jayro

Hi Julius, it's been a while!

Yep, it's an extremely challenging problem.

The initial version of the Math Academy system has been primarily geared toward individual learners, which for a variety of technical and business reasons was the only realistic way to get off the ground.

However, we're implementing a variety of features that will give teachers the ability to direct their class's learning progression while still allowing the system to adapt to and meet each student's individual needs. In some cases, it will provide critical remediation while for others it will offer topic extensions and challenge problems. Additionally, the system will offer a variety of differentiated group and class projects that are unlocked as students demonstrate mastery of the requisite skills.

That's a good point! We definitely need to add some more information to the website. In the meantime, if you send an email to support@mathacademy.com, I'd be happy to give you demo over Zoom and answer any questions you might have.

The Mathematics for Machine Learning course doesn't assume knowledge of Linear Algebra, but covers the basics of Linear Algebra you'll need along with the basics of Multivariable Calculus, Statistics, Probability, etc. it does however, assume knowledge of high-school math and Single Variable Calculus. If you've been out of school for while, our adaptive diagnostic exam will identify your knowledge gaps and create a custom course for you that includes the necessary remediation.

If you're REALLY rusty (maybe you've been out of school for a while 5+ years), or maybe you just never learned the material that well in the first place, then you might want to start with one of our Mathematical Foundations courses that will scaffold you up to the level where you can handle the content in Mathematics for Machine Learning. More info can be found here: https://mathacademy.com/courses

The Mathematics for Machine Learning course would be ideal for anyone who majored in a STEM subject like CS (or at least has a solid mathematical foundation) and is interested in doing work in machine learning.

We just released a comprehensive online course on Multivariable Calculus (https://mathacademy.com/courses/multivariable-calculus), and we also have a course on Mathematics for Machine Learning (https://mathacademy.com/courses/mathematics-for-machine-lear...) that covers just the matrix calculus you need in addition to just the linear algebra and statistics you need, etc. I'm a founder and would be happy to answer any questions you might have.

At Math Academy, we've created a sequence of math courses called Mathematical Foundations I, II, & III that cover everything from 5th Grade Math up through Calculus I & II and will allow anyone to get up to speed on the skills required for university-level mathematics in the most efficient way possible. Our adaptive diagnostic exams will create a custom fit course no matter where you are mathematically and our algorithms will continually adapt to your individual strengths, weaknesses and learning curve.

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

In addition, we have courses on Linear Algebra and Mathematics for Machine Learning, with more coming soon:

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

The system is mastery based, lightly gamified, and completely automated. Our algorithms intelligently apply spaced-repetition to a hierarchical knowledge graph of over 3,000 mathematical concepts to make it substantially more efficient than a traditional course (typically on the order of 4X or more).

I'm a founder and would be happy to answer any questions.

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.

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.

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.

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.

There's a 30-day free trial, so if you cancel during that period you get a complete refund.

At Math Academy (https://mathacademy.com), we implement spaced repetition in combination with a knowledge graph consisting of several thousand math topics and tens of thousands of connections (and growing). We're working on a post that explains how this all works technically.

We have a Linear Algebra course (https://mathacademy.com/courses/linear-algebra) that some of you might find interesting given how often that topic shows up on HN, and we just finished our Math for Machine Learning course (https://mathacademy.com/courses/mathematics-for-machine-lear...) for anyone who might be interested in giving that a look.

I'm the founder if anyone has any questions.

Sorry about the shameless plug.;)

I understand why it might seem that way, but it's really not. We've just put a premium on learning efficiency, and most math classes are highly inefficient - whether K-12 or university.

Just imagine how much more quickly a student could progress through a course if they were to work one-on-one with an expert tutor 5 days per week. Quite a bit more quickly in most cases. Well, our system effectively serves as an expert AI tutor and based on our calculations is on the order of 4 times more efficient than a traditional math class.

But I get the skepticism. I'd probably be skeptical myself.

It's funny you bring that up as it seems to be a common request from adults interested in leveling up their math. I'm sure we could come up with something reasonable.

It's true that the students in the school program are high-aptitude, but something like 70% of the students in the middle school where this all started are on the federal free and reduced lunch program (low SES) along with a couple of the top kids in the original cohort, who I taught personally and they were amazing.

We started with the multiple-choice format as it's a good 90-10 solution in terms of technology, but we now have free=response questions that are automatically evaluated and can handle fairly complex mathematical expressions - man, was that a lot of work!

But we've found the concern over the multiple-choice format to be overblown. People like to believe they can outguess a multiple-choice question by being clever, but that's not reality on our system or elsewhere such as the AP exams, the AMC exams, or the GRE Mathematics Subject Exam.

Later this fall we're going to be introducing a UI for constructing proofs that's looking really cool and should take things up a notch for the more abstract subjects like Abstract Algebra and Real Analysis. Teaching university-level proof techniques is extremely challenging and time-consuming process (most never really get it) even for undergraduate math majors at university, but I think our new tech will make it much less painful and with a much higher success rate.

Through trial and error and the application of some rarely employed, but highly-effective educational strategies like active learning, distributed practice, mixed review, mastery-based learning, interleaving, layering, etc., you end up with a pace of learning that's a little shocking. I realize it's hard to believe -extraordinary claims require extraordinary evidence and all that, but that's what got us started having our 8th-graders take the AP Calculus BC exam as as an outside, objective measure.

