Yesterday I completely finished reading and typing two years (four semesters) worth of algebra notes. (One year undergrad, one year graduate.) I’d been working on it with varying intensity and focus for about one month, so it feels really good to be done with that.
(Aside: For any non-math people that may still be reading out there, this is not algebra in the sense that you’re thinking. It has very little to do with solving 3x+4=7 for x. Here’s an example problem that is sitting in front of me right now: “If G is a finite group of order p^n for a prime p and a positive integer n, show that G has a nontrivial center and that for every k less than or equal to n there exists a normal subgroup of G of order p^k.” And that’s actually one of the easy problems.)
Now I’m in serious study mode. The plan is to work toward committing definitions, concepts, theorems, and proofs to memory. I ordered three linear algebra books from amazon today, and I’m borrowing other algebra texts from a colleague. These textbooks are reading material on top of the aforementioned in-class notes I’ve taken the past two years, and the notes that my graduate algebra professor posted online. I’m going to spend the next month and a half reading, learning, and most important: problem-solving.
In preparation, to know where I should focus these efforts based on past exams, I spent today reading previous algebra qual problems. I started at 9AM and have been working pretty steadily since then, with only a short lunch break (and now a short writing break). Within the first 30-60 minutes, I entered despair and thought “I’ll never know enough to be able to take a test at this level.” Then after lunch I started encountering problems I recognized (proven in class, done on past homework assignments, etc.) and thought “With some studying, I might actually be able to get a handle on this material.” And now, 5 hours into today’s work, I found one part of one problem where I thought “I could totally do this one completely correctly off the top of my head RIGHT NOW.”
I feel comfortable with the general concepts and most of the definitions of terms. In reading these past problems, I understand what they’re asking me to do (most of the time). I just need to practice enough to know HOW to do what they’re asking. If I continue preparing at the rate I’ve been working at this week, I think I can enter the exam room confident enough to not completely sweat through my clothes and start crying uncontrollably. The pressure placed on math phd students with regards to qualifying exams is unbelievable, but I’m trying to overcome that stress and be a realist. We’ll see how it goes.
Leave a Reply