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Here is a self-citation from my 22B notes
(originally written in 2018 when it was Math 22A):
The mother of all problem solving books is Polya's "How to solve it" which
was published in 1945. If you read and absorb this book, you immediately
get measurably stronger in math. Still after more than 70 years, it is the best.
Here are the now famous Polya principles:
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1. Understand the problem: unknowns, data, draw figure.
2. Devise a plan: similar or related problem?
3. Carry out the plan: check each step.
4. Examine the solution: can other problems be solved as such?
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Why is it powerful? Because if one sees a harder problem the first time, one
is totally lost. (Proof: if not, then the problem was easy ....)
Where do we start? This is where it is good already to have a guide
telling you: well, just first start to understand the problem.
Here are documents, written over the years, about problem
solving techniques and related, Artificial intelligence. The later is the task to have
computers solve problems automatically:
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