[Math] What advanced area of mathematics can be delved into with only basic calculus and linear algebra

Question

Hello Mathoverflow Community,

I would really appreciate some advice on this:

All I know is basic calculus and basic linear algebra,
I want to start learning more advanced material on my own while taking more advanced calculus/ linear algebra courses.

Is there any area of mathematics which I can delve into with only this much knowledge?
(ex: topology, number theory, etc.)
or should I instead fully focus on my courses for now?

Thank you very much,

---

Thank you so much for all of your comments

Yes I am a freshman in university, and by basic I meant Calculus I, II, and (now) III, and I'm in a linear algebra I course. I find myself really good at calculus, I pick up new topics really fast. However, I'm still improving in linear algebra.

I have picked up a couple of books on proofs, I seem to be doing well with it,
However I exposed myself to a "Elementary number theory" book and I felt like a bit of background is missing (especially in understanding advanced proofs).

Thank you once again for your amazing advice and comments, it really means a lot to me to get such advice at this stage.

Answer 1

Stillwell's Naive Lie theory was essentially written as an answer to this question. I quote from the introduction:

It seems to have been decided that undergraduate mathematics today rests on two foundations: calculus and linear algebra. These may not be the best foundations for, say, number theory or combinatorics, but they serve quite well for undergraduate analysis and several varieties of undergraduate algebra and geometry. The really perfect sequel to calculus and linear algebra, however, would be a blend of the two —a subject in which calculus throws light on linear algebra and vice versa. Look no further! This perfect blend of calculus and linear algebra is Lie theory (named to honor the Norwegian mathematician Sophus Lie—pronounced “Lee ”).