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Guess! Invent. Imagine. Dream.
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Don't be afraid to make mistakes.
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Did you make a mistake? What did you learn from it?
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Don't be discouraged if you can't solve a problem immediately.
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Try a different approach.
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Try a slightly different problem.
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Try a special case.
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Try a more general problem.
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Study examples.
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Look for counter-examples.
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Have more than one problem to study. When you've momentarily run out of ideas to try on one problem, work on another problem for a while.
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Write down your thoughts in a notebook (problems, questions, ideas, guesses, examples, mathematical soliloquies, what you'd like to be able to show, sketches of proofs, etc.).
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It helps to explain your ideas to someone.
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Ask for help when you need it; offer your help when others need it.
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Work with a group.
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Take breaks.
- Don't wait until you're at a desk to work. Archimedes made his discovery in his bath!
- Carry some mini-problems around in your head to think about when you have time, here and there.
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Have fun!
