Discrete Mathematics: Math 245, Spring 2003 Schedule

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

Day Topics Preparation
Wed. 1/22 Introduction. Statements, negation, conjunction, disjunction. Sec. 1.1
Fri. 1/24 Logical equivalences, tautologies, contradictions.
Conditionals
Secs. 1.1-2
Mon. 1/27 Conditionals and English usage, biconditionals.
Logical arguments.
Secs. 1.2-3
Wed. 1/29 Logical arguments. Sec. 1.3
Fri. 1/31 Logic circuits. Predicates and quantifiers. Secs. 1.4, 2.1
Mon. 2/3 Predicates, quantifiers. Secs. 2.1
Wed. 2/5 Predicates and quantifiers:
Translation from English, truth sets, compound predicates.
Sec. 2.2
Fri. 2/7 Conditional predicates.
Multiply quantified statements.
Arguments with quantified predicates.
Sec.2.3
Mon. 2/10 A logic problem (2.3#27).
Logical arguments and proof.
Sec.2.3
Wed. 2/12 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.
Secs. 3.1, 3.3, 3.4
Fri. 2/14 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, 3.3,
Mon. 2/17 Questions?
Proof of biconditionals.
Proof using the contrapositve.
Sec. 3.5
Wed. 2/19 Floor and ceiling functions. Sec. 3.5
Fri. 2/21 Proof by contradiction and two classy theorems.
Irrationality of sqrt(2), the infinitude of primes
Secs. 3.6,7
Mon. 2/24 Questions? Problems from 3.6, and 3.7. .
Wed. 2/26 EXAM Secs. 1.1-4;  2.1-2;  3.1, 3.3-7;
Fri. 2/28 Sets: the basics. Sec. 5.1
Mon. 3/3 Intersection, union, empty set, universal set. Secs. 5.2-3
Wed. 3/5 Main Properties of Sets (Theorem 5.2.2) Secs. 5.2, 3
Fri. 3/7 Set difference, algebra of sets.
Partitions, power set.
Secs. 5.1-3
Mon. 3/10 Two partitions of the power set.
Cartesian product, relations.
Sec. 5.1, 10.1
Wed. 3/12 Three representations of relations:
set, table, arrow diagram.
Examples: functions, mod n
10.1, p. 559, Example 10.3.8
Fri. 3/14 Properties of relations:
reflexive, symmetric, transitive
Sec. 10.2
Mon. 3/17 Equivalence relations Sec. 10.3
Wed. 3/19 Some important equivalence relations:
mod n, the rationals, topology
Sec. 10.3 (10.3.10 and Exercises. 26, 34)
Fri. 3/21 Partially ordered sets. Sec. 10.5
Mon. 3/24 More on Posets Sec. 10.5
Wed. 3/26 Functions, one to one and onto. Ch. 10
Sec. 7.1,3
Fri. 3/28 The pigeonhole principle. Inverse functions.
Sec. 7.3, 4,
Mon. 4/7 Sequences, summation and product notation. Sec. 4.1
Wed. 4/9 EXAM Primarily Secs. 3.6,7; Ch. 5; Ch. 10.
Fri. 4/11 Sequences. Summation and product notation Sec. 4.1
Mon. 4/14 The well ordering principle. Induction. Sec. 4.2, p. 217-218.
Wed. 4/16 Induction, the quotient remainder theorem Secs. 4.2-3 and p. 418
Fri. 4/18 Strong induction, recursion Secs. 4.4, 8.1
Mon. 4/21 Solving a recurrence relation.
Proving the formula.
Sec. 8.2
Wed. 4/23 Multiplication rule. Language of probability Sec 6.1-2
Fri. 4/25 Counting, the basics. Inclusion, exculsion. Secs. 6.2-3
Mon. 4/28 Four ways to choose, and how to count them. Secs. 6.3-4
Wed. 4/30 Poker hands. Sec. 6.3-4
Fri. 5/2 EXAM. Secs. 4.1-4; 8.1-2.
Mon. 5/5 The binomial theorem and Pascal's triangle. Secs. 6.6, 6.7
Wed. 5/7 Return of exam and review. .