PhD 2023 #001: Baptism by fire (How I failed my first exam as a PhD student)

According to investopedia.com, "baptism by fire is a phrase originating from Europe that describes an employee that is learning something the hard way through a challenge or difficulty."

I regret to start this series with this post. But this experience prompted me to document it all. Something to look back to when all is said and done.

So here’s what happened. I just took my first exam as a PhD Math student. And I did poorly. Not zero, but pretty bad.

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 Our first long exam on Abstract Algebra was on the 20^th . I asked to take the test the day after because I didn’t have enough time to finish the exam that day. I had other obligations. Also, I haven’t studied anything. No notes nor printed copies of the reference book which is Algebra by Hungerford. How could I? I haven’t attended a single lecture. But that’s not an excuse not to prepare beforehand. More on that later.

So the exam day came. And I failed miserably. There’s only one question that I was confident at. But even then I still had doubts. It was about equivalence relations which I was familiar with because I studied it for my Master’s thesis. The rest was a desperate attempt at gaining partial points. So I got 1 out of 5 questions correct. That’s 20%. Maybe 25% if the professor feels generous.

Few things stood out. First, one of the questions there was inadvertently shared to us by another professor in another subject. He was sharing an experience he had while taking an exam as a PhD student. It was about the dihedral group and its subgroups. Of course, I didn’t take it seriously. He was just sharing his experience, right? I mean, what were the odds that it will come out in our exam, too? Highly likely, apparently. 

Another was about Cayley’s Theorem. I’m quite familiar with it because my thesis was in Algebra. Semigroup Theory in particular. But I only remembered the finite case of Cayley’s Theorem. A finite group of order n is isomorphic to a subgroup of the symmetric group Sn. I’m sure there’s a more general statement but at that moment I can’t recall. I only know about the finite case because of my thesis. Otherwise, I wouldn’t know what it’s about. But even if I knew the finite case, I didn’t even know how to set up the proof. Where do I start? What function should I define? I had no idea. I was blanking.

Which brings me to the other question which is about the action of a group. What the heck is an action of a group? Action on what? In that moment, while I was taking the test, I had no freaking idea. Of course, I now know what it is. It was in my notes from 8 years ago. Which is kinda frustrating. But anyway, an action of a group on a set is simply a function from G x S to S. If such a function exists satisfying certain conditions then we say that a group G acts on set S. Quite simple really. If only I took the time to learn it. Or at least attempted to memorize it. Of course, I didn’t do any of that.

And that’s when I realized that I will get stuck if I don’t know the definition of a term. It’s very important in mathematics. If I knew what an action meant, that would have given me an idea how to proceed. But no, I went in there blind.

Because of this, I suddenly realized the gravity of the situation. I guess what frustrates me more is that the exam wasn’t even that hard. If I just did my due diligence, if only I studied weeks earlier, maybe I had a chance of passing it. Maybe.

But that’s the thing though. I didn’t specifically know what the topics were because I haven’t attended lectures. Not that I’m making it an excuse. I’m not. It’s just that scope is too general when I base it on the book only. There’s a certain calm that you feel when you know first hand what topics were discussed in class. Having no idea of what was discussed leaves room for doubt and anxiety.

Nevertheless, it was all my fault. I should have searched for my old notes weeks ago, not a day ago. Printed the reference book a month ago, not a day ago. Oh, well. Lesson learned, I guess. A bitter one at that. It’s a wake up call, for sure. No room for complacency. Remember, what you’re giving up to do this. You’re leaving your job for this.

Did I get overconfident? Probably. Definitely. Now, I know what I’m getting into. I need to recalibrate my efforts. And do better next time. Preferably excellently. I need to offset that deficit. And cramming never works. Not at this level.

So this is what it feels like to be a student, huh? I forgot.