Ask HN: Free online courses for gifted maths students

[hypertexthero]

A friend overseas has a 14-year-old who is very strong at math, but the family doesn’t have much money.

Are there good free online resources for such kids to help them explore and find their preferred directions, from reputable institutions?

A couple I’ve found:

1. https://science.mit.edu/diversity-and-inclusion/outreach-programs/#K-12

2. https://mity.org/online-programs/

Any others?

[impendia]

The gold standard, at least in the US, is Art of Problem Solving.

https://artofproblemsolving.com/

For the most part it is not free, but there are some free resources

https://artofproblemsolving.com/resources

and the paid programs don't cost too much, something like $400 for a 12-week online class. Also, the times are generally chosen to be convenient in the US, which might be difficult for your friend depending on where they are.

If you genuinely want something free, there is a ton out there, much of it good, but you might need to give up on "from reputable institutions". One person might post something online as a labor of love, and often that person might be employed at a reputable university, but if you want something backed up by an organization as a whole -- especially something more than "here are some notes you can read, or videos you can watch" -- then that organization will usually be asking what they stand to gain.

Here are some free notes on a variety of topics from the American Math Society:

https://www.ams.org/open-math-notes?grad_level=5

Here is my own contribution -- 150 pages on combinatorics, probability, and modeling based on TV game shows:

https://www.ams.org/open-math-notes/omn-view-listing?listing...

Best of luck!

[samstave → impendia]

This is wonderful! thank you - I look forward to reading these notes... EDIT: Vid Clips in PDF no longer available :-(

You know what would be a really interesting problem in a weird-way related to game-show math, would be crowd flow specifically through a Casino and and determining probability for people interacting with a particular game, based on crowd flow theory [0] and how you can channel the crowd, knowing their personal avoidance and personal-space behavors to aim the flow through various $->$$$ temptations. and see what gets them to stop, stay, spend.

Human Plinko. For fun and profit!

https://www.nature.com/articles/nature.2014.16385

[mangodrunk → impendia]

Thanks for sharing, your notes look interesting. I’m unable to download the pdf on my phone.

[_6vhu → mangodrunk]

Professor Leonard [0] got me through calculus in university.

[0] https://www.youtube.com/@ProfessorLeonard/playlists

[hypertexthero → impendia]

Thank you!

[giovannibonetti]

I'm surprised no one mentioned Mathacademy [1] yet. It's not free, but offers great value for money ($49/month). Last week someone even posted a great review of it [2].

[1] https://mathacademy.com/ [2] https://gmays.com/how-im-relearning-math-as-an-adult/

[cinntaile → giovannibonetti]

$49/month doesn't work for a family with little money.

[curiousgibbon]

https://nrich.maths.org/frontpage

British, run by some fantastic people from the University of Cambridge. Arguably there is no institution with a better reputation in this domain. I did some front end and back end work for them over a decade ago and there's definitely some good mathematics in there. Their mission is to enrich mathematical learning for all levels, but there's plenty of content designed for gifted teens.

I suggest looking outside the US for a curriculum. The nation that came up with the terms "precalculus" and "prealgebra" surely has a pessimistic view on the value of elementary mathematics. The ideas do not exist only to prop up calculus and algebra!

[hypertexthero → curiousgibbon]

Excellent, thank you!

[coley_moke]

The American Institute for Mathematics has an Open Textbook Initiative at https://aimath.org/textbooks/approved-textbooks.

MathPages.com could be good for enrichment.

[da39a3ee]

At 14, if the kid is very strong at math, they should try first year university classes. There are tons freely available -- just poke around university math dept web pages (e.g. Oxford, Cambridge, Berkeley, MIT). Some have full videos, some have full lecture notes, some have exams with answers, etc.

For a 14 year old I'd recommend US universities as the first year is at a lower level there than UK universities (don't know much about non-anglophone universities). E.g. look for classes called "Precalculus" -- that will not be too difficult for them. And also introductions to mathematical logic (and set theory) to get their math thinking off on the right foot.

The other advantage of this is that it will get them in the mindset that a university environment is where they're going to be in their 20s. Doing an undergrad degree and then probably a masters/PhD, which it sounds like is what this teenager should be starting to think (not yet, but when they're 16/17).

[hypertexthero → da39a3ee]

I’ll look into all of those. Thank you!

[da39a3ee → hypertexthero]

Let me know if you need links

[AVERAGECPPUSER]

Took this algorithms class at University of Michigan last year. https://sites.google.com/site/thsaranurak/teaching/intro-alg...

Thatchaphol Saranurak is widely considered as one of the greatest upcoming TCS talents, pumps out meaningful results like a monster. Expect him to leave Michigan for MIT/Berkely/Stanford tbh. I took this class and it was comparable to the UMich honors math sequence.

[kisonecat]

For in-person summer math experiences, there is https://rossprogram.org/ among other math camps many of which are listed at https://summermathprograms.org/

Ross provides significant need-based financial aid (which can cover all fees for the six-week program).

[jgord]

Not free, but in addition to AoPS.com books and website, I highly recommend :

- Algebra book by Gelfand [ amazon print n demand I guess ]

- A Decade of the Berkeley Math Circle by Zvezdelina Stankova and Tom Rike

- The Art and Craft of Problem Solving by Paul Zeitz

Also have a look at https://mathcircles.org and any math competitions available locally

[feynman423]

https://projecteuler.net

It is not a course but a collection of tasks and problems.

https://cryptopals.com/

Basically the same approach but with a strong focus on implementing cryptography and learning something about cryptology in the process.

[cevi]

This isn't exactly from a reputable institution, but I have a personal website with book recommendations: https://notzeb.com/rec.html

(not having much money is no obstacle to reading books on math, so long as you are aware of Library Genesis)

[AlchemistCamp]

MIT’s OCW is free and includes enough math to keep your friend’s kid busy for a long time.

https://ocw.mit.edu/search/?d=Mathematics&s=department_cours...

[soarerz]

Consider euler circle https://eulercircle.com/ if the kid is interested to learn about modern math. They have online classes, and financials may not be a concern if the student is admitted and is strong enough.

[stared]

I suggest starting with "What is Mathematics?" by Richard Courant (a book, not an online course). It has an excellent overview of mathematics for a young person who one day may want to become a mathematician. Later, it depends on which part of mathematics one loves the most.

[MichaelRazum]

The Problem is math=!math.

To be honest, this might be very challenging. BUT it may be possible. Just try entry level Analysis or Linear algebra. They often start kind of from scratch. How to construct numbers and so on. You could go very slow but at least you would be ready for real math...

[tech234a]

If the kid is interested in college-level courses, MIT makes many of them available for free on OpenCourseWare: https://ocw.mit.edu/

[telesilla]

If the kid does well in tournaments etc they should have no problem getting sponsored, even from overseas if necessary. I had that opportunity and have since passed it on to the next generation.

[alexander2002]

This might Help! https://github.com/ossu/math#core-mathematics

[_the_inflator]

In Germany, you can apply for a Junior Studentship at University and learn Math as a student.

[lulznews]

Just start reading Euclid etc

[sidcool]

How to solve it by Poyla

[dn2e]

Beast Academy?