Wednesday, December 15, 2010

All Done (Mostly)

I still need to write a teaching philosophy statement, but other than that, I'm all done with my first semester of grad school. Woot.

The analysis exam was not as dire as I had anticipated. We had to do 6 problems out of 9, and I finished 5.5 problems. I don't think my answers were completely correct, but the fact that I'll be getting graded out of 90+ points is very cheering. I got a 55% on the midterm and I don't think I'll have less than a 75% on this exam, so that's a large improvement. Given that our professor has told us not to worry about grades (including telling one woman who did much worse than I did on the midterm specifically not to worry about her grade), I'm expecting a B in this class.

The logic final (our only exam in that class) was today. As expected, it consisted of basic skills from the class rather than proofs or things that required us to have memorized a lot of the theorems and tricky things from the assignments. Given that I needed less than 50% credit on it to have an A in the course, I'm fairly secure in that A.

I also think I'll have an A in probability and in my math pedagogy class. That gives me a good GPA for the semester and means that I passed all of my courses (meaning that I got at least a B), which is really what counts. So: woot!

I need to do better in analysis next semester, though. The main key in that class seems to be working through the exercises in the book, so I'm going to plan to do that. Another student in the class and I are planning to work together to read the sections and work on the problems before the material is taught in class, so that if we have questions we'll know what they are in advance. We'll see how that works out, but hopefully I'll have time; I think my course load will be easier this coming semester. (I will need to make time whether I have time or not.)

Now I have a month off. I feel weird about it already. The next semester doesn't start until mid-January. (Yes, this is where you people with real jobs can want to kick my ass. Believe me, I get it.)

Coming up next semester: statistics, the second half of real analysis, and an introductory topology course.

Monday, December 13, 2010

The Probability Exam

Today, we had our final exam in Probability. I got a perfect score on the (very easy) first exam, and then did very poorly on the second exam. Fortunately, the two questions I couldn't answer on there (worth 32/100 points) were left mostly blank by the vast majority of the class, and the professor took them away, so that I ended up with a 90%. Nevertheless, it was a bad testing experience.

I had had an analysis exam the previous day, that I'd done very poorly on, and as I sat to take the probability exam I was exhausted and really couldn't think straight. I hadn't prepared well for it at all, and couldn't do basic things like subtract correctly (even using a calculator) or perform simple algebra tasks, much less think creatively about problems.

I felt reasonably well-prepared for this exam - the last few weeks, the material has seemed to come together for me much more than it did in the middle of the course, and I had good formula sheets written up - but I also worked hard to be rested, correctly fed, hydrated, etc., for the exam. I knew that I would need (because both probability and tests in general demand it) mental flexibility in order to be able to answer the questions.

And I did it. I completely killed the exam - I should have a perfect score, or at least within epsilon of a perfect score. (Really I could have as low as a 95% - who knows what weird errors I could have made - but I definitely got the questions basically correct.) And I didn't just kill the exam by being prepared; I killed it by being smart (relative to my baseline) and mentally flexible.

One question asked us something about three independent random variables, each uniformly distributed on the interval [0,1]. (For the "probabilists" out there: we had to determine the CDF and expected value of the minimum term. Pretty easy stuff.)

The next question asked us to consider the same three variables, and then had some questions that only involved two of the variables. I had a few moments of confusion (of the type that totally derailed me on the secon exam) before realizing that the irrelevance of the third variable meant I could draw the standard [0,1]x[0,1] box and fill in the areas I was being asked about and do the computations using areas (e.g., "What is the probability that Y1 > Y2 given that Y1 > Y2^2" - which is the just the ratio of two areas, given that the distribution is uniform).

The exam wasn't hard either, I should admit, but it did take me just about the entire time.

There were five problems (some with multiple parts) worth 15-20 points each, and then the sixth problem was worth 6 points. He's urged us to consider these last problems as pretty much optional, even though they are part of the full score. If you make sure you can do the basic problems, then it's OK if you can't do the fancy problem. But this fancy problem turned out to be exactly the type of fancy problem that I am good at. It went something like this:
An urn contains 6 red balls and 14 blue balls. Two balls (selected at random) are removed and discarded without noting their colors, and then another ball is drawn. Given that this last ball drawn is red, what is the probability that both of the two discarded balls were blue?
This is exactly the kind of thing where if you just draw a little probability tree it is pretty obvious how to compute it. (I shouldn't say it's "obvious." Many things in probability should be obvious but take me a long time to figure out or I can't figure them out at all. But this type of problem is intuitively easy for me, for whatever reason.)

I have my analysis exam tomorrow, which is triple express doom, and then the (low-stakes) logic exam on Wednesday. After that, I have to write a [maximum] 3-page teaching philosophy and fill out a short survey for one of my courses, and then I'm done.

Monday, December 06, 2010


My life is so weird and messed up lately, and the worst part of it, I feel like there is almost nobody I can talk to about it other than Ed. It feels like he is the only one who actually understands all of our bizarre circumstances well enough to get it. But talking to him is hard on both of us.

I can't get over him and our break up, and I don't even know how to try. I feel a deep bond and partnership with him that isn't going away. I miss every single thing that we had together and no longer have. A lot of the time I would do anything to go back a few weeks and do things differently. (I'd go back further than this, but even the night he broke up with me I didn't make an effort to stop him. We had just started making things better. But I was so worn down and it felt so inevitable that he was leaving me - he had been so relentlessly dissatisfied - that I couldn't fight it anymore.)

I can't express even these simple feelings to people very well, because I just don't say ridiculous things to people even when I feel them. I think this makes me seem robotic or something, but I don't know how to change that about myself. Also, I don't want to say bad things about him to our mutual colleagues (and, even if I'm sometimes tempted, the truth is that in my heart of hearts I don't think he did anything wrong, and he's been amazingly kind and supportive all along).

It would probably help if I didn't see Ed all day every day, but I don't want him to go away either. I certainly can't stand the idea of moving or of having him move and then having to get a new roommate. I want us to continue having this close friendship that we still have.

My life is just really hard right now.