People often talk about the importance of problem solving skills, but there's shockingly few resources that analyze the problem solving process from a general point of view (outside of some problem solving domain). Does anyone have any non-orthodox suggestions for books/essays on problem solving?
Polya's "How to Solve It" and Paul Zeitz's "Art and Craft of Problem Solving" are both great. Are there other resources on this topic that are worth reading?
"Problem-Solving Through Problems" by Loren C Larsen (1983) was my favorite at high school.
The sections headings of Chapter 1 on Heuristics give a flavor of its approach: Search for a pattern; Draw a figure; Formulate an equivalent problem; Modify the problem; Choose effective notation; Exploit symmetry; Divide into cases; Work backward; Argue by contradiction; Pursue parity; Consider extreme cases; Generalize.
I'll add that this book is well above normal high school math. It was our summer reading for Math Olympiad training.
I narrowly missed a place on the Australian IMO team, and at the time was annoyed at myself for being beaten by a 10 year old. He, of course, was Terry Tao, youngest ever winner of a IMO medal, and a Fields Medalist a few years later.
Unfortunately most of the resources that I know of are more geared toward landing a technical interview. Thanks for mentioning those books though -- I'll have to check those out.
It might be too basic for you but I'm really enjoying working through some of the Art of Problem Solving book series (Introduction to Counting and Probability). I have a PhD in biomechanics but still find many problems to be a fun challenge.
Polya's "How to Solve It" and Paul Zeitz's "Art and Craft of Problem Solving" are both great. Are there other resources on this topic that are worth reading?