How to get from high school math to cutting-edge ML/AI | Hacker News Reader

How to get from high school math to cutting-edge ML/AI

justinmath.com

150 pointsahiknsr32 comments

Have been working my way through mathacademy and i feel so motivated. It is almost like a game and i start to feel confident to have a peek at math Olympiad questions. Thanks a lot for your platform.

Love running into Math Academy students in the wild -- thanks for the kind words and I'm so happy that the system is working out for you! After all the work we've put into building this thing, it's the best feeling ever to hear about positive impact it's having on people's lives.

Sounds like you're well on your way to seriously leveling up your math skills, but if you have any questions about how the system works, how to get the most value out of it, the math learning process in general, etc., feel free to reach out anytime.

I love studying there but I would like to be able to explore past lessons (just the information, the theory). How can I do that?

You can view lessons in "reference mode" -- to get there, just click on the old task and then on the name of the topic.

You can also get there from the Table of Contents -- to get there, go to your dashboard (where your learning tasks are), click on the name of your course in the top-left, and you'll be brought to a screen that says "Course Sequence" with a list of courses on the left and units on the right. If you expand the units, you'll see topics, and you can click on a topic to view its lesson in reference mode.

Note that XP & knowledge credit is only awarded for completing learning tasks on your dashboard, not for anything you do within a lesson in reference mode.

Thanks! Will the segments with formulas ever turn into Latex which one could copy and paste?

Not sure, but looking at the interface myself just now, it seems like it's always possible to see the latex of a math field by either 1) right-click > show math as > tex commands (which you can copy/paste), or 2) hover over the field and see the tex commands show up as hover text (but can't copy/paste)

Thanks! I might have never noticed this due to copying the text before it as well haha.

Thanks for the amazing support and the cool product!

Why do you want the latex available? Do you use the computer as a notebook?

Very well. One of the things that needs to be explained, or the information made available is why rote computation and timed tests are important. Both of those are weaknesses of mine and it did not help my motivation not understanding why it was needed. I came to the answer on a post of yours somewhere in Reddit and now I actually want to get better at it. The idea I got from you and my experience is: Timed tests make sure I know and use the optimal approach to solve the exercise. I found this while solving systems of equations, where naively I could carry fractions around making calculation cumbersome and error prone, while an initial analysis trying to find a multiplier that does away with fractions is the right approach. I kept failing until in the review lessons I paid proper attention. Analysis and optimisation is being taught. I had a similar experience about choosing a generic ln or an appropriate base logarithm. Rote calculation was a tough one to swallow until you said that only through much computation one starts seeing patterns that will be useful later in more abstract manipulation. I agree with it but doing the first chapter of spivak’s calculus that focuses on proving very basic entities with math’s arithmetic axioms helped a lot. It is incredibly simple maths but hammers down the axioms that are then the basis of all manipulations.

Also I like the lack of human interaction upon failure. A machine does not get disappointed when I fail, nor annoyed that today I am having a bad day intellectually. It just fails me and gives me the opportunity to do something else and do repeats until it is successful. It also does not let me continue with faulty understanding because the program needs to be on schedule. It gives me an expectation of completion based on current progress history. If am not happy I can just apply myself better. The price being steep also makes it painful when I see no experience gained in the whole calendar week, further adding a motivation.

On a more personal experience I dread tests and especially timed tests. I am kind of “fortunate” that my nightmares often are about failing exams or not having time to finish them. When doing math academy I always was afraid of the “quiz” tab coming up, especially because I have kids and house chores that sometimes need to attend. Anyway in mathacademy quizzes are so frequent they normalize the act of test taking and I feel more like they are a challenge for me to “show off” then something to dread. This is in contrast to my experience in college where there was one make or break exam for the whole semester: fail and you will need to repeat the whole semester.

To finish I so much wish my kids will be able to benefit from this approach. I have been trying to convince others of the worth of relearning maths as an adult. It gives an analytical mind and teaches intelectual humility. I find myself successful in life yet I still struggle in some tests and tasks.

I normally say if you are in need of some reality checks regarding your intellectual ability just do maths. There is always a problem of extreme simplicity that one cannot solve, and makes you feel dumb.

Yeah, I fully agree that in general, we need to integrate explanations of "why is this task optimal for my learning" into the product. It's definitely on the roadmap, but it's a challenging because there's too much info to simply tell a student everything up-front. We have to do it just-in-time. But I'm glad that you were able to find a Reddit post of mine that answered your question. It'll be some time before we have all this info properly integrated into the product itself, but for now, if you're interested in reading more about why the system works the way it does, I'd recommend checking out my working draft of The Math Academy Way (https://www.justinmath.com/books/#the-math-academy-way).

I'm glad that you're having a good experience with the quizzes! That's exactly what we aim for: frequent, low-stakes, broad-coverage quizzes that challenge you to show off what you've learned (instead of stressing you out and overwhelming you). Used properly like this, quizzes are an extremely powerful learning tool. You get the benefits of retrieval practice, the spacing effect, and interleaving, all merged into one. And we pinpoint exactly what skills you need more practice on (which we have you review immediately afterwards), and by carefully calibrating the time constraint, we make sure you're developing your skills fully to the point of automaticity.

This is a very comprehensive resource that not only offers the books, but a canned curriculum(Eurisko) that could be customized to your audience. Say, your colleagues at work(considering they came from STEM background with rusty vector calc like me) A question to the OP is, would it be possible for someone like me to "adapt" this curriculum to conduct my own version of "Eurisko"? What are the licensing terms?

