Concerning Qualifying Exams

Let’s just get this all out on the table. Yes, I’m staying in Iowa City for the summer and doing math the whole time, but to what purpose? Two words: Qualifying Exams. It seems that few people outside of academia understand what I mean by “Qualifying Exams” (or “quals” for short), so hopefully this entry will be a good reference point for what I’m to undergo and how it will be affecting my summer in Iowa City.

The first year: Pre-qualifying

When you enter graduate school in Math (at Iowa at least), your first year is kind of like a super-college rigmarole in which you’re taking classes that should be mostly review (but usually they aren’t) so that you can be brought up-to-speed on the mathematical foundations you’ll need to continue on in your program, start researching, get some results, write them down, and get a PhD in anywhere from 4 to 6 years. The best adjective I’ve used to describe this year is “whirlwind-ish” – at least that’s how it was for most of us. There’s five two-semester courses you could take in your first year:

  • Abstract Algebra,
  • Topology,
  • Analysis,
  • Differential Equations, and
  • Numerical Analysis.

Every graduate student in math, whether they’re pure or applied (I’ll make a post about pure math vs. applied later and then hyperlink it here) has to take three of these in their first year. Taking four at once is possible but not recommended. Five would be suicide. If you’re one of those “poor unfortunate souls” in the pure program, you usually take the first three in your first year and then take Differential Equations your second year. If you’re one of those impertinent folks the AMCS track, you usually take the bottom three your first year and then Topology your second year. If, however, you’re in the AMCS track (AMCS itself merits its own blog post) and your name is either Alex Bates or Rajinda Wickrama, you ended up taking Topology, Analysis, and Numerical Analysis your first year and then must take Differential Equations your second year.

This first year is, on the whole, not the most pleasant experience in the world. One of my colleagues wrote an excellent article on her experiences in her first semester of graduate school in math, much of which I would echo. I would not, however, say that things improved much for me during second semester, other than a greater emotional, mental, and spiritual stability gained mostly through having a daily routine and being a part of my church community. On the whole, things seemed to be a little tougher academically even though we had mostly transitioned to the pace of graduate life. And being a TA wasn’t getting any easier. (Being a TA also merits a post.)


But now, mercifully, I am writing from the other side. I finished my finals and am done with that first year. But now a darker and more ominous challenge lay on the horizon: the aforementioned Qualifying Exams. So what are quals, exactly? And, as the name suggests, what do they qualify you for?

In short, quals are exams that you as a graduate student must pass by the end of your second year to continue on in the program, pick an adviser, start researching, etc. They are offered every Fall and Spring, and usually students take the qualifying exams at the beginning of their second year (for me, August 2017) and in the three subjects that they studied during their first year of graduate school (for me, Topology, Analysis, and Numerical Analysis). There are three “grades” given for performance on the qualifying exams: PhD pass, Master’s pass, or fail. You need to get a “PhD pass” on the three that you take to qualify yourself to continue on in the PhD program. Since I’m in the PhD program, that’s my goal- pass all three at the PhD level. However, there’s a convenient exception if you take them all in August after your first year: it suffices then to PhD pass only two of them and Master’s pass the third.

Moving forward

So, this is essentially what I will be doing all summer: studying for the qualifying exams. At the time of this post’s writing, I have 79 days to go before my first qualifying exam, but it’s not as if I don’t know the material yet – I studied it all this past year. Nor will I be like one running aimlessly or like a boxer beating the air (1 Cor 9:26), but my TA’s from my courses this past year will be holding preparation classes for the qualifying exams during the summer. And the folks in AMCS have generously awarded me with a summer fellowship so I can singlemindedly pursue my studies without having to worry [too much] about money.

So that’s why I’m in Iowa City this summer. And that’s what I’ll be spending my time working on most hours of most days from now until August. But since Iowa City is (apparently) a wonderful place in the summertime, when I’m not indoors studying for 50+ hours a week, you’ll probably be able to catch me outside at the various farmers’ markets, movies on the Pentacrest, or random events I’ll do with folks from my church.

So if you’re someone who knows me personally, please cut me some grace if I ever seem frazzled this summer or “out of it”. If you’re a person of faith, I’d ask you to pray for me that I would do my work with God-glorifying diligence, competence, and creativity. If you’re someone in my program, feel total freedom to and by all means push me this summer to be a better mathematician; I will do my best to reciprocate such efforts. And if you’re not a mathematician, enjoy your summer of not having to do math!


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