.Open Polya - how to solve it
. Source
Princeton 1988 2nd edn isbn0-691-02356-5 QA11P6 1988
.See [Polya88]
. Overview
1. $Understand, 2. $Plan, 3. $Carry_out_the_plan, 4. $Looking_Back.
.Open Details
. Understand
What is the unknown? -- goal/output/conclusion?
What are the data? -- given/input/parameters/hypothesis
What are the conditions? -- operations/relations/premises connect/ given to goal
Check conditions: possible & sufficient ~ redundant~ contradictory ~ separate
Draw a diagram.
Introduce a suitable notation.
Separate the various parts of the condition. Can you write them down?
. Plan
Use plausible, reversed, and lateral thinking to invent a way to solve the problem. Avoid rigor and details.
Look at the goal/end point first!
Have you seen a similar problem before?
.Set
Look for similar goal/given/...
Look for more general/specific.
Look at any previously solved problem/theorem... can you make use of it?
.Close.Set
Can you restate/reverse ths problem?
Review
.List
Did you use all the data/givens?
did you use the whole condition?
Have you allowed all the notions in the problem... if not revise your plan.
.Close.List
. Carry_out_the_plan
Carry out your plan step by rigorous step.
Fill in the details in steps top-down by refinement.+
At each step look for signs of progress,
Check each step for correctness.
.Set
Can you see that it is correct(intuitive)?
Use formal techniques that fill in the details in your plan.+
Can you prove that it is correct?
.Close.Set
. Looking_Back
Can you check the result?
Can you check the steps?
Did you use all the givens?
Can you improve the steps?
Can you see the whole at a glance?
Can you use the result or the method in some other probleme?
How can you share/present/publish the result? +
.Close Details
.Close