Not entirely sure I understand the question, but I'll answer to the best of my understanding: If you'd like to teach a course using one of my textbooks, then go ahead -- it's freely available online so that anyone who wants to learn from it can do so. All I ask is that if you pull readings/problems from the book, you cite the source, like how it's done when a professor pieces together a course using different readings/problems from different textbooks.

But, to clarify: the Eurisko book (Introduction to Algorithms and Machine Learning) only covers a small slice of the total roadmap from high school math to cutting-edge ML/AI. The other resources I recommend are the ones I mention in this post.

Thanks for taking the time to answer. And you did answer the core of my question. Indeed, i will be citing the books as the source. Thanks again for making this resource available for free.

No problem, glad it's helpful! Feel free to reach out anytime.

Thanks for your generous offer. Will ofcourse reach out.cheers

if the aim is to just read and understand the papers, it is just a matter of learning the ap calc and some first-year university maths to get the basics out of the way.

the rest of the journey is to find an ml course which acts like a survey of the current state of the art. this field has complexity due to abstraction and horrendous naming practices. to understand a given paper requires working your way in reverse from concepts around it.

in addition, learn a "maths in code" platform of your choice to map the concepts to something you can run.

I feeling like you described a “draw the rest of the owl” situation with “find an ml course”.

I’m basically in this situation, I’ve implemented products around AI and ML. I understand them at a practical level but want to dive into the theoreticals more. Finding a “survey ML course” is a huge challenge for me. I have absolutely no idea what’s considered state of the art.

i completely understand your point-of-view. tough to give a silver-bullet answer because things move so quickly.

i personally found this course to be a good place for deep learning (again not a survey course that covers classical ML for context) - https://uvadlc-notebooks.readthedocs.io/en/latest/index.html

however, the strategy that should give good results is going for the open-source coursework from one of the major universities. these courses may lag a semester or two from SOTA, but they often give a good overview. pick your poison and go from there. for example the above link was found the same way.

What is the pricing model for this? I’m interested in enrolling.

Looks like just time: https://www.justinmath.com/books/

This is phenomenal. I currently don’t have a great internet connection, so the pdfs won’t load. Do these books have solutions?

You may already be aware, but just in case there's some confusion, I want to clarify: if your intention is to get from high school math to cutting-edge ML/AI using the most direct / efficient / well-scaffolded path, then the resources that I'd recommend looking at are the ones that I refer to within the main body of the post, which are for the most part different from the books on that page.

(But to answer your question: the math books on that page have "correct answer" solutions where you can tell if you got it right, but not fully-worked-out solutions. Introduction to Algorithms and Machine Learning technically does not have any solutions, but most of the problems involve constructing code implementations that match up with worked examples, or that give a desired result, so you can tell if you got it correct and in many cases you can follow along with the worked example to debug your code if it's not producing the desired output.)

Thank you for the response and for making these resources fully available.

Do you plan to make a proofs based book available as well?

My pleasure! I don't plan on writing any more math textbooks.

I had fun writing them and I'm glad that they are making a positive impact, but since then I've been consumed by my work on Math Academy, which I find even more fun/impactful. (We do have a Methods of Proof course out, which is many times more scaffolded, refined, comprehensive, and generally instructionally superior to any textbook I could write independently, not to mention it's adaptive.)

So, long story short, I enjoyed writing those textbooks and am glad they're seeing the light of day, but I've moved on to a new chapter of life and don't plan on writing any more math books in the future (with the possible exception of something super niche like the math behind maximizing learning efficiency in hierarchical knowledge structures).

Understood! How much is it to enroll in your “Methods of Proof” course or in Math Academy more generally? I didn’t didn’t quite understand how it works based on the FAQ, is it lecture-problem based with an interactive testing element for course placement?

Check out https://mathacademy.com/how-it-works, especially the section "The Learning Process," but let me know if you have any follow-up questions not addressed there. Pricing is a flat $49/mo per student, basically an all-you-can-eat buffet of learning.

It's just linear algebra and the chain rule. Both of these are taught in highschool.

That's Stage 1: Foundational Math -- with the addition of calculus-based probability/statistics, and the specification that it's the multivariable chain rule (not just the one in single-variable calculus), as well as differential multivariable calculus in general (gradient vector, etc.).

But there's plenty more to learn in stages 2/3/4 before you reach the cutting edge. Would encourage you to read the article! :)

Should also point out that -- in the USA, at least -- linear algebra, multivariable calc, and calculus-based probability/statistics are not typically taught in high school. There's quite a bit of university-level math that someone needs to know if they want to reach cutting-edge ML/AI.

What percent of high schools offer linear algebra?

Not many. I went to a good school but still had to wait to first-year university to learn linear algebra. Assuming you mean "real" linear algebra with matrices, inverse matrices, determinants (please don't mention Axler's book), and linear operators.

I believe Linear algebra is/was taught in the pre-calc path of the provincial public curriculum (Canada) if you chose it as an optional thing. I did not.

It's common to find a little bit of linear algebra in a serious precalculus course, but nowhere near what's needed for ML. (For instance, I've never seen a precalculus course that covers eigenvectors, diagonalization, SVD, pseudoinverse, subspace projection, etc.)

Reply on news.ycombinator.com