Reflections on my Abstract Algebra class (MA 453)
Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream.
“Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”
–Lockheart’s Lament
I’m staring down the exam paper. Sweat clinches the front of my neck, my hands shaking. What was a Galois field again? Were all groups of a certain order just isomorphic to GF(n)? No, that couldn’t be right. How did we even formulate this notion again? Maybe I should’ve studied more. Maybe I should’ve understood this content on a deeper level, to make it intuitive—just like I had done with physics.
It was a dream. I wish it happened.
I took MA 453 this semester, expecting a rigorous and challenging curriculum - after all, it was about group theory. It had to be hard, right? In the beginning of the semester, I did actually suffer a bit. I found myself sitting at a 67% with the grader mercilessly bashing each line of my proof. I actually found myself enjoying the struggle though - I knew it meant that I was actually growing!
As I contested the grader’s policy and read the textbook though, I quickly found myself feeling much more at ease. The professor agreed that the grader’s policy was “too harsh” and when it came to the exam material, I found myself at ease with midterm #1. There were some questions that required a second or two of thinking, but not more.
As the weeks went on though, I quickly found myself feeling a bit bored. By the time the second midterm rolled around (this time about rings), I found myself feeling a bit too comfortable. And when the exam came, I found myself almost falling asleep by the sheer unoriginality of the problems - they were near duplicates of the ones in the review sheet.
After that midterm, I found myself feeling disappointed. Down.
I knew that I aced that exam, but I realized that it meant I was in a position too comfortable to really grow. So I emailed the professor asking for some harder questions
Dear Professor,
I have a request for our upcoming final exam. Would it be possible to add some extra hard/interesting problems in group theory that requires one to think outside the box? Perhaps even harder than the ones on the homework/textbook.
I feel like it would make the exams more interesting, while also providing a challenge for the students who are seeking one. It can be worth very few points or none at all just to make the content seem more interesting.
I am just stating this because I felt like the second midterm was too tedious, and the problems felt too standard.
I’d appreciate a few extra bonus problems (worth very few points or just for fun) that would engage my mind a bit more.
Sincerely,
Kai Liu
My email went unanswered. The class average was a 67%.
Some Raw Reflections
“Our outer selves are mere reflections of our inner self.”
I did not grow in taking this class. I was never challenged. Below is a rant about the class that summarizes everything pretty well, before I continue.
It did not feel like a class. It felt like a self-studying seminar with little collaboration among most of the math students at Purdue.
I felt alone, weary, and tired. Math was always interesting, motivating, and fascinating to me. This math was not—it was too sterile, too uncreative, and too boring.
It was uninspirational, and a complete opposite of everything that I knew and loved about math. I hated it. I hated myself for not pushing myself hard enough. And I hate the fact that 4 years later, I’ll probably forget it all—with about 100 hours wasted.
Why did I even take this class in the first place???
There’s a lesson I’ve learned in my first semester at Purdue:
I can take “hard” math classes without truly learning math.
I can take on “awesome” research without expanding my worldview.
I can surround myself with friends while still being lonely.
I can join seemingly technically challenging clubs without truly growing.
I can do things without growing from them. I was doing things that I thought would be hard without really assessing how it would fit with my current self. I did not pay enough attention to my own qualities or formulate my own purpose, but instead gave the reins to these other opportunities which took me in circles.
The Greater Implications
College isn’t like high school anymore.
The high school mentality focused too much on external metrics—GPA, extracurriculars, and attaining amazing awards in competitions.
I did those well. But now it’s time to change.
College should be a time of personal growth. A time to deeply reflect on our current purpose and take on or start opportunities that align with this. With the freedom, the solution space is far larger, so it requires purposeful exploration in informed directions rather than meaningless meanderings.
It is not the time to prioritize fancy titles, cool-sounding clubs, or classes. It is a time to prioritize our own inner growth—before you do take on something, ask yourself: am I doing this for my inner self or to improve my outer image? If it’s the latter, then drop it immediately. If it’s the former, then pursue it with all your passion.
We all only have one life. You can waste it on chasing titles, but you’ll die looking like everyone else. You can spend it on true inner growth, fundamental alterations to our character, way of thinking, and experiences. Then every future second will feel more fulfilling than the last. Death will not seem so ominous, nor will you care about how you look after.
Maximize the present. Forget the past. Don’t worry about the future.
Today is the only guarantee that you have.
Live it.
“Quit; don’t quit. Noodles; don’t noodles. You are too concerned with what was and what will be. There is a saying: yesterday is history, tomorrow is a mystery, but today is a gift.”
–Master WuGui