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Anyone know of any good mathematical texts?

  • Thread starter ascapoccia
  • Start date
I'm a graduating senior who found out much too late in my academic career that I absolutely love mathematics. I've taken all the basic calculus courses, a three quarter series on real analysis, abstract mathematics (essentially a proof course), and an applied linear algebra course. However, the university will not let me stay long enough to continue and get a major or even a minor in mathematics. Because of this, I would need to extend my study beyond coursework.

This leads me to ask : What texts anyone would recommend to read for someone like me, with a basic understanding of theory and proofs, in order to better understand mathematics? I'm much more interested in theory than application, especially since my major is economics and there isn't much application of mathematical theory in my field beyond the courses I've already taken. I was wondering if perhaps anyone knew of some interesting or foundational books I could use to further my study of mathematics. or if there happens to be anyone who knows of a text on the application of mathematical theory to economics beyond the introductory calculus series?

Thank you for your responses.
Mathematics is huge, and there are good books in every field. It's kind of hard to give recommendations without having an idea of what area of mathematics you want to learn about.

So I'm just going to throw out a few mathematics books that I really liked and maybe you could pick up one that sounds interesting.

What is Mathematics - Courant & Robbins

Introductory Functional Analysis with Applications - Kreyszig

The Shape of Space - Weeks

Foundations of Applied Mathematics - Greenberg

Numerical Linear Algebra - Trefethen & Bau

Calculus on Manifolds - Spivak
Thanks, I'll look into some of those.
Artin - Algebra. Abstract algebra and rigorous linear algebra will blow your mind.

Munkres - Topology. The cleaner version of real analysis.

As maze said, Spivak's manifolds.

Stillwell - Intro to topology and combinatorics (or something like that).

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