Hi Max,

Forget buying books. Just buy access to a good university library. That will be much cheaper. Make sure it also gives you access to online journals.

I would suggest starting with group theory, analysis(real and complex), elementary number theory, algebraic number theory, analytic number theory and then working your way up to algebraic geometry, differential geometry and so on.

I found the books published by the Mathematical Association of America very useful to get some intuition.

You may also want to browse through the American Math Monthly. It has lots of tutorial-style articles on various subjects. Search mathscinet for articles which have won expository writing awards. For example, I found this article quite useful

MR0401754 (53 #5581) Abhyankar, Shreeram S. Historical ramblings in algebraic geometry and related algebra. Amer. Math. Monthly 83 (1976), no. 6, 409--448.

Make an attempt to connect the problems which occur across various areas of math. See DIEUDONNE's Panorama of pure mathematics for a good overview of various areas of math.

MR0662823 (83e:00003) Dieudonné, Jean Alexandre A panorama of pure mathematics. As seen by N. Bourbaki. Translated from the French by I. G. Macdonald. Pure and Applied Mathematics, 97. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. x+289 pp. ISBN: 0-12-215560-2 00A05

Hope you have an interesting journey...!

This figure connecting all math may be helpful in your future research Sourced from http://space.mit.edu/home/tegmark/toe.gif alt text http://space.mit.edu/home/tegmark/toe.gif

Forget buying books. Just buy access to a good university library. That will be much cheaper. Make sure it also gives you access to online journals.

I would suggest starting with group theory, analysis  (real and complex), elementary number theory, algebraic number theory, analytic number theory and then working your way up to algebraic geometry, differential geometry and so on.

I found the books published by the Mathematical Association of America very useful to get some intuition.

You may also want to browse through the American Math Monthly. It has lots of tutorial-style articles on various subjects. Search mathscinet for articles which have won expository writing awards. For example, I found this article quite useful

MR0401754 (53 #5581) Abhyankar, Shreeram S. Historical ramblings in algebraic geometry and related algebra. Amer. Math. Monthly 83 (1976), no. 6, 409--448.

Make an attempt to connect the problems which occur across various areas of math. See DIEUDONNE's Panorama of pure mathematics for a good overview of various areas of math.

MR0662823 (83e:00003) Dieudonné, Jean Alexandre A panorama of pure mathematics. As seen by N. Bourbaki. Translated from the French by I. G. Macdonald. Pure and Applied Mathematics, 97. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. x+289 pp. ISBN: 0-12-215560-2 00A05

Hope you have an interesting journey...!

This figure connecting all math may be helpful in your future research:

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