A Ramble About Qualifying Exams

This is my typical study environment. (Because Who needs a desk when you've got the floor?)

Today I'm talking about about qualifying exams! But no, I won't be dishing out advice on preparing for these exams. Tons of excellent advice is readily available online, so I'm not sure I can contribute much that isn't already out there. However, it's that very web-search that has prompted me to write this post.

You see, before I started graduate school I had heard of these rites-of-passage called the qualifying exams.* And to be frank, I thought they sounded terrifying. A sequence of exams, the results of which determine whether or not I'm 'qualified' to stay in the program? From the information I found online and from the first-hand stories I heard from actual graduate students, I was under the miserable assumption that it's impossible to pass these exams unless

  1. you're constantly depressed (and any accidental feelings of happiness should be followed by remorse)
  2. your health has sufficiently deteriorated due to lack of sleep, forgetting to eat, drinking too much coffee** etc.
  3. your only extracurricular activities consist of 1) crying and 2) re-evaluating your life goals

Sounds traumatic, right? Well, now that I'm on the other side of things, I'm happy to report that it was not that bad! Difficult? For sure. But impossible? No.

Don't get me wrong though! I'm not saying quals are a walk in the park. Far from it. And of course the experience is different for every student. Even so, I'd like to ramble on a bit about my trauma-free experience, not because I think it's interesting (it's not, truly), but just in case a prospective or first-year graduate student will Google, "how to prepare for math quals," stumble upon this post, and walk away feeling like all is not lost. (I personally savored 'qual success stories' before entering graduate school because they always gave me a glimmer of hope.)

 

the best part of taking a topology course is that one gets to use colored pencils on a regular basis. 

 

Now lest you think quals are manageable only for "extraordinarily gifted" students, let me be quick to say that I do not consider myself as possessing exceptional (or even ordinary) mathematical talents. What do I mean? To put it simply:

Math has never come easy to me. 

I just happen to love it.

A lot.

Interestingly enough, I didn't even like math until my sophomore year of college! And while I'm divulging all my secrets, I might as well tell you*** that I also did not earn a master's degree before entering my PhD program. (Some students may find their quals doable since they've seen the material previously in a master's program.) In fact I had never taken a graduate-level course before! This of course made the transition to grad school challenging. For instance, my algebra professor covered everything - everything! - I knew from college within the first three weeks of my first semester. Three weeks, people! THREE WEEKS. I felt as if I had had the mathematical-wind knocked out of me. 

 

Yes, i created flash cards for my algebra qual. you may think that's silly, but see that card in the upper left-hand corner? i had written incorrect information on the back of it, and one of my classmates pointed out the mistake in a group study session A week BEFORE THE exam. Embarrassed, i went home that night and carefully shored up my misunderstandings. And as it turned out, one of the problems on the qual the following week was based on the information on that very card. And you bet i got it right that time! (not surprisingly, it also became a blog post.)

 

Fortunately things have gotten easier as the semesters go on. Not the material, mind you, but the speed at which I can comprehend and analyze new material. It's very much like lifting weights. Your muscle fibers tear during the process and then they rebuild. Even though it's painful, your strength - your ability to handle greater loads - increases. 

But metaphors aside, I was well aware of my background, and so I started preparing for the quals from "day one." This just means that my one and only goal was to pass these exams. So I solved my homework problems, took lecture notes, took notes on my lecture notes, and studied for my midterm/final exams all the while knowing that the material could appear on the quals. I deliberately chose not to attend many seminars, or take special-topics courses or independent studies, or attempt to read articles/papers on the side. Now it goes without saying that this path is not necessary (or even helpful) for every student! It's just the path that worked best for me.

So here's the deal. At my school, we are required to pass three exams - offered each September and May - chosen from six subjects: real analysis, abstract algebra, topology, logic, complex analysis, and differential geometry. Some students take (and pass!) all three of their quals at once. But I chose to take one qual at a time. Here's what my timeline looked like, beginning with August 2014 when I first entered graduate school:

As you can see, I started studying for the algebra and topology quals five months in advance. Here, "studying" equates to working on problems from old quals, solving and resolving homework exercises, reviewing major theorems/proofs, asking lots of questions, and even starting a blog! Also, my classmates and I formed study groups, and this was a tremendous help.

I mean, t-r-e-m-e-n-d-o-u-s.

Admittedly, I'm not much of a group-work kind of person. I usually prefer to study alone. But I'm certain that I would have failed all of my exams if not for my classmates - who are amazing, by the way! - and their help. (If you're one of them and are reading this now, thank you!!)

 
some scratch notes i made the night before my topology qual. Pretty ain't it?

some scratch notes i made the night before my topology qual. Pretty ain't it?

 

Well, I think that's about it! So you see? There was nothing too exciting to report. Really, a qual is just one big final exam. And like any exam, you (presumably) devote 100% of your efforts from the start of the semester to avoid cramming/panic attacks/etc. So in that sense, the quals weren't such a big deal. But again, everyone's experience is unique. If you ask any other graduate student, they'll likely have a very different story to tell!

And as promised, I haven't (intentionally) given any advice on preparing for the quals. But if you are looking for some, this link might be a good place to start. Asking professors and other graduate students in your program for tips is a good idea as well. Of course, if you have any specific questions/comments, feel free to leave them below!

So to all those preparing - mentally or mathematically - for their qualifying exams, I wish you all the best!

 

 

* For those not in the know, the qualifying exams (a.k.a preliminary exams) are a series of two to four - depending on the university - written exams that graduate students must pass within their first year or two of study. Students who do not pass the exams are not able to remain in the program. (At my school, if we happen to fail an exam, we have exactly one chance to retake it.)

In some programs, such as mine, students must also pass an oral examination. In this exam, administered after the quals are passed, the student gives an oral presentation to a committee of faculty members on a specialized topic. Passing the oral exam is next on my agenda.

** Ha! Who am I kidding? There's no such thing as "too much coffee."

***I suppose my reason for sharing this is to let you know that one does not need to be a genius to pass one's quals. (Of course, it doesn't hurt either!) One does, however, need to work hard.