Proof

Proof is central to mathematics inquiry. It is at the heart of what we mean when we claim to know that a mathematical result is true. Proving theorems is the exciting, frustrating, and unavoidable challenge faced by all mathematics researchers. Proofs are also a means of gaining insight into a mathematical question.

Consult the discussions and exercises in the proof section of the teacher handbook.

For specific proof techniques, see:

Conditional Statements

Proof by Contradiction

Mathematical Induction

Parity Arguments

Pigeonhole Principle

Many interesting examples of proofs can be found at Cut-the-Knot. See, for example, Proofs in Mathematics.

See also Moment of Truth and the essays in The Mathematical Experience by Philip Davis and Reuben Hersh published by the Houghton Miffllin Company (see sample essays Proof and The Prime Number Theorem).