Tentative Weekly Schedule
MATH
220 Fall 2016
Week 1
- Statements
- Open Sentences.
- Compound Statements.
- Implications
- Converse statement
- Negations
- Logical Equivalence
Week 2
- Some Fundamental Properties of Logical Equivalence
- Quantified Statements and Negation Rules
- Trivial and Vacuous Proofs
Week 3
- Integers and some of their elementary properties
- Direct Proof
- Proof by Contrapositive
Week 4
- Proof by Cases
- Disproving Statements
- Proof by Contradiction
- Review of the three main proof techniques
Week 5- Existence Proofs
- Uniqueness Proofs
- Mathematical Induction
Week 6
Week 7
Week 8
- Functions: Definition and Basic Properties.
Week 9
- Surjective and Injective Functions.
Week 10
- Composition and Invertible Functions.
Week 11
Week 12
- Exam 2.
- The Integers: Axioms and Basic Properties.
- Induction (proof).
Week 13- The Division Algorithm and Greatest Common Divisors.
- Primes and Unique Factorization.
Week 14
- Equivalence Relations
- Congruences.