## Discrete Mathematics: Math 245, Fall 2010 Schedule

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

Day Topics Preparation
Mon. 8/30 Introduction. Statements, negation, conjunction, disjunction. Sec. 1.1
Wed. 9/1 Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals.
Secs. 1.1-2
Fri. 9/3 Conditionals and English usage.
Logical arguments.
Secs. 1.2-3
Wed. 9/8 Logical arguments.
Logic circuits.
Secs. 1.3-4
Fri. 9/10 Logic puzzles Secs. 1.3-4
Mon. 9/13 Sets: subset, union, intersection.
Predicates, truth set of a predicate.
Secs. 5.1, 2.1-2
Wed. 9/15 Quantified predicates. Negation.
Translation from English.
Secs. 5.1, 2.1-2
Fri. 9/17 Multiply quantified predicates. Secs. 2.3
Mon. 9/20 Arguments with quantified predicates.
Logic puzzles.(2nd Ed. 2.3#27, 3rd Ed. 2.4#31)
Secs. 2.3 (2nd Ed) 2.4 (3rd Ed.)
Wed. 9/22 Cartesian product, power set, partitions.
Theorem 5.2.2: Properties of sets.
Proving theorems about sets.
Secs. 5.1-3
Fri. 9/24 Disproof by counterexample.
Partition of a set. The power set.
Secs. 5.1-3
Mon. 9/27 Mathematics: Axiom, Definition, Theorem, Proof
Axioms for the integers.
Ch. 3.1 (and my lecture notes Ch 3.
Wed. 9/29 Questions before the exam?
Properties of order and divisibility.
Ch. 3.1,3 (and my lecture notes)
Fri. 10/1 EXAM Ch. 1, 2, 5
Mon. 10/4 Divisibility
The Quotient Remainder Theorem.
Sec. 3.3 (1st part).
Wed. 10/6 The Quotient Remainder Theorem.
The Euclidean algorithm.
Sec. 3.4
Sec. 3.8
Fri. 10/8 Primes and the Unique Factorization Theorem.
Proof by contradiction.
Secs. 3.3.3, 3.6
Mon. 10/11 Rational numbers and irrational numbers.
Proof by contractiction.
Secs. 3.5.
Wed. 10/13 Representation of integers in binary, octal, etc.
Floor and ceiling functions.
1.5, 4.1 (just one page).
Sec. 3.7
Fri. 10/15 Sequences, summation and product notation. Sec. 4.1, Sec 8.1
Mon. 10/18 Explicitly defined sequences and
recursively defined sequences
Sec. 4.1, Sec 8.1
Wed. 10/20 The well ordering principle. Induction. Sec. 4.2,4.
Fri. 10/22 Proof by mathematical induction.
Some induction proofs.
Sec. 4.2-3, p. 217-218.
Mon. 10/25 EXAM Ch. 3
Wed. 10/27 Induction proofs for divisibility and inequalities Sec. 4.2-3
Fri. 10/29 Recursively defined functions and strong induction. Sec. 4.4, 8.1
Mon. 11/1 Functions Sec. 7.1, 10.1
Wed. 11/3 Relations and functions.
The inverse of a relation.
Sec. 7.1, 10.1-2.
Fri. 11/5 Functions: injective, surjective, bijective. Sec. 7.1-2.
Mon. 11/8 Composition of functions. Sec. 7.4.
Wed. 11/10 Questions before the exam? .
Fri. 11/12 EXAM. Secs. 4.1-4; 8.1-2.
Mon. 11/15 Properties of relations on a set:
reflexive, symmetric, transitive
Sec. 10.2
Wed. 11/17 Equivalence relations Sec. 10.3
Fri. 11/19 Equivalence relations Sec. 10.3
Mon. 11/22 Partial orders. Sec 10.5
Wed. 11/24 Partial orders. Sec 10.5
Mon. 10/29 Counting: The multiplication rule, the addition rule.
Possibility trees.
Sec. 6.2-3
Wed. 12/1 From the addition rule to inclusion-exclusion. Sec 6.3
Fri. 12/3 EXAM Secs 7.1,2,4 (1,3,5 in 2nd Ed.)
Secs 10.1,2,3,5.
Mon. 12/6 Four ways to count. Sec. 6.1,4
Wed. 12/8 From counting to probability.
Poker hands.
Binomial theorem. Pascal's triangle.
Sec. 6.4, 6.6, 6.7
Fri. 12/10 Questions and exam prep. .
Mon. 12/13 (10:30-12:30) FINAL EXAM. Cumulative.