Discrete Mathematics: Math 245, Spring 2004 Schedule

I will try to keep to this schedule but will update it as needed.

Definition of the rational numbers.
Partial order relations.
Day Topics Preparation
Wed. 7/13 Introduction. Statements, negation, conjunction, disjunction.
Logical equivalence, Theorem 1.1.1
Sec. 1.1
Th. 7/14 Conditionals, converse, inverse, contrapositve and biconditional.
Logic circuits
Sec. 1.1-2
Sec. 1.4
Mon. 7/18 Conditionals and English usage.
Logical arguments.
Sec. 1.2-3
Tu. 7/19 A bit about sets.
Predicates and their truth sets.
Quantified predicates.
Sec. 5.1
Sec. 2.1
Wed. 7/20 Quantified predicates: negation and multiple quantifiers.
Arguments with predicates.
Sec. 2.2, 3
2.4
Th. 7/21 Fundamental properties of the integers.
Divisibility theorems and proofs.
Sec. 3.1
3.3,
Mon. 7/25 Three theorems we assume:
The quotient-remainder theorem.
If prime p divides ab then p divides a or b
Unique factorization of integers.

Secs. 3.4

Sec. 3.5
Tues. 7/26 Exam: Logic
Unique factorization of integers.
Rational numbers.
Ch. 1, 2
Sec. 3.3,5
Wed. 7/27 The floor and ceiling functions.
Proof by contraposition and contradiction.
Three classic theorems.
Sec. 3.5
Secs. 3.6,7
Thurs. 7/28 Infinitude of primes
Properties of Sets:
The empty set;    Theorems 5.2.2 and 5.3.3
Sec. 5.1-3
Mon. 8/1 Set difference and symmetric difference.
Algebraic proofs of set properties.
Partitions of a set
The power set of a set.
Sec. 5.1-3
Tues. 8/2 Exam: Integers and proof strategies
The Cartesian product of sets.
Relations from A to B, and functions.
Secs. 3.1, 3.3-7
Secs. 10.1, 7.1
Wed. 8/3 Relations and functions:
inverse relation, injective, surjective functions.
Relations on a set A :
Reflexive, symmetric, transitive properties.
Sec. 7.1-3,

Sec. 10.2
Thurs. 8/4 Transitive closure.
Equivalence relations and partitions.
Sec. 10.2
Sec 10.3
Mon. 8/8 Examples of equivalence relations:
integers mod n, the Mobius strip.
Sec. 10.3

Sec 10.5
Tues. 8/9 Partially ordered sets.
Sequences, summation and product notation.
Sec. 10.5
Sec. 4.1
Wed. 8/10 EXAM
The well ordering principle. Induction.
Sec 5.1-3, 7.1-3, 10-1,2,3,5
Sec. 4.2, p. 240-241.
Thurs. 8/11 Some induction proofs. Sec. 4.2-3.
Secs 8.2.
Mon. 8/15 Recursively defined sequences and formulas for them.
Arithmetic, geometric and other sequences.
Strong induction.
Sec. 8.1,2,
4.4
Tues. 8/16 Some strong induction proofs.
Counting the basics
Sec. 4.4, 8.1,2
6.1,2
Wed. 8/17 EXAM.
Inclusion/exclusion principle.
Secs. 4.1-4, 8.1-2.
Sec. 6.3,4.
Thurs. 8/18 4 ways to choose.
Binomial coefficients.
Pascal's triangle.
Sec. 6.4, 6.6, 6.7
Mon. 8/22 Probability, poker hands.
Questions?, Review.
Sec . 6.4.
Tues. 8/23 Final Exam. .