I'm a Ph.D. student in pure math (algebraic topology) going into my fourth year. I'm interested in visiting Earth.
I have a dream book in mind: in my dream book, the discussions begins with particular real-world problems, as concrete as can be, and then discusses how various math techniques can be applied. A chapter might start with a description of an easy-to-understand, complicated-to-solve problem, and then survey various approaches, to whet the reader's palate to learn more about each one.
The title might be A Survey of Applied Math for Pure Mathematicians, in the vein of Spivak's Physics for Mathematicians. It might also be written somewhat in the spirit of A User's Guide to Algebraic Topology, which aims to move quickly, allowing the reader to fill in what details she wishes.
