A complete educational program in algebra and geometry for a school course?

Question

Mathematics

We need a list of references to completely eliminate gaps from school mathematics (grade 11).
I would also really like to learn how to prove theorems, but I don’t know a suitable problem book ..
Please recommend literature (textbook + problem book), which also contains derivations of important formulas and I could learn to think like a real mathematician.
I plan to become a free student at NMU, but I don’t know how to prove at all ... It would be ideal if they threw off a textbook that provides examples of many proofs.

Answer 1

I'm in the process of learning myself, so I could be wrong. But I would venture to suggest that in order to be able to prove theorems or complete assignments for proofs from leaflets, you need to prove theorems from textbooks, read it - put the book aside - proved it, it didn’t work out - we read the book again.

Answer 2

The ability to prove theorems is the ability to think logically.
For example, they proved the Great Fermat theorem (the proof is a whole book !!), i.e. it just takes a few days to rewrite it. Fermat himself proved this simply by reading some text, and simply the lack of space in the margins did not allow him to state the proof. But in any case, he did not mean such proof - he had some other and very simple ... or he was mistaken))