Came here to recommend this. I completed my bachelors in mathematics back in 2003. However, recently I am thinking of going back to school to study graduate level mathematics or higher, and possibly do a PhD in a related field. My tentative plan over the next couple of years is as follows

1) Art of Problem Solving - all of the books to review mathematics at middle/high school level 2) Roughly follow the plan mentioned in https://www.susanrigetti.com/math to redo an undergraduate degree 3) Also complete the books here - https://foundations-of-applied-mathematics.github.io/ 4) Move on to more advanced graduate level mathematics

I also came here to say this.

I have a PhD in engineering that was fairly mathematical, but I was missing lots of fundamentals and working through those books has changed my life, and the way my brain works, in a massive way.

They aren't cheap, but they are worth every cent. I am very grateful for having discovered them.

AoPS leans a little too hard into silly contest math / trivia tricks, not into deep understanding of the underlying mathematics. Also, they have low production values, lacking the nice graphics used in professional school textbooks (before Eureka and the greedy cult of throwaway monochrome textbooks ruined everything) to help students visualize 2D/3D functions and geometry.

The AoPS books jassume that if you are smart enough to learn the tricks and hard problems, you are smart enough to learn deep math later.

Which is a strange premise, because the PhD geniuses who created AoPS, base their credibility on the fact that they aced all these contests when they were kids... But they did it without any of these materials!

They created a "teaching to the test" curriculum, which, while mathematically sound, created a rat race that makes the contests harder every year, requiring more memorization and silly speed training, as more people memorize all the strategize that the original contests expected student to try to creatively discover on their own.

+1 What I find really useful about these books is they allow self-teaching. (in my case a 13 year old kid) The books follow a methodology of presenting problems and having you try to solve them before walking you through the explanations. The chapters build up to "challenge problems" which are carefully crafted to require you to apply what you've learned from the current and earlier chapters. Most of the challenge problems are lifted from math competition problems (with citations), but their use is very well curated.

We are using the printed books, but there are online resources available.