How to Solve Problems

Reference: G. Polya, How to Solve It, A New Aspect of Mathematical Method, Second Edition, Princeton University Press, 1945, 1985.

The following is a paraphrase of pages xvi-xvii.

1) Understand the problem	Write down the facts (knowns). What are the implications of the facts? Are there any contradictions or confusing parts? What fundamental definitions and principles can we apply? Is there a clarifying figure? Choose clear notation.
2) Devise a plan	Have you seen a related problem? How are the parts of the problem related to each other?
3) Get unstuck	Try to solve a simplified form of the problem. Talk to someone about the problem.
4) Carry out the plan	Carry out the solution plan. Can you check any parts of the solution?
5) Reflect on the solution	Does the solution make sense (intuition, related problem)? Does your argument make sense? Can you derive the result differently? Were there fundamental ideas/principles? Will the result or solution approach be useful in the future?