These are notes for a course in math proof: An introduction to writing proofs, the basic types of proofs, and an introduction to important mathematical objects such as functions and relations. The logic and set theory are presented in a naive way.

The first link in each item is to a Web page; the second is to a PDF (Adobe Acrobat) file. Use the PDF if you want to print it.

These notes are the most recent versions; they're listed in order of presentation.

- Logical connectives

[PDF] - Truth tables

[PDF] - Truth-teller or liar problems

[PDF] - Quantifiers

[PDF] - Rules of inference

[PDF] - A graphical table with the rules of inference - use this as quick reference when you're doing logic proofs

[PDF] - Direct proofs

[PDF] - Conditional proofs

[PDF] - Existence proofs

[PDF] - Limits (epsilon-delta proofs)

[PDF] - Proof by contradiction

[PDF] - Proof by cases

[PDF] - Induction

[PDF] - Counterexamples

[PDF] - Sets

[PDF] - Set algebra

[PDF] - Limits at infinity

[PDF] - Cartesian products of sets

[PDF] - Infinite unions and intersections

[PDF] - Relations

[PDF] - Equivalence relations

[PDF] - Divisibility

[PDF] - Modular arithmetic

[PDF] - Functions (injective, surjective, and bijective functions; inverses; composition)

[PDF] - Cardinality; countable and uncountable sets; the Schröder-Bernstein Theorem

[PDF] - Partial orders and total orders

[PDF] - Inequalities

[PDF]