Students will learn how to prove theorems by mathematical induction. They'll practice induction on theorems involving sums, inequalities, divisibility, and recurrences. They'll also see a false proof that all horses are the same color, and be given an explanation of why the proof is fallacious. Many proofs by induction, throughout mathematics, require knowledge particular to a given theory, but here we'll consider problems requiring just elementary algebra. Proof by induction is one of those concepts which is nonintuitive, so don't be surprised if students find this difficult to learn. Before attempting the problems in this section, students should know the basic properties of sigma notation.