I have recently graduated from high school, and intend on continuing mathematics study in university. For the next couple of months, I don't really have anything to do, and would like to continue doing math in my spare time.
The math I've done so far (and enjoyed) is calculus and optimisation, linear algebra, vectors, vector calculus, complex numbers, and matrices.
I guess my question is, how do I do this? I've had an idea of working through problems from my high school text book, or even borrowing a university level textbook. Are either of these good ideas?
How do you study math in your spare time?
Best Answer
I think your next move should be Algebra. Without a good understanding of groups you will probably get stuck in every branch of your studies. This notion it will be the starting point of so many developments in Mathematics that it is not even worthwhile defending my thesis since no mathematician born after 1850 would oppose it.
Personally like and would study Herstein "Algebra" or Artin. Workout all the examples and all the exercises since at this stage the mathematics is still very very fundamental and you really have to digest every step of the matter. I think a good study of these subjects will take a couple of months. When you're finished maybe you can switch to Differential Geometry.