It’s been awhile since my last post. Alas grad school got out of hand again, yet optimism has flowed back once again. The last struggle I’ve had with grad school has been about failing my first phd comprehensive exam, in Algebra, back in January. I’m afraid my second phd comprehensive exam in Analysis, which I took in May, I didn’t pass either. Like with the algebra exam, however, I was borderline close. Unlike the algebra exam, however, I ended up getting a lot more advice of what to do the next time I prepare for the comps, which has been enlightening as well.
I did suffer from extreme anxiety when I wrote the exam, which was I believe is mainly due to the time constraint. Even with the extra time granted by the disability office, I still found the amount not enough for this exam, and I couldn’t seem to complete enough of these exams to pass and feel like I could’ve completed more on these exams if more extra time was granted. As such, I found it pretty difficult to pace myself which unfortunately caused a lot of anxiety when I took the exam, which I also feel had an affect on my performance.
I got the useful advice of putting pressure on myself to answer questions in as short as time as possible when I start studying again, which will help decrease the anxiety when I take the exams as well. A week before I wrote the analysis comp I did a dry run on an old comp I hadn’t even looked at a week before and thought the dry run went better than the real attempt so I’ll practice that more often. I also heard the department has had some successful PhD students who failed both comps the first time but then passed both the second time, which is encouraging as well.
And because I studied so hard and did all of the right things for the second exam, it has made it all the more apparent to me that timing is the real issue. And because of that I’ve been able to pull down the resources I need. My disability advisor actually completed a master’s in pure math at the University of Waterloo herself and attempted the PhD comps herself and knows what they’re like. We are thus currently coming up with a plan to get more extra time. She is also granting that shortly before I write the exams for real the second time that I write a few practice past exams at the disability office, which will make it easier to be more comfortable when I write the real ones. Another drawback on the analysis comp had been that my anxiety caused me to not even read past a few words on a couple of the questions, again the time constraint contributing significantly to this problem. With all the advice/resources described above, however, will also help eliminate this problem. I also made another visit to the psychologist I’ve been seeing and got some useful feedback regarding remaining positive and focusing on the process instead of the result.
Graduate school continues to be a struggle, but so far I have found that my struggles so far in it have resulted in a positive net gain overall that may have not resulted had the struggles not taken place. My first term of my master’s didn’t go that well, yet I persevered and as such I took twice as many courses covering a lot of areas in more depth in math. Had I not received five PhD rejections last year, I would not have had the opportunity to do original publishable research while still in my master’s (the paper of which I’m pleased to announce has been accepted for publication in International Journal of Number Theory and I will be presenting it at the Canadian Number Theory Association at U of Ottawa this week). Similarly, after I pass my comprehensive exams next year (assuming I do pass them and remain in the program), I will have spent twice as much time studying the material than if I had passed them the first time. It thus wouldn’t surprise me if this resulted in me being truly versed in both the broad branches of pure mathematics that are algebra and analysis. The material will be staying with me well after the exams and thus being that much easier to recall, teach, and apply throughout the rest of the time I do math.