none of my practice tests ever went over 800 (on a scale to 900), but my final score was much better. I did enjoy revisiting first year mathematics and answering again all the questions about limits and derivatives, I also managed to use up a stack of scrap paper that I had been hoarding on my desk, so I guess it help. Of all the tests, this was the most important one, where preparation was essential. I think I did just enough to obtain a fairly decent score, more preparation probably would have helped to make me more confident, but that would have meant maybe a few months instead of 2-3 weeks.
- I am attending some courses. Some of them I am attending more often than others, sometimes there is simply too much homework to actually go to school. It sounds ridiculous but given that my classes are in Amsterdam and Utrecht, going to school means spending 3-4 hours a day on public transport, and sometimes I simply don't want to invest so much time into getting to school. But I have been quite lucky with my classes:
- I am immensely enjoying my class in commutative algebra. Both our lecturers are good in the class and if I forget about all the homework I messed up, there is just lots of math I enjoy: all the integrality questions and dimension of (affine) varieties is really dear to my heart. Also, most recently we talked about Hilbert series and Hilbert polynomials and understanding these brings so much joy into my life (because they just tell you so much about the ideal / variety / meaning of life). Except for the policy on homework that is ridiculous: it does make me a way worse mathematician. We are forbidden from discussing the (graded) homework with other students, we have a page limit on our solutions, which just damages the writing skills so much. I think imposing a stigma if someone wants to ask a question is the worst thing a teacher can do to their students and also encouraging people to write math in large blocks of unintelligible text full of shortcuts (because nice layout and indenting takes up space, you know, let alone diagrams, equations and god forbid careful case distinction) is also in the opposite direction to what should teachers do. Still, the material in the course is good and luckily there were only three graded assignments, so now I can happily talk to people about commutative algebra again...
- Another excellent class is my p-adics course. We are closely following the book of Koblitz (p-adic things and zeta functions in the name). The instructors are amazing and the homework is just the best homework I have seen: really engaging, interesting questions for which we have just enough tools to solve them, the problems do not take hours to type down and I've just felt so happy doing most of them (except for one part of the lastest homework sheet that stressed me out incredibly much). I don't actually like the things we are doing in this course, all the analysis and series and such, but it does make me feel like I am learning a lot and I am simply getting so much from this course.
- I am taking some more algebraic geometry, too, because there's never enough algebraic geometry. Some of the lectures have been a bit hectic, but the homework is fun, the things we are doing are engaging: we still only talk about varieties, but knowing a bit more from the viewpoint of sheaves just helps me appreciate the beauty of the classical theory even more. I think I am not precise enough in all my statements about geometry, so it is also a good drill having instructors that are far from lenient in mathematical reasoning. Just good practice and like I said, there is never enough algebraic geometry, especially for someone like me who has never really bothered learning it properly...
- Then there's the Galois representations. The course is fairly advanced and we are covering so many new topics that it is a bit over my head at the moment, the homework typically takes the whole week to sink in and understand what one is supposed to do. But I am taking my time, slowly getting through all this representation stuff. But it is getting too far into representation theory, in which I just have to take so much stuff for granted, that it doesn't make sense to me to try to understand it so deep: there are too many gaps still left. I will see how that goes further, I have already learnt so many interesting things from there so I hope I will be able to consolidate the knowledge at some point.
- I would almost forget about algebraic topology, well, that's in Utrecht, so that doesn't happen to me that often. Also, most of the homework has been standard homological algebra, took too long to write down (seriously, typing down the homework shouldn't take twice as long as solving it). But it's a fairly standard course in algebraic topology so I hope I know what I am doing.
- And Dutch. I am almost fluent in Dutch now, well, at least in my personal dialect that includes a lot of made up words from English or German. People don't understand me very well but I don't understand them either, so I guess we are even. I still have a few months to continue learning, so hopefully the mutual understanding will only improve.
- I've been also living, at least a bit. We started baking with my flatmates, so far only simple things, but brownies are always good and the marble cake we had was also amazing. We also dare to cook some more interesting dishes than pasta (which is what I would cook for myself basically daily), with the pinnacle so far being a leek quiche and spinach pancakes. I am running a bit, exercising and trying to get fit again.
- And I have mostly been in Leiden. I like it here. Seriously. This is an awesome place. Come and see for yourself!
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