Please consider this as a soft-question as this question might be vague and please forgive me for not being clear.
Is there a general procedure of how to map one problem to another?
For example let S and L be two problems. Then solution to S implies solution to L and solution to L implies solution to S.
How would one go on to prove that solving S is the same as solving L and vise versa.
I know in computer science they do this for decision problems.
Here are the things I am interested in:
1) Is there a general procedure to show equivalence of two problems? I guess probably not, since this can be highly dependent on the problem itself.
2) Is there beginner literature on this subject?
3) Are there examples between equivalence of two problems in very different areas of math. For example, are there examples of equivalence between a problem in graph theory and number theory.
Thank you very much. Would be happy to answer any of your questions.