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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, ect.) 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 going rather 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 writting understanding advanced proofs).

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

show/hide this revision's text 2 added 608 characters in body; edited body; added 117 characters in body; deleted 2 characters in body

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, ect.) 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 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 going rather 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 writting proofs).

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

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