What are some common proof strategies in mathematics?

proof-writing big-list reference-request soft-question

There are many interesting problem-solving techniques listed at the Tricki.

http://www.tricki.org/


Here is a list of 36 methods of proof.


Maybe this book can help you a little:

Daniel J. Velleman, How to Prove It: A Structured Approach

Related

Why is the expected value $E(X^2) \neq E(X)^2$?
Why are fractions the same as divisions? [duplicate]
Meaning of the spectral norm of a matrix
Homotopy groups of $S^2$
Why is the rational number system inadequate for analysis?
Examples of compact sets that are infinite dimensional and not bounded
If $A^2 = I$ (Identity Matrix) then $A = \pm I$
Prove that if $AB$ is invertible then $B$ is invertible.
How does the exponent of a function effect the result?
Why ${ \sum\limits_{n=1}^{\infty} \frac{1}{n} }$ is divergent , but ${ \sum\limits_{n=1}^{\infty} \frac{1}{n^2} }$ is convergent?
Limit question - L'Hopital's rule doesn't seem to work
Do I need to cite an old theorem, if I've strengthened it, wrote my own theorem statement, with a different proof?