Problem Solving Techniques

Re:Problem Solving Techniques by georgewsinger on Sunday November 08, 2020 @03:33PM (#25028737)

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?

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Re:Problem Solving Techniques by stevesimmons on Sunday November 08, 2020 @06:02PM (#25029919)

"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.

Links:

* Official Springer book web site: https://www.springer.com/gp/book/9780387961712

* Amazon: https://www.amazon.com/Problem-Solving-Through-Problems-Prob...

* Poor quality scanned PDF: https://math.la.asu.edu/~ifulman/spring13/mat194/problem-sol...

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Re:Problem Solving Techniques by stevesimmons on Monday November 09, 2020 @04:16AM (#25032903)

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.

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Re:Problem Solving Techniques by golergka on Sunday November 08, 2020 @08:29PM (#25030600)

Theory of inventive problem solving, an in-depth methodology developed in the soviet union.

https://en.m.wikipedia.org/wiki/TRIZ

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Re:Problem Solving Techniques by denvaar on Sunday November 08, 2020 @03:59PM (#25028966)

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.

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Re:Problem Solving Techniques by sdenton4 on Sunday November 08, 2020 @04:07PM (#25029051)

Zeitz is a fantastic book, which I absorbed in early university. It's still a helpful bedrock for my problem solving skills today.

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Re:Problem Solving Techniques by projectileboy on Sunday November 08, 2020 @04:04PM (#25029023)

Street Fighting Mathematics, and The Art of Insight in Science and Engineering, both by Sanjoy Mahajan. You can find the PDFs online.

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Re:Problem Solving Techniques by Jugurtha on Sunday November 08, 2020 @06:55PM (#25030202)

- "The Complete Problem Solver", John R. Hayes

- "General Methods for Solving Physics Problems", Belikov.

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Re:Problem Solving Techniques by montalbano on Sunday November 08, 2020 @08:10PM (#25030518)

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.

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Re:Problem Solving Techniques by Caylio on Sunday November 08, 2020 @08:13PM (#25030532)

Mathematical problem solving by Alan Shoenfield

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