Math Academy, update 2: I completed Mathematics for Machine Learning

I’ve now completed my third Math Academy course, Mathematics for Machine Learning. I’m celebrating by posting another update on my Math Academy experience and my thoughts about Math Academy in general. (For my experiences with my first course, Mathematical Foundations II, see my original series of posts summarizing the book The Math Academy Way and reviewing MFII. For my experiences with my second course, Mathematical Foundations III, see my previous update.)

My usual disclaimer applies: Not everyone will share my opinions on Math Academy, and not everyone will want to use the Math Academy system as I do. But my comments may be useful or interesting to at least some people.

Steady as she goes

Im my last update I opined that keeping to a reasonable XP goal each and every day was the best approach to maintaining steady progress in Math Academy courses. For Mathematics for Machine Learning I set a daily goal of 40 XP. According to my activity log for the 105 days I spent in the course, I averaged 48 XP per day. There were only 11 days when I did less than 40 XP, and only one day when I skipped Math Academy entirely and didn’t do any XP at all.¹

At the other end of the scale, there were only five days where I did 70 XP or more, and only two days when I did 100 XP or more. (One of these was the last day of the course, when I was close enough to completing it that I decided to just go the extra mile and get it done; that was also my maximum XP total at 102.) In general my strategy has been to do enough work each day to get at least 40 XP. The major exceptions to this were when I failed quizzes. Then I would do reviews and retake the quiz the same day, which padded my XP total a bit.

Coach is always right (or you should find a new coach)

One of the things people bring up from time to time is wanting a lot more flexibility in deciding which order to do lessons. This is also related to the complaint made by Oz Nova in his article “A balanced review of Math Academy” about the rigidity of the knowledge graph:

Why do some learning resources designed for autodidacts—such as Math Academy . . .—rely so heavily on dependency graphs? The generous answer may be that it’s unrealistic for the learner to know an appropriate ordering, and perhaps motivating for them to be shown the “ideal.” The cynical answer is that these programs take the idea of mastery learning too far, and have become dogmatic. . . . After all, it’d be easy enough to present users with a suggested sequencing without strictly requiring that it be followed.

A minor nitpick: Math Academy does not completely impose a strict ordering on students. Yes, the system decides what topics to present next, but when a student is presented with a list of lessons and reviews, they do not have to do them in the presented order.

But, as it happens, I am fairly religious about following the sequence of topics suggested by Math Academy: I do any suggested reviews first, going in sequence from first to last presented, and then do all the suggested lessons in sequence from first to last presented. I also generally do any presented quizzes as soon as they are presented, and only rarely choose to postpone them.

If we take at face value Justin Skycak’s analogizing learning math to developing athletic talent, then in essence I’m just following the instructions of my “coach.” Presumably the people who developed Math Academy know a lot more about math education than I do, and they have the benefit of lots of data about what works well and less well with Math Academy students. I‘m therefore not inclined to question their judgment about course and topic sequencing, any more than a freshman player would presume to tell their coach that they should change the content and sequence of their drills.²

Of course, sometimes players chafe at a coach’s instructions, and find that the coach’s approach doesn’t match well with their own talents and style. It‘s also true that some coaches are more competent than others. If a player finds they’re in a less than optimal situation, they can always find another coach, transfer to another school, or ask to be traded. As I’ve mentioned before, Math Academy is not for everyone.

“Among the chief glories of Western civilization”

Oz Nova also has some things to say on the topic of self-motivation and why (in his opinion) schemes like XP goals, leaderboards and leagues, and related Math Academy features fall short:

Every person has their own mix of motivation and the last thing I want to do is to judge another’s. But speaking personally, if a book promises to help me grapple mathematically with the chief glories of Western civilization, now THAT might sustain my interest.

This is from the introduction to Differential Equations with Applications and Historical Notes by George F. Simmons, a book as close as possible to perfect, for me, for this topic. It is not just motivating but stirring, driving, elevating. By math textbook standards, it overflows with fascination, excitement, even love.

The Simmons treatment is so vibrant that something like Math Academy sits lifeless in comparison.

Since I’ve had trouble learning about differential equations and would like to know more about them, I got a copy of Simmons’s book. I found it to be well-written and sprinkled through with information about the historical development of the topics covered, including mini-biographies of the mathematicians who developed them.

Is this motivating? It’s hard to say. As I’ve previously mentioned, I have a practical approach to learning mathematics, primarily focused on what I can do with it, so I’m probably not the best person to judge. I also often find myself distracted by sidebar material like this, so much so that I neglect the main discussion.³ From that point of view there’s a lot to be said for Math Academy’s “lifeless” approach.

Having said that, it’s possible that Math Academy might benefit by including more material on the historical background of the topics in its courses. Perhaps this could be included as a reward (not a sidebar), for example, after successfully completing a quiz or course.

Onward to (more) eigenvectors

As you may recall, my original motivation for signing up with Math Academy was to learn what an eigenvector was, and by extension to complete my study of linear algebra. The Mathematics for Machine Learning course covers various topics in linear algebra, multivariable calculus, and probability and statistics, and includes a fair amount of material about eigenvalues and eigenvectors, including their application to principal component analysis.

So in a sense I’ve already achieved my goal, as I now know what an eigenvector is. But I don’t want to stop here. My next task is to finish the real Linear Algebra course; I’ve already covered three quarters of its topics, per my dashboard page, so even allowing for having to relearn some topics I should be able to complete it well before the end of the year (my original timeframe). Then I’ll go on to Multivariable Calculus and Probability and Statistics, rounding out my knowledge of topics that the Mathematics for Machine Learning course provided an introduction to. That will be more than enough to occupy me in the coming months, then I’ll see where my Math Academy journey takes me after that.