[jayro]

At Math Academy (https://mathacademy.com), we created a series of courses, Mathematical Foundations I, II, & III, that will take a student from basic arithmetic through calculus and prepare them for university-level courses like Linear Algebra, Multivariable Calculus, Probability & Statistics, etc. You can jump in at any with an adaptive diagnostic that will custom fit the course to you based on your individual strengths and weaknesses.

https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-iii

We also have courses on Linear Algebra and Mathematics for Machine Learning:

https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/mathematics-for-machine-lear...

It's not free, but our adaptive, AI-driven algorithms makes it the most efficient way to learn math that you're going to find. We've had numerous students master 3-5 years of math in a single year.

We're still in beta and haven't done a proper Show HN yet, but we're getting there!

I'm the founder, so I'd be happy to answer any questions.

[cashsterling]

600 USD a year is definitely worth it to learn any highly technical topic: mathmematics, physics, chemistry, CS, engineering, etc.

BUT... I'm highly skeptical of any online math course that claims many students have mastered 3-5 years of math in a year. How many hours of study in what subjects? How was mastery measured... did they take the grad school math GRE and ace it? Mastery takes continued practice... I'm highly s

Most online math courses I've looked into [for my friends, my kids, etc.] are "paper thin" and contain less than 25% of the topical matter, descriptive detail, and depth of a good book on the subject... and I'm actually being generous.

I hope your courses are going at least as deep, or offer the capability to, as good books on the various topics. For instance, if linear algebra does not go as deep as Strang + VMLS[0]... folks should just get those two books (VMLS is free), plus watch some youtube, like 3blue1brown.

[0] https://web.stanford.edu/~boyd/vmls/

Edit: btw... not trying to be overly harsh, just skeptical. If your courses end up being half as good as advertised I'll 100% sign up at some point.

[Math-Ninja]

Hi, I'm Alex, the curriculum director at Math Academy.

I can completely understand the skepticism and agree that many online courses are paper thin. That's where we're different.

For example, our BC Calculus course comprises 302 topics, each containing 3-4 knowledge points, so ~1060 knowledge points in total. Students must master each knowledge point to move on to the next. Our spaced repetition algorithms ensure that students are repeatedly tested on the material (we have quizzes every 150 XP or so). If they fail a question on a quiz or topic review, the system requires that they retake the failed topic. Students _cannot_ complete a course without mastering the entire thing.

Each knowledge point is connected to key prerequisites in the same course and lower courses. If a student stumbles on a particular knowledge point, our system can determine the most likely point of confusion and refer them to the associated key prerequisite topic (which they must pass to continue making progress).

We also have a couple of dozen multistep questions, similar to those you'd find on the BC exam (although the BC exam has about 4-5 parts per question, ours have about 9-10).

Regarding results, we had an 11-year-old sit the BC exam recently, and it looks like they will get a 5, the top mark. (For those that are unaware, students usually sit the BC Calc exam at the end of high school in the US, so 18). I admit that's an extreme case, but it's not isolated. I could reel off many success stories of students achieving real results on real tests after self-studying using our curriculum. We also have an associated school district program in Pasadena, California, where dozens of 8th-graders have achieved 4s and 5s in the BC exam, mostly learning using our system.

In terms of the required effort - provided you have no issues with the necessary prerequisite knowledge, you can get through our entire BC Calculus course by committing 40-50 minutes per day, five days per week, for around 5-6 months. Of course, if there are gaps in the prerequisite knowledge, then it'd take a little longer - but thankfully, our algorithms can detect missing knowledge and fill the gaps. That’s one of the advantages of having an intelligent, interconnected system comprising over 3000 topics!

As for our higher-level courses - some of these are still in development. However, our linear algebra course is comparable to several high-quality books on the subject (I like Lay, Anthony & Harvey, and Axler, though we use others). It currently has 176 topics, but many foundations are laid out in our Integrated Math III / Precalculus courses (vectors, matrices, basic determinants, inverse matrices, linear transformations in the plane), so the real number is around 200.

https://mathacademy.com/courses/linear-algebra

(click on the "content" tab to get a complete list of topics).

Could one of our students ace the GRE? That's a great question. We still need content on several key areas required for the GRE (e.g., Abstract Algebra, Real Analysis, Complex Analysis, and Graph Theory). These courses are still in development - we already have a lot of this content behind the scenes. That said, I'm confident that our students have the necessary tools to succeed in the parts of the GRE we currently cover. We don't "teach to the test," not even with BC Calc, but equipping our students with the necessary knowledge and skills to go from 4th grade math right the way up to acing the GRE (just as we've done with BC Calc) is one of our medium to long-term goals.

Happy to answer any further questions about the curriculum you may have.

