## Discrete Mathematics: Math 245, Fall 2002 Schedule

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

Day Topics Preparation
Wed. 9/4 Introduction. Statements, negation, conjunction, disjunction. Sec. 1.1
Fri. 9/6 Logical equivalences, tautologies, contradictions.
Conditionals
Sec. 1.1-2
Mon. 9/9 Conditionals and English usage, biconditionals.
Logical arguments.
Sec. 1.2-3
Wed. 9/11 Class canceled .
Fri. 9/13 Logical arguments. Sec. 1.3
Mon. 9/16 Logic circuits. Predicates and quantifiers. Sec. 1.4, 2.1
Wed. 9/18 Predicates, quantifiers, truth sets. Secs. 2.1
Fri. 9/20 Conditional predicates.
Multiply quantified statements.
Sec. 2.2
Mon. 9/23 Arguments with quantified predicates.
A logic problem.(2.3#27)
Sec.2.3
Wed. 9/25 Three proofs:
The sum of evens is even.
If a divides b and b divides c then a divides c.
Consecutive integers have opposite parity.
Sec. 3.1, 3.3, 3.4
Fri. 9/27 Three theorems we assume:
The quotient-remainder theorem.
If prime p divides ab then p divides a or b
Sec. 3.4, 3.3,
Mon. 9/30 Questions?..
Unique factorization of integers. (leftover from Fri.)
Proof of biconditionals.
Proof using the contrapositve.
Sec. 3.5
Wed. 10/2 EXAM Secs. 1.1-4;  2.1-2;  3.1, 3.3-4;
Fri. 10/4 Floor and ceiling functions. Sec. 3.5
Two classy theorems.
Sec. 3.6,7
Wed. 10/9 Review exam. .
Fri. 10/11 Irrationality of sqrt(2)
Sets: the basics.
Secs. 3.7
Sec. 5.1
Mon. 10/14 Properties of Sets Sec. 5.2-3
Wed. 10/16 Problems from 3.6, and 3.7.
.
Fri. 10/18 Set difference, algebra of sets.
Partitions, power set.
Sec. 5.2, 3
Mon. 10/21 Two partitions of the power set
Cartesian product, relations.
Sec. 5.1, 5.3, 10.1
Wed. 10/23 Arrow diagrams, tables of relations
Functions, mod n
Sec. 10.1,
p. 559, Example 10.3.8
Fri. 10/25 Properties of relations:
reflexive, symmetric, transitive
Sec. 10.2
Mon. 10/28 Equivalence relations Sec. 10.3
Wed. 10/30 Partially ordered sets. Sec. 10.5
Fri. 11/1 Partially ordered sets.
The rational numbers.
Sec. 10.5
10.3.10 and 10.3 ex. 34
Mon. 11/4 Questions?
Functions, one to one and onto.
Ch. 10
Sec. 7.1,3
Wed. 11/6 EXAM Primarily Secs. 3.6,7; Ch. 5; Ch. 10.
Fri. 11/8 Functions, one-to-one, onto and both. Sec. 7.3
Sec. 4.1
Mon. 11/11 Sequences, summation and product notation. Sec. 4.1
Wed. 11/13 The well ordering principle. Induction. Sec. 4.2, p. 217-218.
Fri. 11/15 Induction, the quotient remainder theorem Sec. 4.2-3 and p. 418
Mon. 11/18 Strong induction, recursion Sec. 4.4, 8.1
Wed. 11/20 Recursion. Sec. 8.2
Fri. 11/22 Probability and counting. Sec. 6.1
Mon. 11/25 Multiplication rule Sec 6.2
Wed. 11/27 EXAM (a second try!). Primarily Secs. 3.6,7; Ch. 5; Ch. 10.
Mon. 12/2 Counting. Sec. 6.2-3
Wed. 12/4 Review of induction.
Return of 2nd exam, take 2.
.
Fri. 12/6 EXAM. Secs. 4.1-4; 8.1-2.
Mon. 12/9 Poker hands. The binomial theorem and Pascal's triangle. Sec. 6.4, 6.6, 6.7
Wed. 12/11 Return of exam and review. .