In one of my favorite Go books entitled Lessons in the Fundamentals of Go, the author Kageyama expresses the same sentiments: mastering the basics is fundamental for progression at every point in the player's career. He begins the book with what is very much an exercise taking some time and thought: there were no shortcuts to solve this problem for the beginner this book is aimed for. It is the same in programming: mastering anything (even the fundamentals) involves much time and effort.
As I become stronger at the game, I am finding new wisdom in the same advice Kageyama gives. I can read the same paragraph a few months apart and get different tangible results out of it. I have often had the same experience programming: I can use certain expressions and programming constructs without knowing the intricacies of them, but as I progress in my programming career, I am also able to understand these constructs, often at a lower level, to my great benefit.
I frequently go back to this book and always find new wisdom to improve my game. I strive to do the same with programming: just because I know how lambda functions in Python work does not mean I should be ignorant of the possibility that I may not know everything about them and tangentially related concepts.
I'm planning to start with high school geometry. If I can find a copy, I'm going to use the same textbook as I used in high school. It was really good. Not sure about what I'll use for a trig textbook. For calculus I'll use Tom Apostol's Calculus vols I and II - that's what we used at Caltech.