UPDATE 2025-05-20: After thinking about it overnight, I’ve decided to take Math Academy’s suggested track and do Mathematics for Machine Learning next. In addition to linear algebra, it has a mix of other topics I want to have a good grounding in for a hobby project I’m undertaking. But I stand by my comment that Math Academy could improve the way it presents suggested tracks to students and better support more flexibility in learning paths.

Earlier this year I published a series of posts about Math Academy, summarizing the book The Math Academy Way and reviewing the service itself based on my experience thus far in completing the Mathematical Foundations II course. I’ve now completed the Mathematical Foundations III course as well and am starting the Linear Algebra course, the key to my quest to know what an eigenvector is Mathematics for Machine Learning course.

This is a good time to stop and present my updated thoughts on the Math Academy experience. Not everyone will share these opinions, and not everyone will want to use the Math Academy system as I do. But my comments may be useful to at least some people.

Class completions are the only milestones worth celebrating

Lots of people post daily or weekly about how many XP they’ve done that day or week, or celebrate their passing a certain milestone like 4,000 or 5,000 XP. I have nothing against such people, but I just don’t see the point of that. An XP total is an arbitrary figure and doesn’t necessarily bear a direct relation to what you’ve learned.

If your goal is to drive from New York City to Los Angeles, or from Paris to Berlin, it doesn’t matter how many miles or kilometers your car’s odometer shows, or even how many miles or kilometers you drive in a given day. All that matters is whether you reach your destination. You can celebrate when you get there. (As a corollary, that means I won’t be posting again about my Math Academy progress until/unless I complete the Linear Algebra Mathematics for Machine Learning course.)

But if you do have a burning desire to see my progress and verify it, you can look at my activity log for the time I spent doing Mathematical Foundations III and my certificate of completion for the course.

League participation is optional and potentially distracting

As I wrote in my earlier posts, I started out participating in the league updates. It was fun to a certain extent to compete against other people, but eventually I got a little too stressed out not just trying to qualify for promotion, but trying to be in the top 1 or 2 slots for the week.

I can see where competing against others and vying for promotion might serve as an external source of motivation for many people, and there’s nothing wrong with that—it’s good that Math Academy includes that feature. However, in my case I was motivated enough already, and doing leagues as well was a bit too much of a muchness. So, I eventually decided to stop worrying about the leagues and just concentrate on making progress in my course. As of now I see no reason to regret that decision.

You should try to do something every day (but not overdo it)

Even though I quit the leagues, I still made it a point to do lessons every day, ideally enough to exceed the 50 XP per day quota I had set for myself. I think I succeeded in that goal—I can’t recall any days on which I didn’t do anything at all, although there have been a few days when I just did one or two reviews.

Many areas of Math Academy appear to assume a student will be doing lessons five days a week, but I strongly recommend scheduling yourself to study every day if you can do it. There will always be emergencies that take precedence over doing a lesson, but I think it’s too easy to slack off and fall out of the habit if you deliberately miss a day or two.

At the same time, I encourage you not to overdo things. This is one reason I don’t pay much attention to people posting insanely high daily or weekly XP totals. Maybe they have the spare time to spend several hours a day working Math Academy exercises, but you probably don’t. Consistency, not speed, is the key; slow and steady wins the race.

During the Mathematical Foundations III course I typically found myself exceeding my 50 XP per day quota—it was too tempting to do one more lesson, or to do a review as soon as possible after missing a quiz question. For the Linear Algebra Mathematics for Machine Learning course I’ve decided to lower my quota goal to 40 XP; I have another projects I want to work on, and want to preserve time for them. Even at 40 XP a day I should be able to achieve my goal of finishing Linear Algebra Mathematics for Machine Leaning by the end of the year.

Math Academy should let you select your desired course sequence

When I finished Mathematical Foundations III, the system immediately began offering me lessons for the Mathematics for Machine Learning course. This is apparently because this is the default track that the system lays out for you. But, as I’ve noted multiple times, I don’t want to take Mathematics for Machine Learning, at least not now. I want to take Linear Algebra. (Yes, I know that Mathematics for Machine Learning includes a large chunk of linear algebra, but I want the full course of it.) (UPDATE: As noted above, I decided to take Mathematics for Machine Learning after all, and come back to the full Linear Algebra course later. But I still stand by my comment in the next paragraph.)

Unfortunately, I can’t find any way in the Math Academy interface to change the track that I’m on. The system knows (or should know) what courses are prerequisites for other courses, so it would be nice if I could see the tree of possible courses, select a goal to work toward (which for me right now would be completing the Probability and Statistics course), and then offer the courses in sequence needed to meet that goal.

Math Academy is (still) a great service

Despite the nitpicks I have about certain aspects of Math Academy and the online interface, I still think Math Academy is a wonderful service and have no regrets whatsoever about signing up for an entire year. I can’t speak to how it would be as a service for K-12 students, but if you’re a self-motivated adult learner interested in picking up math for the first time or as a refresher, Math Academy is well worth the money.

As for me, I have Linear Algebra Mathematics for Machine Learning to look forward to, and more courses currently being offered that I’d like to take beyond that. And with Math Academy adding more new courses this year, I’ll probably find a few more that I’d be interested in. Math Academy offers enough to keep me busy through the end of my current subscription, and I suspect I’ll be renewing it for next year as well.