Snap. I am also a physicist trying to learn math. In my case it's:

- Introduction to Analysis (Mattuck)

- Elementary Differential Geometry (Pressley)

both chosen because they have solutions in the book, which I find important for self-study.

Also just got (hot off the presses)

Visual Differential Geometry and Forms (Needham)

Looks fantastic!

Topology is next on the list...