Motivation: Both out of my interest of the subject, and as a way to save up time at later dates for other purposes, i have pre-studied my high school's math curricilum, plus more. Currently i'm trying to learn how to draw, which limits the amount of time i have for doing math quite significantly. I still have two years left in high-school, and i have a lot of knowledge right now that i don't want to just forget and have to relearn all again at a latter date. I also have a big chance (no reply on job application yet) of getting a job as a math tutor. So it's pretty important for me to remember what i've learned. I do write extensive notes, but still found that after about $1.5$ months of no math, i had forgotten a ton, which ended up wasting alot of time.
I want then - to some extent - to put off a limited time of my day that will help me stay "mathematically fit". I'm thinking that math problems are the best way to do that. Specifically, if they combined various fields i've learned, then i'd have to more frequently recall more things, and i would start understanding things at a deeper level than earlier.
What precisely i am looking for: Very briefly and broadly, what i currently know - at a high-school level - is:
- Algebra/precalculus
- Geometry and trigonometry
- Algebraic geometry (mostly just conic sections and their connection though)
- Probability theory and combinatorics
- Complex numbers
- Limits and sequences and infinite series
- Vectors and matrices. Transformations and 3D space.
- Calculus. Vector calculus.
- Multivariable calculus
- Linear algebra
- Differential equations (only up to and including second order linear though).
I'm looking for books with problems that require knowledge from various of these fields. Ideally, problems that combine some of them. I know that there obviously isn't any problems book with specifically just these fields, but one with just a some of them would be great.
Thanks for the help!