## Discrete Mathematics: Math 245, Fall 2003 Schedule

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

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Day Topics Preparation
Wed. 9/3 Introduction. Statements, negation, conjunction, disjunction. Sec. 1.1
Fri. 9/5 Logical equivalences, tautologies, contradictions.
Conditionals
Sec. 1.1-2
Mon. 9/8 Conditionals and English usage, biconditionals.
Logical arguments.
Sec. 1.2-3
Wed. 9/10 Logical arguments. Sec. 1.3
Fri. 9/12 Logic circuits. Predicates and quantifiers. Sec. 1.4, 2.1
Mon. 9/15 Predicates, quantifiers, truth sets. Secs. 2.1
Wed. 9/17 Translation from English.
Compound predicates.
Multiply quantified predicates.
Secs. 2.1,2
Fri. 9/19 Arguments with quantified predicates.
A logic problem.(2.3#27)
Sec. 2.3
Mon. 9/22 Fundamental properties of the integers.
First proof: The sum of evens is even.
Sec.2.3
Wed. 9/24 Two more proofs:
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. 9/26 Three theorems we assume:
The quotient-remainder theorem.
If prime p divides ab then p divides a or b
Unique factorization of integers.
Sec. 3.4, 3.3,
Mon. 9/29 Questions?
Rational numbers.
The floor and ceiling functions.
Sec. 3.5
Wed. 10/1 Sets: the basics Sec. 5.1
Mon. 10/6 EXAM Secs. 1.1-4;  2.1-2;  3.1, 3.3-4;
Wed. 10/8 Proof by contradiction. Two classy theorems:
The sum of a rational and an irrational.
Irrationality of sqrt(2).
Secs. 3.7
Fri. 10/10 Another classy theorem:    The infinitude of primes.
Intersection and union of sets.
Sec. 3.7
Sec. 5.1
Mon. 10/13 Properties of Sets:
The empty set;
Theorems 5.2.2 and 5.3.3
Set difference and symmetric difference
Sec. 5.1-3
Wed. 10/15 Algebraic proofs of set equalities,
Venn diagrams as an aid.
Power set, partitions.
Secs. 5.2,3
Fri. 10/17 More on partitions.
Two partitions of the power set.
Secs. 5.2, 3
Mon. 10/20 Cartesian product. Relations Sec. 5.1, 5.3, 10.1
Wed. 10/22 Arrow diagrams, tables of relations
Functions, mod n
Sec. 10.1,
p. 559, Example 10.3.8
Fri. 10/24 Properties of relations:
reflexive, symmetric, transitive
Sec. 10.2
Mon. 10/27 Class cancelled due to fire. .
Wed. 10/29 Class cancelled due to fire. .
Fri. 10/31 Equivalence relations Sec. 10.3
Mon. 11/3 Partitions and equivalence relations. Sec 10.3
Wed. 11/5 Examples of equivalence relations
The Mobius strip, the rational numbers.
Partially ordered sets.

10.3.10 and 10.3 ex. 34
Sec. 10.5
Fri. 11/7 Partially ordered sets. Sec. 10.5
Mon. 11/10 Functions, one-to-one, onto and both. Sec. 7.1,3
Sec. 4.1
Wed. 11/12 . .
Fri. 11/14 EXAM Primarily Secs. 3.6,7; Ch. 5; Ch. 10.
Mon. 11/17 The well ordering principle. Induction. Sec. 4.2, p. 217-218.
Wed. 11/19 Some induction proofs. Sec. 4.2-3, p. 217-218.
Fri. 11/21 Induction proofs. Sec. 4.4
Mon. 11/24 Recursively defined functions. Strong induction . Sec. 4.4, 8.1
Wed. 11/26 Strong induction, the Fibonacci numbers. Secs 8.1-2.
Mon. 12/1 Counting and probability. Sec. 6.1-2
Wed. 12/3 EXAM. Secs. 4.1-4; 8.1-2.
Fri. 12/5 Inclusion/exclusion principle.
4 ways to choose.
Sec. 6.3,4.
Mon. 12/8 Binomial coefficients.
Pascal's triangle.
Sec. 6.4, 6.6, 6.7
Wed. 12/10 Poker hands. The binomial theorem. .
Fri. 12/12 Review for final. .