Primary reference: Chapter 4 (Direct Proof) of Book of Proof by Richard Hammack
The following is an outline of content covered in this unit.
The meaning of the words theorem, proof, and definition, as well as proposition, lemma, and corollary
Rewriting a mathematical statement in the form “If P, then Q”
The precise definitions of the terms even, odd, same parity, opposite parity, divides, divisor, multiple, prime, composite, greatest common divisor, least common multiple
Foundational mathematical facts that we will use without proof throughout the course. See this page for a fairly complete list of these facts.
The recipe for writing a direct proof of a conditional statement “If P, then Q”:
<aside>
Proposition. If $P$, then $Q$.
Proof. Suppose $P$.
…
Therefore $Q$.
</aside>
Breaking a proof into multiple cases, e.g. depending on whether a given integer is even or odd, or depending on whether a given integer is positive, zero, or negative.