[no_wizard]

When I am ready to dive into this again, I will definitely look at this. I know I need concrete time dedicated to this sort of thing (repetition is the only way to master it really) but I'll circle back around to this soon!

[Gerard0]

Looks great and was ready to sign up but I surely wasn't expecting that price! I am not saying it is not worth that, but as someone who has tried to start learning math on my own only to quit afterwards for whatever reason, it's a big risk to take.

[jayro]

I guess you have to think about it like this.

How much would it be worth to you to learn 3-5 years of math in a single year without getting stuck? And I mean really learning it to the point where you're able to solve the more difficult problems and are not merely able to recognize some of the symbols and terminology and talk like you know it. If you're just kind of curious about some advanced math topics you see pop up on HN from time to time and aren't really willing to invest any real time, effort or money into learning the material, which is totally fine and is probably where most people reading this comment are, then sure, spending more than $40 on a book or watching some free online videos will seem expensive.

But the reality is that very few people will be able to learn a significant amount of math by simply working through some problems in a book. Eventually they'll get stuck or just run out of gas, and when I say eventually I mean probably in 2-3 weeks. But if you're that one student who successfully taught themselves multiple courses worth of mathematics on their own from a few books and outside of any educational institution, then hats off to you! You're like that guy who put on 30 pounds of muscle doing pushups and pull-ups at the local park. You know, ... that ONE guy. ;)

But if you want a sure fire way of mastering a large amount of mathematics as efficiently and painlessly as possible, then you want a system like Math Academy that will adapt to your individual learning curve and knowledge frontier and push you through the material using the most effective pedagogy available - careful scaffolding, active problem-based learning, spaced repetition, gamification, etc.

The bottom line is this. Our system is more effective than any course available and is much cheaper for what you get. In fact, we just had a group of students ages 11-13) start with basic pre-algebra in the fall of 2021 (as in Solve x - 4 = 10) and from what I've heard all did extremely well on the AP Calculus BC exam a couple weeks ago. That's like 6-7 academic years of math in 18 months and we're expecting mostly if not all of them to earn a 5 (the top score).

But take my word it. Try it out for yourself. You automatically get a full refund if you cancel in the first 30 days, so there's no risk. And we're always available to answer your questions and support your progress.

[admsmz]

I’ve been a paying customer since October last year. I discovered it after someone recommended it in a hackernews comment.

I’m guessing you’re mentally comparing this to all the possible books you could buy instead for that price. But how many of those books would you actually read, let alone finish? A better comparison is, having an MIT educated math tutor on call for $50 a month.

I have a bachelors in physics but it still feels great to learn new things that my education skipped. For example, we skipped singular value decomposition at my university in the interest of time. Mathacademy says, screw it, we’re teaching everything!

[Math-Ninja]

Hi Gerard.

Math Academy does not charge your card for the first 30 days. If you find it's not a good fit for then you can cancel within this period and you won't be charged. 30 days hopefully gives you enough time to determine whether it's a good fit or not.

[pmoriarty]

> our adaptive, AI-driven algorithms makes it the most efficient way to learn math that you're going to find

Can you elaborate on this? What do these algorithms do?

[jayro]

Geez, I'm trying to figure out how to describe in a short paragraph or two what it would take a book to explain. Here's my best shot.

We've created an extensive knowledge graph representing all of mathematics (3,000 topics and counting) from 4th Grade Math up through our university-level material, and our algorithms traverse the graph to identify the optimal learning tasks to assign to the the student at any point based on their performance on previously completed learning tasks: diagnostics, lessons, reviews, quizzes, etc.

There are actually multiple graphs, including one that defines the direct prerequisite relationships between topics as well as one that describes encompassing relationships (e.g. the topic on Solving Two-step Linear Equations fully encompasses the topic on Solving One-step Linear Equations Using Multiplication), but there are other graphs as well.

In addition, the algorithms have to deal with spaced repetition, which is vastly more complicated to sort out within the context of a hierarchical knowledge structure with both full and partial encompassings. (Without encompassing relationships, the backlog of reviews would quickly slow progress to a crawl).

We actually have some deep-dive writeup in the works that attempt to explain how all of this works at a level that will be accessible to most people, but it's more than I can describe here, unfortunately.

Anyway, I hope this helps a little.

[rodneyzeng]

I did not see any content related to number theory and combinatorics (or counting) in the list of courses.

[jayro]

We should have those courses ready within the next year. Multivariable Calculus should be available in another few weeks, then Probability & Statistics at the end of July, then Methods of Proof, followed by Discrete Math, and Abstract Algebra later this fall. But courses in Number Theory, Graph Theory, Combinatorics, Real Analysis, etc. are all planned.