First Exams Getting Closer

Now that the first exam is only seven weeks away, it is time for a résumé of the past months of studying. The distance learning university is operating in two-week long cycles. For each of her courses, the student has two weeks to absorb the content of the current chapter and work out answers for the problem sheets. The answers are then submitted for review. Some of the courses offer online submission, while others still require you to send in your answers by mail. This brings back memories of when I was preparing for Externenabitur, sending many letters to Germany (and sometimes faxing, but that is not an option now). The reviewed work will be sent back to you eventually, with the reviewer's side notes pointing out mistakes or alternative solutions. How long it takes for your work to be reviewed varies across courses—01141 Mathematische Grundlagen turns out to be particularly slow, while it usually does not take long for the PDFs and Maple worksheets that I upload for 01202 Elementare Zahlentheorie mit Maple to become available for download from the course's online exercise system annotated and scored.

The problems vary greatly in difficulty and relevance for the exam. While some make you practise things that are a sine qua non, or algorithms that are good for snatching some points on an exam (like solving systems of linear congruences using the Chinese Remainder Theorem), others are more luxurious, and solving them requires going a bit more in depth with the concepts or theorems around which they are built. There is an expression I remember from when I was still in school in Germany, where you were told that it is sufficient for a problem sheet to be sinnvoll bearbeitet—which means that your submission should document that you have made an effort, and that your efforts are at least in line, mathematically, with the problems, not completely off. Sometimes I can just tell something is too hard for me, and at the same time not really worth the effort, because I am almost certain that a similar problem would never feature in an exam. Sure, there is solving it for learning's sake, but when it is something like the transformation of a differential equation with calculations that are simply horrendous, come on...

Ah, yes, differential equations. I did not know what I was getting myself into there. I booked the course after I had started working on my other courses already and it seemed like I might stomach a little more workload. Turns out that most of my studying has gone into ODEs this semester. I did have some previous knowledge of multivariable calculus, but generally speaking there was much catching up to do, and never really having dealt with differential equations before, it could feel like my brain was being mangled a bit sometimes. WTF is a Bernoulli, WTF is a Riccati, how do I obtain an integrating factor that depends on x + y... Those who are more advanced probably just laugh at this stuff. I think I got more used to it gradually, although some of it still seems like magic where you shift terms around for a while until you finally arrive at something that resembles a solution of your equation.

As for my studying 'technique', there are not many intricacies involved at all. The gist of it is that I do some (at least ~2.5h) deep work every day, for which it is necessary to get up early on weekdays, because there is no way I am doing this when I come home from work. Loop Habit Tracker (a 'Seinfeld Calendar' app for mobiles) helped me kick off this habit, but now that it is established, I do not need the app anymore. Getting up is mostly automatic, and the concept of 'willpower' does not seem to apply. I enjoy sitting at my desk in the early morning hours, when I can see the dusk of a new day through the skylight. Granted, I do not get the amount of sleep that is usually recommended, and I would be in denial if I thought it did not affect me, but you learn to operate yourself as best you can while fatigued. Sleeping in is still enjoyed on weekend mornings.

For a long time now, I have had that thought in the back of my head that it could be fun to try my hands on a little public self-tracking. And what better opportunity than when I can combine the self-tracking with documenting my math studies. So I finally got a tiny external webcam, which is now taped to my desk and pointed at myself. The next thing I needed was for my computer to periodically take a snapshot, and after I looked around for a solution, I concluded it would probably be simplest to write a bash script that invokes a command-line webcam app. The scripts may be found here, mostly so I have them stored somewhere, and my new github is not completely empty; but maybe they'll be useful to someone who would like a similar setup. One of the scripts solves a problem that I had with my pictures' timestamps being off after uploading them to Google Photos. The quick fix was to just add geolocation to the JPEGs using exiftool. On Google Photos, I am collecting the pictures in weekly albums which are public and linked to in this part of my site.

As far as the actual exams are concerned, time will tell. Shortly. I reckon I can do it. These past days and weeks I have spent much of my study time practising with previous years' problems, which makes the amount of knowledge I need to have activated seem more manageable. The school conveniently offers the exams in Zürich, so that is where I will be going. Needless to say there will be another update some time after the last exam—or after the results are back.