I've been studying math as a hobby, just for fun for years, and I had my goal to understand nearly every good undergraduate textbook and I think, I finally reached it. So now I need an another goal. I've just found a very nice book /S. Ramanan – Global Calculus/ from the "Graduate Studies in Mathematics" series and it looks nearly awesome:
- Sheaves and presheaves
- Differential manifolds
- Lie groups
- Differential operators
- Tensor fields
- Sheaf cohomology
- Linear connections
- Complex manifolds
- Ricci curvature tensor
- Elliptic operators
But it's only 316 pages and it seemed not very fundamental and detailed for me (but yes, it's still great). So here's my question: what huge complicated calculus textbooks like this one do you know that I should aim to understand? The Big Creepy Books, you know :) I'm very interested in algebraic and differential geometry, general and algebraic topology, Lie groups and algebras, pseudo- and differential operators. I don't know very much about all of this yet but I'm trying so hard to do, it's so exciting! ;)
I've already covered:
- Algebra: Chapter 0 (Graduate Studies in Mathematics) by Paolo Aluffi
- A Course in Algebra (Graduate Studies in Mathematics, Vol. 56) by E. B. Vinberg
- Linear Algebra and Geometry (Algebra, Logic and Applications) by P. K. Suetin, Alexandra I. Kostrikin and Yu I Manin
- Topology from the Differentiable Viewpoint by John Willard Milnor
- Topology and Geometry for Physicists by Charles Nash and Siddhartha Sen
- Mathematical Analysis I and II by V. A. Zorich and R. Cooke
- Complex Analysis by Serge Lang
- Ordinary Differential Equations by Vladimir I. Arnold and R. Cooke
- Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics) by Sigurdur Helgason
So I'm looking for something like Ramanan's book, but maybe more detailed and fundamental.