Yeah, pretty close, although it's not like most universities will allow students to skip straight to graduate school. Our first cohort of students just graduated this past year, so we're just now getting a sense of how this is likely to play out.

My son, who's majoring in CS, is starting with 300 (junior-level) courses in both math and CS - although the departments were happy to allow him to start even deeper in the curriculum if he wanted. Another student, who collaborated with one our our math PhD instructors on some original research that's about to be published, is starting with at least one graduate math course this year (the last I heard, anyway).

Well, it turns out that when you have mathematically-talented students completing Calculus in 8th-grade, and move on the Linear Algebra and Multivariable Calculus in 9th, you eventually reach Real Analysis and Topology by the end of high-school - although, we haven't gone quite as deep in those particular subjects as the others mentioned. But we do comprehensively cover Differential Equations, Discrete Mathematics, Probability & Statistics and Abstract Algebra.

Good morning, HN! It's Jason (the founder). My wife (co-founder and co-conspirator) just woke me up to alert me to a sudden spike in demo requests, so I'm a little blurry-eyed at the moment (was up late last night trying my best to get the marketing site functional), but I'd be happy to answer any questions you might have.

This is a fun book (published in 2001) about how a professor and his graduate assistant developed a world-class checkers-playing algorithm using neuroevolution:

https://en.wikipedia.org/wiki/Blondie24

https://www.amazon.com/Blondie24-Playing-Kaufmann-Artificial...

(Edit) One of the funniest parts I remember is that they had to leave it running on a Pentium III for like a month or something.

Atari 800XL.

Nice work! I think we need to bring you on the show.

Jason here! I totally agree - the name "Memory Hole" doesn't really make any sense at all given what it means -https://en.wikipedia.org/wiki/Memory_hole

But something about it always made me laugh, so that's what I called it.

Anyway, I'm so glad that someone FINALLY got around to building the damn thing! I guess the lesson here is that if you want something done, either do it yourself, or ... be prepared to wait a really long time. ;)

Here's a podcast interview with Mike Taber about his new book: http://techzinglive.com/page/1541/280-tz-interview-mike-tabe...

Adventures of a Mathematician: http://www.amazon.com/Adventures-Mathematician-S-M-Ulam/dp/0...

Yep!

How facts backfire - Researchers discover a surprising threat to democracy: our brains

"In a series of studies in 2005 and 2006, researchers at the University of Michigan found that when misinformed people, particularly political partisans, were exposed to corrected facts in news stories, they rarely changed their minds. In fact, they often became even more strongly set in their beliefs. Facts, they found, were not curing misinformation. Like an underpowered antibiotic, facts could actually make misinformation even stronger."

http://www.boston.com/bostonglobe/ideas/articles/2010/07/11/...

"Research shows that even when news reports have been retracted, and we are aware of the retraction, our beliefs are largely based on the initial erroneous version of the story. This is particularly true when we are motivated to approve of the initial account." - http://mindhacks.com/2011/05/04/why-the-truth-will-out-but-d...

Original Paper: http://pss.sagepub.com/content/16/3/190

Here are some additional stories on the topic that are worth reading:

* Physicists Seek To Lose The Lecture As Teaching Tool http://www.npr.org/2012/01/01/144550920/physicists-seek-to-l...

* At M.I.T., Large Lectures Are Going the Way of the Blackboard http://www.nytimes.com/2009/01/13/us/13physics.html?pagewant...

* First-year physics course being transformed through experiment http://web.mit.edu/newsoffice/2001/physics-1219.html

* The Tomorrow's College Lecture Series - Don't Lecture Me http://americanradioworks.publicradio.org/features/tomorrows...

* Inventing a New Kind of College http://americanradioworks.publicradio.org/features/tomorrows...

Honestly, I can't remember if I have, but it would be interesting to read something about it. I wonder if it's kind of the same problem as trying to teach concepts to kids that are just at the limit of their ability to comprehend even if they are naturally gifted. It's tough, man. My experience of trying to explain functions, arrays, loops and conditionals to young kids is tricky, but I think you just have to apply the same techniques as you would teaching math and eventually you'll figure out some techniques that work. You can try breaking it down into the smallest of steps and go very slowly with lots of practice. Sometimes analogies help, but sometimes not. Sometimes, you can just show them a bunch of simple examples which they'll be able to pattern match against until they can absorb it, but sometimes not. More than anything, I think you just have to be patient and experiment.

As an example, my daughter Izzy, who's 7 and in second grade, is really struggling with her math and it's pretty frustrating frankly. But my wife has been trying lots of stuff with her like watching Khan Academy videos, doing practice problems on www.ixl.com, working through Singapore and JUMP math workbooks, working with physical objects as examples - counting change, poker chips, or whatever.

The bottom line is that every kid is a little different and what works for some may not work for others, unfortunately. ;)

Edit: In regards to how to teach symbolic logic to children who may not be naturally talented, you might want to check out JUMP Math: http://jumpmath.org. They seem to be doing some innovative things. Here's an interview with the founder: http://www.youtube.com/watch?v=g3YWnbxOxMQ.

Wow, thanks for that!

It's so hard to make broad generalizations about how to teach kids to code because it really depends on so many different factors (age, interest, ability, etc), but after a lot of trial and error I do think we're zeroing in on a workable set of strategies for our little group.

(I was in the middle of writing a much longer response, but I decided to save it for the show this weekend because among other things I need to try to get some work done. ;))