## Discrete Mathematics: Math 245, Fall 2011 Schedule

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

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Day Topics Preparation
Mon. 8/29 Introduction. Statements, negation, conjunction, disjunction. Sec. 2.1
Wed. 8/31 Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals.
Secs. 2.1-2
Fri. 9/2 Conditionals and English usage.
Logical arguments.
Secs. 2.2-3
Wed. 9/7 Negation
Logical arguments
Circuits.
Secs. 2.2-3
Fri. 9/9 Class cancelled: power outage. .
Mon. 9/12 Logical puzzle (2.3 #37,38).
Disjunctive normal form (2.4 #18, 20)
Secs. 2.3-4
Wed. 9/15 TEST: Logic Secs. 2.1-4
Fri. 9/17 Sets: subset, union, intersection. Secs. 1.1-2, 6.1-2 (pp. 336-344)
Mon. 9/19 Predicates, truth set of a predicate.
Quantified predicates.
Secs. 1.1-2, 3.1
Wed. 9/21 Translation from English and negation.
Multiply quantifed predicates.
Secs. 3.2-3
Fri. 9/23 Arguments with quantified predicates.
Logic puzzles.
Sec. 3.4
(2nd Ed. 2.3#27, 3rd 2.4#31, 4th. Ed 3.4#31.)
Mon. 9/26 Proving theorems about sets Secs. 6.1-2
Wed. 9/28 Disproof by counterexample.
Algebraic proofs
Secs. 6.3
Fri. 9/30 Partitions, the addition rule, inclusion/exclusion Secs. 6.1 (p. 344-348), 9.3
Mon. 10/3 Cartesian product, the multiplication rule.
Power set.
Secs. 6.1 (p. 344-348), 9.2 (525-529)
Wed. 10/5 Mathematics: Axiom, Definition, Theorem, Proof
Axioms for the integers. Properties of order and divisibility.
Ch. 3.1 (and my lecture notes Ch 3.
Fri. 10/7 TEST: Sets, proofs, counting. Ch 3, 6, Secs. 9.2, 9.3
Mon. 10/10 The Quotient Remainder Theorem.
The Euclidean algorithm.
Sec. 4.4
Sec. 4.8
Wed. 10/12 Representation of integers in binary, octal, etc.
Primes and the Unique Factorization Theorem.
3rd E.: Sec. 1.5 (pp. 57-60, 70-73) 4.1 (pp. 211-213) 3.3 (pp. 153-4).
4th Ed.: Sec. 2.5 (pp. 78-81, 91-93), 5.1 (pp. 240-242), 4.3 (pp.176-7)
Fri. 10/14 Primes and the Unique Factorization Theorem.
Rational numbers and irrational numbers.
3rd Ed. Sec. 3.3 (pp. 153-4); 4th Ed. 4.3 (pp.176-7)
Secs. 4.2, 4.6
Mon. 10/17 Floor and ceiling functions. Secs. 4.5.
Wed. 10/19 Question before the test?
Sequences, summation and product notation.
Sec. 5.1
Fri. 10/21 TEST. Ch. 4
Mon. 10/24 Summation and product notation.
Explicitly defined sequences and
recursively defined sequences
Sec. 5.1, 5.6
Wed. 10/26 The well ordering principle. Induction. Sec. 5.2, 5.4.
Fri. 10/28 Proof by mathematical induction. Sec. 5.2-3,
Mon. 10/31 Induction proofs for divisibility and inequalities Sec. 5.2-3
Wed. 11/2 Recursively defined functions and strong induction. Sec. 5.4
Fri. 11/4 Solving recursive sequences. Sec. 5.6,7
Mon. 11/7 Functions and relations.
Sec. 7.1, 8.1.
Wed. 11/9 TEST. Ch 5.
Fri. 11/11 Veteran's day: no class. .
Mon. 11/14 Relations, functions.
The inverse of a relation.
Sec. 7.1, 8.1.
Wed. 11/16 Functions: injective, surjective, bijective.
Composition of functions.
Sec. 7.2,3.
Fri. 11/18 Relations on a set.
Properties: reflexive, symmetric, transitive
Sec. 8.2
Mon. 11/21 Equivalence relations and partitions. Sec. 8.3
Wed. 11/23 Equivalence relations: important examples. Sec. 8.3
Mon. 11/28 Antisymmetric relations.
Partial orders.
Sec 8.5
Wed. 11/30 Partial orders. Sec 8.5
Fri. 12/2 TEST Secs 7.1-3, 8.1-3, 8.5.
Mon. 12/5 Four ways to count. Sec. 6.2,5
Wed. 12/7 From counting to probability.
Poker hands.
Sec. 9.1,2,5
Fri. 12/10 Binomial theorem. Pascal's triangle. Questions and exam prep. Sec. 9.7
Fri. 12/16 (10:30-12:30) FINAL EXAM. Cumulative. See Review Sheet