The Future of Proof-Based Courses on Math Academy

And why we refer to ourselves as still being "in beta."

There is sometimes confusion about people thinking Math Academy is stopping at its current level of depth/difficulty, when in reality, we are still building out the curriculum. It is nowhere near finished.

Yes, currently, our only proof-based course out is Methods of Proof. Does it cover epsilon-delta proofs? Yes. Does it cover papa Rudin? No, because that’s well out of scope. Does that mean we’re stopping short of papa Rudin? No, it just means we haven’t built up to that yet.

Another example: we have a computation-based Linear Algebra course that will be a prerequisite for a proof-based “Advanced Linear Algebra” or “Abstract Linear Algebra” course later down the road. That second Linear Algebra course will go deeper into the theory and proofs that one might encounter while taking a linear algebra course at an elite university that uses, say, Axler’s book.

Unfortunately, people sometimes move the goalposts and say “your [first] Linear Algebra course is not as intense as Axler,” when this isn’t even an apples-to-apples comparison. That’s like pointing at a high school calculus class and complaining that it’s not as intense as a real analysis course – of course it’s not! It’s a completely different course; in fact, a prerequisite course; and it’s not meant to cover the same material.

Axler is really a second course in linear algebra, even if some universities throw students into it as their first course (which ends up causing a lot of unnecessary struggle). I often joke that Axler’s book “Linear Algebra Done Right” should really be called “Linear Algebra Done a Second Time.”

In general,

• we are building our curriculum from the ground up,
• we are scaffolding everything to the max, and
• it's mastery-based (students are only asked to learn things after having mastered the prerequisites),

so, naturally, we are going to be doing computation-based versions of courses before proof-based versions.

But that doesn’t mean we’re not going to be getting the proof-based versions eventually! The proof-based courses are ultimately just different courses, and we are getting the prerequisite courses in place to build up to them. The proof-based courses are 100% on our roadmap.

The situation right now is we have this unfinished system that is useful enough that a lot of people are getting value out of it.

People are ripping it out of our hands, and we’re like “it’s not finished!!!”

Many people’s reactions are “I don’t care, it solves my problems in its current state, I want to use it!”

Other people’s reactions are “this could be better.”

… to which all we can say is “OMG, we know, we know! Shit’s hard! We’re working on it! Try to understand our vision and give us the necessary time to achieve it!”

This is one of the reasons we refer to ourselves as being “in beta.”

And it’s not just more courses that we need to roll out, but also a ton of additional core software functionality (e.g., behavior coaching).

And it’s also our grand plan to augment the learning experience to include interesting stories about the history of math, notes about cool applications (and projects actually carrying out some cool applications), etc.

We’ve just been focusing on core functionality to start, but our long-term vision is for this system to eventually include every single dimension that you would expect from an amazing human tutor, not only structured / scaffolded / adaptive / efficient pedagogy but also behavior / motivation coaching and interesting tidbits that add more “flavor” to the learning experience.

That’s why the interface is still rough around the edges in places – we are still focusing on getting core functionality in place, and there is a LOT of core functionality that remains to be built.