I am an upcoming year 12 student, school holidays are coming up in a few days and I've realised I'm probably going to be extremely bored. So I'm looking for some suggestions.
I want a challenge, some mathematics that I can attempt to learn/master. Obviously nothing impossible, but mathematics is my number 1 favorite thing and I really want something to keep me busy and something that can further my understanding of mathematics. Also I would be interested in any mathematical focused book suggestions.
So far in school I've done the usual:
Matrices, transformation matrices, Sine Cosine and Tangent (graphs and proofs), lots and lots of parabolas/quadratics, statistics, growth and decay, calculus intro, Calculus derivation and integration, vectors, proof by induction and complex numbers.
Any suggestions would be heavily appreciated.