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I am currently trying to self study more advanced mathematics. I have taken up to multivariable calculus and have taken a class for an introduction to mathematical proofs/logic (sets, relations, functions, cardinality). I want to get a head start on the abstract math that would help me get a deeper understanding of mathematical tools used in physics. Could anyone, maybe, give me some recommendations on a linear algebra, real/complex analysis book(s)? My hope is to eventually get an understanding of topology, differential geometry and tensor calculus. Next year I am going to take a two semester sequence in abstract algebra so I won't need any self learning of that (at least I hope not).

I hope that is enough information.

Thanks!

Tom