Biological Sequence Analysis

I work in that area :) The skills needed will vary a lot. Hence my concern about studying H&H. It's a good idea, as real analysis is the foundation. But it will take too much of your time to get to something useful. Probably you should try to learn more applied material in parallel and let both threads merge in the future. For maximum likelihood, you need to learn convex optimization right after real analysis. The canonical reference is [1], but there's also a very simple and pragmatic linear algebra textbook by the same author that also covers some of the optimization basics [2]. This might be a good entry point, certainly easier than Spivak or H&H. There's also [3,4], which you probably know about. These are great and emphasize the modeling part. Maximum likelihood (via EM) is in the appendix, and you don't really need to know a lot of math to get going.…

(I'm going to ignore the prohibition on "programming/technical books".) - GEB - SICP - anything by Paul Auster or Hermann Hesse - most Haruki Murakami, especially "The Wind-up Bird Chronicle" - Joan Didion, "Where I Was From" - Richard P. Gabriel, "Patterns of Software" - Durbin, Eddy, Krogh, and Mitchison, "Biological Sequence Analysis" - Italo Calvino, "if on a winter's night a traveller"