It’s hard to explain the qualifying exam process to non-math-grad people, but I’ll try… It’s a pass/fail exam and you can’t advance in the program without it. Here, they offer 5 or 6 different specialty areas, and you have to pass exams in 2 different areas within 5 total attempts. I took my first attempt at my first exam yesterday. The way the algebra exam is structured here is that it’s broken down into 3 categories: groups, rings & fields, and modules & linear algebra. Usually there are 12 total questions (4-3-5 or 4-4-4) and you are supposed to do 8 complete problems with at least 2 out of each section. The exam we got yesterday had 15 total questions, 5 in each section, and we got to choose 8 problems with at least 2 from each section. So, we got more selection than usual. The problems are complex and long, and you basically are not allowed to assume anything – you have to build all the math you need from scratch.

The general understanding I have is that you have to turn in 4 completely correct solutions for the grading committee to even consider passing you. If you turn in 6 or more completely correct problems, you’re almost guaranteed to pass. If you turn in something in between there, the committee basically votes on whether or not you deserve to pass. I fall into the last category, the one where my fate is now in the hands of the committee. I turned in 7 problems. I’m confident that 4 of them were pretty much completely correct. The other 3 I turned in were of varying completeness. On two of them I was just missing one little part of the argument (well, I think it was a little part, but if that was those parts turned out to be the major point of them putting the problems on the exam, the committee might think I missed the whole point and not give me any credit for it). The last problem I turned in was a pretty easy 2-part problem that I’d done before. I couldn’t remember the trick to the second part, though, so I’m sure that won’t earn me any points. I didn’t have enough work done on any of the other problems to think turning something in would help so I didn’t turn in an 8th problem – hopefully that doesn’t count against me…

So, now I just wait. It’ll take anywhere from a week to a month to find out if I passed. If I failed, I have to decide if I want to retake it in January or in August.

In other news, there’s a week until classes start again! I have to plan the course I’m teaching in that time. Other than that, I intend to relax and do whatever I want. This will likely entail sitting around the apartment watching movies and TV on DVD pretty much nonstop. I may do some reading, recreational or mathematical, but I haven’t decided yet. I also have to send some letters and e-mails and maybe make some phone calls since I’ve been basically incommunicado the past few weeks because of the qual.

Ah, nothing beats this feeling. Life is good.