## Discrete Mathematics: Math 245, Spring 2004 Schedule

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

Day Topics Preparation
Mon. 1/12 Introduction. Statements, negation, conjunction, disjunction. Sec. 1.1
Wed. 1/14 Logical equivalences, tautologies, contradictions.
Conditionals
Sec. 1.1-2
Fri. 1/18 Conditionals and English usage, biconditionals.
Logical arguments.
Sec. 1.2-3
Wed. 1/21 Logical arguments. Sec. 1.3
Fri. 1/23 Logic puzzles. Logic circuits. Sec. 1.4, 2.1
Mon. 1/26 Sets, predicates, truth set of a predicate.
Quantified predicates.
Secs. 2.1
Wed. 1/28 Quantified predicates.
Translation from English.
Multiply quantified predicates.
Secs. 2.1,2
Fri. 1/30 Arguments with quantified predicates.
A logic problem.(2.3#27)
Sec. 2.3
Mon. 2/2 Fundamental properties of the integers.
First proofs: The sum of evens is even.
If a divides b and b divides c then a divides c.
Sec. 3.1, 3.3, 3.4
Wed. 2/4 Three theorems we assume:
The quotient-remainder theorem.
If prime p divides ab then p divides a or b
Unique factorization of integers.
Sec. 3.3, 3.4,
Fri. 2/6 Divisibility theorems and proofs. Sec. 3.4
Mon. 2/9 Rational numbers.
The floor and ceiling functions.
Sec. 3.5
Wed. 2/11 Proof by contraposition.
More on sets
Sec. 3.6
Sec. 5.1
Fri. 2/13 Properties of Sets:
The empty set;
Theorems 5.2.2 and 5.3.3
Set difference and symmetric difference
Sec. 5.1-3
Mon. 2/16 Proof by contradiction. Two classy theorems:
The sum of a rational and an irrational.
Irrationality of sqrt(2).
Secs. 3.7
Wed. 2/18 Another classy theorem:    The infinitude of primes. Secs. 3.7
Fri. 2/20 Practice Test Secs. 1.1-4, 2.1-3 3.1, 3.3-6
Mon. 2/23 EXAM Secs. 1.1-4, 2.1-3 3.1, 3.3-6
Wed. 2/25 Algebraic proofs of set equalities.
Partition of a set, power set, Cartesian product.
Secs. 5.1-3
Fri. 2/27 Relations.
Arrow diagrams, tables of relations.
Functions.
Sec. 10.1
Mon. 3/1 Properties of relations on a set:
reflexive, symmetric, transitive
Sec. 10.2
Wed. 3/3 Equivalence relations Sec. 10.3
Fri. 3/5 Partitions and equivalence relations.
Examples of equivalence relations:
integers mod n, the Mobius strip.
Sec 10.3
Mon. 3/8 Partially ordered sets. Sec. 10.5
Wed. 3/10 Partially ordered sets. Sec. 10.5
Fri. 3/12 Functions, one-to-one, onto and both. Sec. 7.1,3
Sec. 4.1
Mon. 3/22 Inverse functions. Cardinality
Pigeonhole principle.
Sec. 7.3, 4
Wed. 3/24 Definition of the rational numbers.
Sequences, summation and product notation.
Sec 7.6
Sec. 4.1
Fri. 3/26 Practice exam. Secs. 3.6,7; Ch. 5; Ch. 10.
Mon. 3/29 EXAM Secs. 3.6,7; Ch. 5; Ch. 10.
Fri. 4/2 The well ordering principle. Induction. Sec. 4.2, p. 217-218.
Mon. 4/5 Some induction proofs. Sec. 4.2-3, p. 217-218.
Wed. 4/7 Induction proofs. Sec. 4.2-3
Fri. 4/9 Using the well ordering principle. Sec. 4.4, 8.1
Mon. 4/12 Recursively defined functions. Strong induction . Secs 8.2.
Wed. 4/14 Strong induction. Second order recurrence relations. Secs 8.2,3.
Fri. 4/16 Counting and probability. Sec. 6.1-2
Mon. 4/19 Inclusion/exclusion principle.
4 ways to choose.
Sec. 6.3,4.
Wed. 4/21 EXAM. Secs. 4.1-4; 8.1-2.
Fri. 4/23 Binomial coefficients.
Pascal's triangle.
Sec. 6.4, 6.6, 6.7