Groupy

Due to my mathematical ineptitude, I'm not very fast at solving problems in group theory. This can have disastrous consequences on examinations. So, in order to correct this deficiency, I asked my algebra professor where I could obtain problems similar to those that will be on our final. My plan was to practice speed by doing heaps of problems in rapid succession. Her most useful suggestion was to look on the web for preliminary and qualifying examinations given to graduate students. Many reputable schools publish their old exams or lists of practice problems to assist graduate students in studying.

The preliminary exams were not particularly useful due to their very broad content. On the other hand, the qualifying exams for Ph.D. students are in more specific areas like algebra or even just group theory. I downloaded a few exams, and started tackling the group theory questions. As I worked through more and more problems, I realized to my surprise that these problems were often easier than the ones on our exams. This was not uniformly true: Berkeley and Harvard had a few tricky questions on which I was clueless. Nevertheless, I think it's fair to say that the problems and exams in my class are at least as hard as the qualifying exams given to graduate students at reputable institutions (maybe not the top-10 for mathematics, but still good places): Dartmouth was mostly trivial, Rochester was mostly doable, and others didn't seem too bad.

Damn algebra.