I am looking for books for the full high school maths curriculum, just to refresh myself (it's been years). it must have questions & solutions.
I think you posted this question earlier today and I had about a three paragraph response with a ton of advice but then you deleted the post (apologies if that wasn't you). So... here is the abbreviated version. Read the following books,
- Practice Makes Perfect: Algebra. [Amazon Link]
- Practice Makes Perfect: Precalculus. [Amazon Link]
- Practice Makes Perfect: Calculus. [Amazon Link]
If you are interested in getting access to higher mathematics afterwards I recommend the following book by Chartrand, Polimeni, and Zhang. It is an incredible introduction to proofs and various areas of mathematics.
"Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. [Amazon Link]
There is an entire chapter devoted to each of the following:
- Communicating Mathematics
- Naive Set Theory
- Direct Proof
- Proof by Contrapositive
- Existence and Proof by Contradiction
- Mathematical Induction (and Strong Induction)
- Equivalence Relations (Equivalence Classes, Congruence Modulo n, Modular arithmetic)
- Functions (Bijective, Inverse, Permutations)
- Set Theory (up to Schroder-Bernstein Theorem and the Continuum Hypothesis)
- Number Theory
- Calculus (Limits, Infinite Series, Continuity, Differentiability)
- Group Theory (up to Isomorphic Groups)
With Three Additional Chapters online covering:
- Ring Theory
- Linear Algebra
That should keep you busy for a while, and after reading through Chartrand/Polimeni/Zhang, you will know what area of mathematics you are more interested in or if you still want to learn more!