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dcw303

AOPS audience is gifted high school kids, so it doesn't get up to the college level. The core texts are:

- Prealgebra

- Intro to Algebra

- Intro to Counting & Probability

- Intro to Geometry

- Intro to Number Theory

- Intermediate Algebra

- Intermediate Counting & Probability

- Precalculus

- Calculus

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Ah, okay. I actually took calculus in 8th grade. I studied another two years past that, dropped out, and then later did a complete 180 and graduated with a literature degree.

I'm now over 40 and interested in relearning the math I learned long ago and pushing a bit further than I had before.

There’s also an intermediate number theory class that’s basically at the level of a college elementary NT course (one that does not assume abstract algebra), an Olympiad geometry class, and a group theory class. The first two do not have a text, the third has a text but you can’t get it without enrolling.

I bought the whole set for my kid. He's also doing Brilliant.

It starts at somewhere that the kids are at the end of primary school (at least in the UK) and ends somewhere in high school. My kid could already do all the pre-algebra stuff, so that book went fast. The way I see it, the kids waste a lot of time in the middle years when they already know the arithmetic and pre-algebra, but might as well be doing a bunch of more interesting things.

I think it's a weird way to learn math, and I learned it this way in school. Most of these courses just teach information memorization and recall. sin(x)^2 + cos(x)^2 = 1, etc.

I would start with something like Elementary Analysis: The Theory of Calculus, and work from there. You'll eventually arrive at the same place -- Calculus but from a much stronger mathematical foundation.

You learned using the AOPS books? Don't be fooled by the titles, these books exclusively use a proof-based approach to construct a pretty wide foundation around these topics.

AoPS are among my favorite math books, but they're definitely not proof-based or particularly rigorous in terms of formalism.

They do focus on complex problem solving, which is equally important. The key value-add of AoPS are interesting, often beautiful examples and problems.

However, they don't do proofs or formalism much. They don't do applications or show what math is useful for. And they completely, totally, and universally screw up units (you'll have problems trying to equate a length with an area and similar; that's true of their classes as well, and RSM is similar).

I don't think there's a one-stop-shop for math, though, which does everything right. AoPS is at the peak of their particular game (which is right in the name: problem-solving).

That's best complemented by:

- Something which does data, applications, visualizations, and storytelling well.

- Something which does early exposure / surface learning well

- Something which is more formal and rigorous in terms of proofs and derivations

- Something which touches on a broad set of interesting topics (graph theory, oddball parts of geometry, etc.)

- In 2024, I would add something which does computational mathematics well

Nothing I know of does all those well in a one-stop-shop.

I have not found that to be the case, the books I have read have gone into deep foundational detail to build up knowledge. Perhaps you're referring to Vol 1 & 2 of "The Art Of Problem Solving"? I haven't read them but from what I know they are a distillation of core concepts for students looking to do competitive maths.

It's confusing because that title is also the name of the publisher / website of the series of the books I'm reading.

Are you doing the online classes or only the books? I wanted to register for the online classes but they seem to be heavily oriented towards interactive learning.

Just self study with the (physical) books. I did also try the ebook combo for the Prealgebra book, but I found typing latex in the answers to the exercises was cumbersome.

I think the online classes with interactive lessons is a separate thing, but I don't have any experience with that.

The ones that have “instructors” and class times have chat-based sessions that you can skip if you prefer. Part of the homework is based on an adaptive problem system (Alcumus, which you can actually use for free) and part is weekly problem sets mostly based on the textbook. Writing (proof) problems are graded by a human so it is a useful way to get feedback on your proof-writing skills (if you know you are worse at it than a college math major).

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