## Discrete Mathematics: Math 245, Spring 2010 Schedule

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

Day Topics Preparation
Wed. 1/20 Introduction. Statements, negation, conjunction, disjunction.
Logical equivalences
Sec. 1.1
Mon. 1/25 Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals.
Secs. 1.1-2
Wed. 1/27 Conditionals and English usage.
Logical arguments.
Secs. 1.2-3
Mon. 2/1 Logic circuits. Sets Secs. 1.4, 5.1
Wed. 2/3 Sets, predicates, truth set of a predicate.
Quantified predicates.
Secs. 5.1, 2.1-2
Mon. 2/8 Translation from English.
Multiply quantified predicates.
Secs. 2.3-4
Wed. 2/10 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.)

Secs. 5.2-3
Mon. 2/15 Sets: Cartesion products, power set, partitions.
Proofs: Venn diagram, element-wise proofs,
algebraic proofs.
Secs. 5.1-3
Wed. 2/17 Practice with proofs of set theorems.
Mathematics: Axiom, Definition, Theorem, Proof
The sum of evens is even, etc.
Secs. 5.2-3 3.1
Mon. 2/22 Fundamental properties of the integers.
Divisibility
Secs. 3.1, 3.3, 3.4
Wed. 2/24 The quotient-remainder theorem.
Unique Factorization.
Secs. 3.1, 3.3, 3.5
Mon. 3/1 EXAM Ch. 1, 2, 5
Wed. 3/3 Rational numbers and real numbers.
The floor and ceiling functions.
Secs. 3.5,6,7
Mon. 3/8 Irrationality of sqrt(2).
Sequences, summation and product notation.
Sec. 3.7
Sec. 4.1, Sec 8.1
Wed. 3/10 The well ordering principle. Induction. Sec. 4.2,4.
Mon. 3/15 Proof by mathematicalinduction.
Some induction proofs.
Sec. 4.2-3, p. 217-218.
Wed. 3/17 Recursively defined functions and strong induction. Sec. 4.2-3
Mon. 3/22 A bit more on induction.
Functions and Relations
Sec. 7.1, 8.1
Wed. 3/24 Functions: injective, surjective, bijective. Sec. 7.1-2.
Mon. 4/5 Questions before the exam?
Functions: composition.
7.4.
Wed. 4/7 EXAM. Secs. 3.1-7, 4.1-4; 8.1-2.
Mon. 4/12 Properties of relations on a set:
reflexive, symmetric, transitive
Sec. 10.2
Wed. 4/14 Equivalence relations Sec. 10.3
Mon. 4/19 Partitions and equivalence relations.
Examples of equivalence relations.
Partial orders.
Sec 10.3

10.5
Wed. 4/21 More on partially ordered sets.
Counting.
Sec. 10.5
6.1-3
Mon. 4/26 From the addition rule to inclusion-exclusion. Sec 6.3
Wed. 4/28 The rational numbers using equivalence relations.
Possibility trees.
Sec. 10.3.10
Sec 6.2-3.
Mon. 5/3 Four ways to count. From counting to probability. Sec. 6.2,4
Wed. 5/5 EXAM. Secs 7.1,2,4 (1,3,5 in 2nd Ed.)
Secs 10.1,2,3,5.
Inclusion-exclusion.
Mon. 5/10 From counting to probability and gambling.
Binomial theorem.
Pascal's triangle.
Sec. 6.4, 6.6, 6.7
Wed. 5/12 Questions and exam prep. .
Mon. 5/17 FINAL EXAM. Cumulative.