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My problem solving strategy involves looking at the problem and collecting as much relevant information as possible, elaborating the given information and waiting for a general strategy to develop. This of course happens after I understand the question and before I come up with strategy.

Many Problem Solving Strategies mention for example, Understanding, coming up with a plan, implementing the plan.

The strategies never mention the crucial event between understanding and coming up with a plan. What does your thought process involve while solving problems?

Or after understanding the problem, what measures ease your development of strategy?

P.S. Happy to delete if this is not suitable. Just leave a comment.

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up vote 1 down vote accepted

My general guidelines for solving problems:

  1. Identify what I am trying to solve. Is this a variable, algorithm or something else?

  2. Identify what else do I know that may be useful to solve this issue. This is tricky because there may be a great deal of other information that may help in trying to solve the issue.

  3. Formulate an arrangement of the elements from the first 2 steps in order to set up a plan to resolve the issue. This can be setting up equations, constructing models, writing software, or any of 101 other things that may help to process what I have to get where I want to be.

  4. Follow the plan to get a result that is of the type noted in the first step.

  5. Verify that this is correct and be prepared to justify why this is correct.

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You might want to have a look (there are others) at some of these sorts of books and practice the general art to learn better proof strategies.

General Proof Strategies

  • How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library), G. Polya

  • How to Prove It: A Structured Approach, Daniel J. Velleman

  • The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs, Antonella Cupillari

  • How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, Daniel Solow

You might also want to look at the Triki and at Open Courseware at places like MIT and also at Khan Academy.


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Nice recommendations, as usual ;-) – amWhy May 4 '13 at 0:22

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