The Art of Problem Solving

What Hacker News says

1. 019341097Apr 2024
   You might really enjoy working through the Art of Problem solving series. They’re early math -> calc books for kids that are getting into math competitions, and they explain so much in so much detail and really get to the root of why while also developing intuition. Get the e-book version. The explainers are incredible.
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2. dcw303Jan 2024
   I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra.

   I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedagogy as Math Academy as described in TFA.

   So I gave up on that and instead have been shipping several kilograms of dead tree across the pacific in the form of The Art Of Problem Solving series of textbooks. They are great, the lesson structure and building up of complex ideas from first principles is outstanding. They will humble you though, as the exercises are tough. They're also quite expensive but IMHO worth it.

   Math Academy does look interesting, If I was not halfway through my series I would probably take a look. But I do enjoy having reference books on hand. Many times I've jumped back to brush up on a topic that has slipped from memory.

   I solve my exercises with the most low tech solution possible, but I like the freedom it gives me to try new approaches, and nothing beats the latency between idea to ink on paper.

   edit: also wanted to add that I've enrolled Chat GPT4 as my tutor. Contrary to many other's experiences that I've read, I find it to generally be very good at reasoning in this level of mathematics. It's helped me many times when I've gotten stuck. And on the occasions where it bullshitted its way to an incorrect answer, I always challenge it if I don't understand, and we ultimately find out if it hallucinated something (rare, can usually be fixed by restating the problem), or I gave it the wrong input to start with (unfortunately more common than I'd like)

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3. dcw303Nov 2023
   Math as prep for 3d game programming. I've been out of school a long time, and when I was there I didn't even get to the pre-calculus level.

   This year I've churned through all the introductory level texts from Art Of Problem Solving. Yes, they're written for high schoolers and you need to have some humility to admit you might be missing or have forgotten some fundamentals, but the lesson strucutre really appeals to me. It's the only series I've found that respects the learner and really builds up knowledge one piece at a time.

   Before I start the intermediate texts and the calculus book, I've taken a detour to "Linear Algebra: Theory, Intuition, Code" and it's sticking a lot better now than previous attempts on the subject. So that gives me some confidence.

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4. HuShifangOct 2023
   Second the Beast Academy recommendation. I'd add, it's the younger version of Art of Problem Solving. The interactive games are extremely well designed from a pedagogical standpoint, the videos are fun and clear, the visuals are appealing, etc. (And I will say, there's a TTS button on the screen so that a kid who can't read can still hear the instructions, which are usually pretty intuitive anyway, especially after the video walkthrough. And the accompanying comics have proven more supplemental than essential for us.)
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5. fn-moteJul 2023
   This is such a fraught topic.

   First point: a lot of students get "accelerated" by their parents as a way of improving their academic performance and aiming the toward an elite college. Of course you look outstanding in school if you have covered the material a year before at the local cram center. These "accelerated by rote" students memorized the multiplication tables early, so they were put in "advanced math"... but their rate of comprehension is ordinary. Their problem solving skills are ordinary. They took "advanced math" in summer school so when they take the course in the ordinary school year they have a leg up. I don't think this has to be bad, but it's not the "gifted acceleration" and can be tough on these students if expectations are that they are "fast".

   A second point: acceleration traditionally means moving through the same material faster. If you have a gifted child PLEASE work with them on a breadth of things, don't just race them through multivariable calculus. Math contests are a good source of broader problems. Art of Problem Solving gets a huge shout-out for what is now years and years of acceleration and enrichment material. Look at them if you are a parent in this situation. (Actually, they are suitable for self-study.)

   Edit: I am all in favor of kids learning new things as fast as they want. I don't see racing through the standard curriculum (in any country) as a route to happiness.

   Random brain-stimulating math book: Donald Knuth, "Surreal Numbers".

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6. gpt5Jun 2023
   If you, or someone else is seriously considering learning math from the basic at a high level, I’d recommend picking up “art of problem solving, pre-algebra” book, and walking up from there.

   These sets of books are universally considered to be among the best math education resources by mathematicians and others, and they start from the very basic (such as the number line and basic operations), but without the need of practicing elementary school material like counting.

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