Discrete Mathematics

Instructor - Robert Hochberg 
Office-         STC C-121 
Phone-         328-9685 
Email-         hochberg@cs.ecu.edu
Text - Essential Discrete Mathematics for Computer Science by Feil and Krone
Office Hours
Tuesday and Thursday
7-8am and 11am - 12:30pm
And by appointment, of course

 
General Notes

Homework Assignments

Thursday
October 22
Topics Covered
Proof of the equivalence of PLNN and PMI.  Lots of examples of proofs by induction.
Tuesday
October 20
Topics Covered
Introduction to mathematical induction
Thursday
October 15
Topics Covered
Commonalities between set systems, propositional logic and circuits.
Simplifying boolean circuits,
Tuesday
October 13
Fall Break
No Class
Thursday
October 8
Topics Covered
Switching circuits, their simplification, and some theorems of Boolean algebras in general.  DNF.
Homework #5, due Tuesday, October 20
Chapter 3 #2, 3, 7 (first part only), 9, 10, 13 (do the addition in binary), 14, 15, 45, 46, 48, 50, 51, 53, 54
Tuesday
October 6
Exam 1
This will cover Chapter 0 (excluding propositional logic and truth tables), Chapter 1 and Chapter 2.
The best study guide for this exam are the first four homework assignments.  You will be asked to prove things.
Thursday
October 1
Topics Covered
Switching circuits and review for Exam 1
Tuesday
September 29
Topics Covered
Propositional logic from Chapter 0. Start of Chapter 3.
Homework #4, due October 6
Chapter 2 #2, 8, 10, 12, 24, 26, 32. 
Thursday
September 24
Topics Covered
Properties of relations:  transitive, symmetric, reflexive.  Equivalence relations.
Tuesday
September 22
Topics Covered
onto functions, invertible functions, logarithms, floor and ceiling functions, intro to relations
Thursday
September 17
Topics Covered
Review of Sets homework.  1-1 functions, inverses.
Tuesday
September 15
Topics Covered
Q&A on Homework 3, Cartesian products of sets, proof that if A and B are not empty,
then AxB = BxA if and only if A = B.  Start of Chapter 2 - Functions and Relations.
Thursday
September 10
Topics Covered
Set relations subset and equality.  Proofs that A is a subset of B and proofs that A equals B.
The power set of a set, the empty set.
Thursday
September 3
Topics Covered
Review of Homework 2
Definitions and examples of set operations:  union, intersection, symmetric difference, minus and complement

Homework #3 due September 17
Chapter 1 #2, 4, 6, 8, 9, 11, 13, 15, 18, 25, 30, 32, 36, 37, 44
Tuesday
September 1
Topics Covered
Proof that sqrt(2) is irrational.  This proof is in Chapter 0 of the text.
Began work on Chapter 1, Sets. 

Homework due September 3
Read Chapter 1 of the text
Thursday
August 27
Topics Covered
Implications, Direct Proofs, Indirect Proofs (Proofs by Contrapositive), Proofs by Contradiction

Homework#2, due September 3
Chapter 0, Problems #6, 7, 14, 15, 16
And these problems:
A.  Prove that if a number's last digit is "8," then it is even
B.  For what values of n is the sum 1+2+3+ ... + n an even number?  Prove your answer.
Tuesday
August 25
Topics Covered
Introduction to Proofs, definitions of odd and even,
proof that the product of two odd numbers is odd
proof that an A by B rectangle it tileable with 1x2 dominos if and only if at least one of A, B is even.

Homework#1, due September 1
This worksheet
Read Chapter 0

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