I’ll preface this semester reflection by saying this: I’ve just arrived home from West Lafayette, and am now quarantining at my second cousin’s guest house in Pasadena. I feel very lucky to be able to quarantine, and to do it in such a fashion that it is a vacation. I feel very lucky to have been able to continue my studies during this time as well. The semester wasn’t fun all the time and it certainly wasn’t easy, but regardless I am extremely thankful to have had the opportunity to learn over the last 16 weeks. It’s a privilege and gift that I am making sure to not take for granted. Okay. Now we’re ready to begin.

I spent a lot of time navigating my way through brick walls this semester. Some weeks they were just a couple feet high, and other weeks they seemed nearly insurmountable. At the time, I didn’t realize what I was facing, or how it would help me; it was only once I read the quote above on my first night back in California that I realized what had happened, so I wanted to take some time to reflect.

This semester, I took my heaviest course load yet: 17 credits, 3 CS classes and 2 math classes. I was also a supervisor for the 3D printing club at Purdue, fulfilling orders at home and then bringing prints to campus, as well as TA’ed for CS 180. Along the way there were a lot of brick walls; impossible deadlines, impossible topics, impossible questions that twisted my mind in ways I didn’t think were possible. Below are the brick walls I remember the most, and how I surmounted them:

Real analysis

When I mentioned above that some topics seemed impossible and posed impossible questions, I was referring to real analysis. This was my first real pure math class; before I had taken a proof-based linear algebra class, and a discrete math course, but this was a whole different endeavor compared to those.

I knew from the jump that this class was going to be a series of brick walls for me, since I’ve never been the best at math, so I began preparing over the summer. I read Jay Cummings wonderful real analysis textbook, which also taught me an important lesson: don’t read just to read. I read this entire book and absorbed nothing; I skipped end of chapter exercises, didn’t rewrite crucial proofs, and I was rewarded by having no more knowledge of real analysis than when I had started. This was an important lesson for this class; simply being present wasn’t going to cut it. I would have to actively engage myself and go beyond what is normally sufficient in other math classes. This meant being honest with myself about when a proof or concept just didn’t click in my mind. You can’t get over a brick wall if you refuse to look at it. So, about every week or so, I found myself being honest, admitting things to myself like “I honestly do not understand how to prove that a sequence is Cauchy” or “Quite frankly I do not understand uniform continuity past its geometric interpretation” or, the big hitter at the end of the semester “I understand all these concepts but fail to bridge them together to solve complex problems”. At the beginning, addressing these was like pulling teeth; it meant going the extra mile and watching YouTube videos and extra lectures and doing proofs from my textbook until they made sense and I could thoroughly explain each step to myself. The hardest was spending an hour on a concept in the hopes of being able to cross it off of my To-Do list, only to have to admit to myself that while that particular brick wall was now a foot shorter, it was still there.

Now at the end of this course, I can see how much it has changed how I think. Proving calculus to myself has shown me how to construct arguments from smaller building blocks, and how to prove concepts thoroughly and succinctly. It has been a great and almost startling experience; there are times I would be reading from my differential equations textbook and they would assert a theorem with no proof, and it seemed almost blasphemous. It prompted me to go beyond the scope of that course and prove these concepts to myself, which helped my understanding greatly. Likewise, I saw my understanding of CS theory improve, as I was able to think more creatively about certain computational problems, and construct better proofs for my homeworks in my data structures and algorithms course. One of the highlights was making a connection between this class and my numerical methods course; a fixed point iteration scheme will converge to a root if it is contractive. Neat!

This cements the important conclusion I have come to: surmounting brick walls as they come makes all of those in the future just that much shorter. Keep at it, and you will be rewarded.

late mornings and early evenings

Quarantine makes you notice things you never cared for before the pandemic because you never had enough time to give them thought. For me, the thing I noticed was how late the sun rose and how early the sun set during late Fall and early Winter in Indiana. In the semester prior, I had been too busy rushing to a class, lab, or club meeting to care when it got dark outside. It seemed trivial. But now, here I was, getting up everyday at 6 AM, getting ready for a day that consisted of me cross the 5 feet from my bed to my desk, and staying there for essentially the whole day, studying, finishing assignments, and watching lectures. I didn’t mind this at the beginning of the semester, as I rose with the sun and got to see the morning light hit the flat Indiana landscape. But now I was waking up hours before the sun rose; I was working in darkness until I slept and waking up and once again working in that same darkness. It was a brick wall I hadn’t expected. At first, I just tried to power through it, taking a ‘mind over matter’ stance. As you can imagine, willing your Circadian rhythms away is an arduous task that I had little success with. I got more proactive, and began going on runs when I woke up. That allowed for a productive time shift that let me begin work at my desk at least when the sun was rising, instead of when it was still pitch black outside. However, I still felt the fatigue of the semester. It began to feel like I was just ticking things off of my To-Do list. I loved the course material, but had fallen into a bit of a routine. I knew what to expect, and what I had to do to be successful. I had lost a bit of that X-factor in your day that makes things interesting.

Then a particularly hard project for the CS course I TA got released. It was kind of the culmination of everything they had learned up until that point, and tested them on some key and tricky concepts. Suddenly my office hours and lab sections were flooded, and I couldn’t have been happier.

While I was facing brick walls in my own courses, I now had many students coming to me with their own, and I was in a position to help them resolve their problems which felt really good. In addition to the brick wall they themselves brought to the table(“I have a null pointer exception”, “My code doesn’t behave how it should”, “I’m not passing test case X”), there was also the mini challenge of teaching them how to solve their problem, or why their error was occurring. Each student has a different way of learning, and so sometimes I would explain something how I remember it(a direct mapped cache is like a row of book shelves!) and I would ask if they were following what I was saying and they would respond with ‘not quite’, aka the polite way of saying you are speaking gibberish. So, it was back to the drawing board, to figure out a way to get them the information they needed without directly telling them to write certain lines of code. This whole process, of being presented with a bunch of mini brick walls and helping students overcome them really helped me. It was a perfect productive distraction from my own school work, and while it didn’t completely solve the fatigue I felt from daylight savings and the semester, it certainly helped. I had one student who, upon finishing this challenging project, emailed all the other TAs who had helped him and myself, saying ‘thank you’. It made my day, and reminded me that if I can help these people overcome their own brick walls, then I can surmount mine too.

conclusion

I had expected this article to be longer and more comprehensive; I had plans to go on to Brightspace(the class management service Purdue uses) and total up how many hours I spent watching lectures, maybe how many lines of code wrote. . . but I think some things are better left unknown, so I’m going to end this here. There were other notable brick walls for me, but I’m content to let them begin to fade. This was a good semester, with lots of challenges and lots of rewards. The brick walls came, and they went, and it’s nice to be on the other side of the 16-week-long brick wall I was looking at at the beginning of the semester that seemed nearly impossible. I’d be lying if I said I wasn’t excited for next semester though; I have so many new classes to look forward to and so much to learn. Onwards and upwards, right?