[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.

[dsacco]

Concrete Mathematics is solidly an undergraduate text. Much of the material in it would already be taught well before graduate school. The preface actually states the book takes comes course material taught to graduates and junior/senior undergraduates and presents it for a “wider audience (including sophomores).”

Otherwise I basically agree with your comment. I just take issue with calling Concrete Mathematics a graduate textbook, because I hear people say that as though it’s not an appropriate recommendation for learning. That gives me the impression they’ve not actually opened up a graduate textbook in math or computer science. Concrete Mathematics might not be year one material, but you can do it after a calculus course and maybe an algorithms course. Contrast this with an actual graduate course, like convex analysis and optimization. Textbooks at that level would definitely not be accessible for most undergrads.

[jacobolus]

Fair enough. It’s still not an easy book for someone to self-study after having no university-level mathematics, just as a side hobby.

I would certainly recommend giving it a shot for anyone interested, as it’s a lovely book full of fun problems. As you say, it’s accessible to well prepared undergraduates.