Wow, what a year! I hope everyone reading this is doing well and taking care of themselves. All things considered, I do not have much to complain about other than being stuck inside since March due to the pandemic. Despite a rough semester, I finished strong thanks in no small part to the excellent professors and classmates I had the privilege of being with. I even had the opportunity to join a summer research project (more on this below).
It has been a long time since I have written anything. Part of the reason for my silence earlier in the year was how busy I was with school. More recently, the reason has been a general lack of motivation or ability to do things. I suspect it is a side effect of being stuck inside for so long with so little exercise or social interaction. It has been difficult to motivate myself to read or write, or to do anything that does not have a firm deadline attached to it. Once I noticed this, I knew I had to make some changes. I’ve since been eating healthier, getting more exercise, and being more diligent about setting small goals for myself around reading and writing. It has helped. As a continuation of those goals, I am returning to writing on this blog.
As a quick review of my spring semester: it was a busy one. I had five math courses and one non-math class. The math courses were numerical analysis, abstract algebra, complex analysis, an algebraic topology reading course, and the second semester of advanced engineering mathematics (which was essentially a course in Fourier analysis). Honestly, it was a lot to handle and was not made any easier by the pandemic interrupting the semester halfway through. The one nice thing about having so many different courses at once was that I able to see more connections between areas than if I had just taken one or two courses. There was also a nice contrast between the applied courses like numerical analysis and more theoretical courses like abstract algebra.
The pandemic hit my semester like a ton of bricks. I think most of the faculty and students had been expecting a transition to an online format but when it came, it happened fast. One day I came home from school and never went back. We had a week off for the university to set up the online infrastructure, followed by a trial week of classes that was full of technical difficulties and then another week off for spring break. We lost almost an entire month right in the middle of the semester. The formats for the online classes were inconsistent and varied greatly from professor to professor, which made things difficult. All of my math professors did their best to meet the demands of the moment and I am grateful to all of them. My one non-math professor essentially abandoned the class and left us with nothing more than a due date for the final essay.
Cheating seems to have exploded. Suddenly, some people who were barely passing tests before were getting perfect scores on everything. Students sent each other copies of assignments or paid other people to take tests for them. There are numerous websites where you can buy the solutions to textbook problems. All of these issues were present before the pandemic, of course, but the online format has emboldened the cheaters to a discouraging degree. I do not think the measures that some professors have tried to combat it with were particularly effective, either. Watching a student take a test through their webcam is great in theory, but not when there are dozens or possibly even hundreds of students taking the exam at the same time. It is just not possible to monitor everyone, and it would be a simple matter to pre-stage notes out of view. All it really does is stress out the students and exhaust the professor.
As I mentioned earlier, I was lucky enough to be able to join a research project this summer. I heard about it through the reading course, since that course and the project were both about algebraic topology. More specifically, we are using a technique called persistent homology for topological data analysis. I would love to write more about this in future posts, but the gist of it is that we are looking at ways of describing the ‘shape’ of high dimensional data. Seeing the shape of data in two or three dimensional space is easy, but it is more difficult in higher dimensional spaces. In the era of big data, some data sets may have hundreds of thousands or millions of dimensions. Persistent homology lets us extract the shape of high dimensional data and describe it mathematically.
So that is where I’ve been and what I’ve done. I’m excited to get back into blogging. In the coming days and weeks I have a site revamp planned, some book reviews, and a few assorted posts. It’s going to be a good time.