About two weeks ago, I made a post saying how I got into the Johns Hopkins University Master’s program for AI, and the excitement of such an event led me to trying to refresh up on my math skills. I quickly rediscovered my love for the rigor of mathematics and the satisfaction of solving problems and doing proofs. However, I’m still feeling rather frustrated that my progress is slow. Perhaps, this is to be expected. Math is a difficult subject to learn after all and one cannot simply speed run the process. That being said, knowing how much more math I have to learn, I’m left wondering if I can even get through more than a few drops of entire bucket. So I feel stuck between: 1) going too slow where I’m not progressing and 2) going to fast where I’m not learning the maths properly. Generally, when there are two contending factors like this, the answer is usually somewhere in the middle. I guess the way I think about the two is like two different artists. One was an artist can conjure an image is to carefully draw each stroke with certain precision. This process will take a long time, but at the end, the picture will be accurate and complete. The other way of drawing an image is to do a quick sketch that captures the vague idea, but doesn’t lend itself well to exploring the finer details. Most artists probably don’t draw like the first one. Also most artists don’t just stop at the second method. What they do is refine over time. They create a sketch (unless you’re like Kim Jung-Gi and draw everything perfect at the get-go) and slowly layer and sculpt the image until they are just tinkering with the details. Perhaps, I could take a similar approach where I do multiple passes over time on some of the math ideas I’m exploring. My natural tendency is to fully capture the idea before moving on because math is truly a subject that builds on itself, but if I always give into this tendency, I might not make it very far. Another piece to this is the source of motivation. I like math more so for its potential applicability and not as much for its “intrinsic beauty”. That being said, I feel a chasm between linear algebra and machine learning. All I know is that the bridge is there, but at the moment I can’t see it and that can make concepts a little more difficult to grasp for me. I don’t really have any helpful advice for myself here other than to remind myself that if I don’t learn the linear algebra ideas well, it’s going to cause me great heartache down the road. So far, the way I’ve been studying is going through the Mathematics for Machine Learning book, handwritting notes, and trying some of the exercises at the end of the chapters. And that process, though slow, has been kind of working, but when I got to the subject of linear mappings (though a simple idea at its core), I started to feel overwhelmed and slightly burnt out. I don’t think it was so much as learning the concepts as it was trying to decipher the formal mathematical text and determine whether or not these certain ideas are standalone or serve as a foundational basis for learning the next concept. When I was studying Leetcode for coding interviews, I would often get stuck on learning how to do a problem. The way I remedied this was by using Anki flashcards as as schedule for implementing the solutions even though in the beginning, I did not understand how they worked. I simply just copied verbatim the solutions over and over again. It was through this repetition that things started to click in a way that I wouldn’t have been able to understand were I to grok my way through the solution (at least not without great effort). The spaced repetition of implementing the solutions, though time consuming, was actually pretty effortless and it felt certain that I would eventually come to a point of understanding. I might deploy the same strategies with learning math. I might start with memorizing the definitions of mathematical ideas and then memorizing the solutions to exercises (if I don’t know how to solve them on my own). I’m not sure how effective this strategy will be, but at least I won’t feel stuck.