My recent focus on Machine Learning and language models quickly made it clear that I was going to need a much stronger grasp of probability theory and linear algebra. While programming problems have usually been solvable by butting my head against them enough times, ML is different. To really understand the models there is a mountain of math that must be understood and cannot be faked or waded through. Previous attempts at learning have been met with mixed success - several times over my adult life I have purchased a linear algebra textbook, started reading through it, and tried to muddle through. I never had much luck, but fortunately the ability to learn this outside of a formal classroom setting has recently had some step change improvements. The path I took was Math Academy to classes from MIT’s EdX Data Science MicroMasters.
If not familiar, Math Academy is an online learning platform that structures math learning in an opinionated way. It uses some clever techniques such as a dependency graph, spaced repetition and direct text based lessons to build proficiency at a place the software assesses is the learner’s frontier of knowledge. While the program started out of an experimental California High School program, the web based platform has been popular with adult learners in addition to children as it has classes all the way up to university-level coursework.
While I found Math Academy was not enough on its own, it was the key piece that let me overcome the initial push to start learning. I started at Math Foundations II, which is mostly early High School math and realized there were some real and fundamental gaps in my mathematical foundations which had made previous efforts to learn much more difficult than they should be. While this meant I was revisiting Trig and factoring polynomials, after a few months of focused effort, I was back to the edge of what I learned the first time around. After progressing from Foundations II to III to Math for Machine Learning I was being exposed to things I had not studied previously. This is also where Math Academy on its own was not enough.
Enter the MITx Data Science MicroMasters program. The program is taught by MIT faculty and “designed to mirror on-campus graduate-level coursework—featuring a similar pace and level of rigor as on-campus courses at MIT”. Each class is a 10-15 hr per-week commitment. I started with the Machine Learning course which is taught by some world-class professors (Regina Barzilay). The course began with a test of the calc and linear algebra prerequisites, and the fact that these were all familiar and approachable was a testament to Math Academy. (For anyone considering this course there are python pre-reqs of at least one intro-level class).
So has this been a success? It has certainly been effective for getting over the initial hurdle of learning - previous attempts at learning Math have been picking up a Linear Algebra book and sitting down and reading like until I lost interest. A separate question is have these learning methods taught me to a useful level of expertise? I can now much more effectively read ML papers, and have been able to apply these tools to projects when I might have tried a more brute force approach previously. If trying to learn outside of a classroom, I think neither resource is enough on its own, but together they offer something comparable.
https://mathacademy.com/ https://micromasters.mit.edu/ds/ https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/