[bkcooper]

Concrete Mathematics

Spivak

Jaynes

All good books, all pitched at a level that is very ill suited for what is being asked for.

To the GP, "math for English majors" is a common enough course schema that I think looking at a few syllabi might score you something.

[jonnybgood]

I specifically mentioned those because they have little to no prerequisites other than high school math which I interpret can be read by any non-math major. They’re very self-contained but have very little hand-holding. I think just absorbing a little of these books will establish a decent foundation.

[jacobolus]

Concrete Mathematics is pitched at graduate students in computing. Spivak’s Calculus is an introductory real analysis book pitched at undergraduates who have gone through a computational calculus course already and want to study the subject more formally and rigorously; it has many difficult problems and would generally benefit greatly from the structure and expert feedback of a university course. Jaynes’s book is probably most relevant to science students who are at least at the advanced undergraduate level. How to Solve It is a dictionary of heuristic problem-solving techniques which is most useful to someone who is already (deeply) familiar with mathematical problem solving, and wants to codify their existing methods. Even advanced undergraduate math students who read it aren’t going to fully understand the book IMO; I would recommend Pólya’s other books (Mathematics and Plausible Reasoning, Mathematical Discovery), or maybe start with a gentler book like Mason, Burton, & Stacey, Mathematical Thinking.