These notes are the basis for our Math 3345 lectures. There may be material discussed in class which is not included in these notes, and vice versa.
Lecture 1: Setting the stage, logical sentences
Lecture 2: Negation, conjunction, disjunction
Lecture 3: De Morgan's laws, distributive laws
Lecture 4: Conditional sentences, converse and contrapositive
Lecture 5: Biconditional sentences, conditional proof
Lecture 6: Conditional proof, tautologies
Lecture 7: Quantifiers
Lecture 8: Generalized De Morgan's and distributive laws
Lecture 9: Order of quantifiers, unique existence
Lecture 10: Induction
Lecture 11: Parity
Lecture 12: Axioms for the integers
Lecture 13: The well-ordering principle
Lecture 14: Divisibility
Lecture 15: Primes
Lecture 16: The infinitude of primes
Lecture 17: Real and rational numbers
Lecture 18: Irrational numbers
Lecture 19: Division Algorithm
Lecture 20: Greatest common divisors, Euclidean Algorithm
Lecture 21: Reverse Euclidean Algorithm, congruence of integers
Lecture 22: Modular arithmetic
Lecture 23: Every integer is a product of primes
Lecture 24: Division by a prime, unique factorization
Lecture 25: Prime factorization and divisibility
Lecture 26: Irrational square roots, sets
Lecture 27: Set-builder notation, subsets
Lecture 28: Subsets, algebra of sets
Lecture 29: DeMorgan's laws for sets, sets of sets, generalized unions and intersections
Lecture 30: More generalized unions and intersections, ordered pairs
Lecture 31: Cartesian products, functions
Lecture 32: Range, graphs
Lecture 33: Function composition, surjections and injetions graphs
Lecture 34: Bijections, inverse functions
Lecture 35: Cardinality
Lecture 36: Countable sets
Lecture 37: Uncountability of R