Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary surface. Or group theory by motivating it from crystal structures. Probability and statistics motivated from making exit poll predictions.
NOTE: I'm looking for math books that actually teach how to use the theory to approach a problem-- something beyond regular applied math books. Books such as Probability Theory by Jaynes
One go-to book for that sort of thing is For all practical purposes.
It's aimed more at a general audience, though, so the depth of math is limited. It gives a good sampler of diverse applications. I don't know if it has any discussion of topology, but it does cover a lot of discrete math things that are very accessible.