Introduces students to reading and writing mathematical proofs. Topics include sets and logic, methods of proof, equivalence relations, functions, and cardinality, and topics from number theory and calculus.
- State, interpret, and apply the definitions, theorems, and properties involving sets, divisibility, congruence, the algebra of real numbers, equivalence relations, functions, and cardinality. Communicate mathematical reasoning using appropriate mathematical vocabulary.
- Use logic and methods of proof, including direct proof, proof by contrapositive, proof by cases, proof by contradiction, existence proof, and induction proof, to produce valid mathematical proofs.
- Assess mathematical reasoning, both correct and flawed.
- Generate conjectures and determine their truth value, providing counterexamples or proofs as appropriate.
- Draw Venn diagrams to indicate set operations and to aid in the construction of proofs.