These notes are intended to give examples of some of the types of special proofs that appear in many courses in mathematics. They can be used as a framework to construct your own proofs. It is important to remember, however, that there are many different approaches to proofs that make use of other facts in certain subject. For example, the examples we give here on showing a function is one-to-one might not be used in ring theory or calculus.
A number of terms will be used without definition and we encourage you to read the appropriate notes on that section. Use these links to get to the relevant set of notes: logic; sets; methods of proof; functions.