Discrete Mathematics Chapter 2.1 Notes
I) Sets
1) A set is an unordered collection of objects, called elements or members of the
set. A set is said to contain it elements. It is common for sets to be denoted using
uppercase letters. Lowercase letters are
2/27/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin, ROBERT SEDGEWIC, KEVIN WAYNE
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 13 (CLRS)
Quiz 2 on Wednesday in class (closed book, on computer,
bring scrap paper)
1
2/27/17
POLL EVERYWHE
1/31/17
COMP 550: ALGORITHMS AND
ANALYSIS
JAN-MICHAEL FRAHM
including slides from: Ming Lin, Mike Scott
Quizz 1 (4:15 pm for 30 min)
laptop needed
pen needed
1
1/31/17
SEARCHING
SORTING AND SEARCHING
CS 307 Fundamentals of
Computer Science
3
SEARCHING
G
3/1/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin, ROBERT SEDGEWIC, KEVIN WAYNE
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 13 (CLRS)
Quiz 2 today in class (closed book, on computer, bring scrap
paper)
1
3/1/17
POLL EVERYWHERE
Will
2/20/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 8, 9, 12 (CLRS)
Assignment #3 due Wed. Feb 22, 3:35 pm
1
2/20/17
LINEARITY OF EXPECTATION
Let X and Y be random variables, and a, b be rea
3/27/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter (CLRS), 16, 23
Homework 5, due Wednesday March 29, at class
time (3:35 pm)
2nd Midterm April 3rd (black pen, scrap paper, closed
book, ca
3/6/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin, ROBERT SEDGEWIC, KEVIN WAYNE
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 22.1-22.3 (CLRS)
Homework 4 released, due Wednesday March 22nd, at class
time (3:35 pm)
Assignment 3 (soon t
1/23/17
ALGORITHMS AND ANALYSIS
JAN-MICHAEL FRAHM
ANNOUNCEMENTS
Homework #1 due this coming Wednesday, 1/25/2017
1
1/23/17
DIVIDE-AND-CONQUER
Recursive in structure
Divide the problem into several smaller sub-problems that are
similar to the original bu
2/16/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin, A. Klappenecker
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 6, 7 (CLRS)
Midterm lessons to be learned (Monday class)
Assignment #3 released due Wed. Feb 22, 3:35 pm
1
2/16/17
COUNTI
1/25/17
ALGORITHMS AND ANALYSIS
JAN-MICHAEL FRAHM
ANNOUNCEMENTS
Assignment 2 is out and due Wed. Feb 1 at 3:35 pm
Monday January 30, 1. Quiz (in class), closed book
Office Hour change Bhavya Vyas @SN-312:
2pm - 3:30pm Wednesdays
10:30 - noon Thursdays
2/1/17
COMP 550: ALGORITHMS AND
ANALYSIS
JAN-MICHAEL FRAHM
including slides from: Ming Lin, Mike Scott
ANNOUNCEMENTS
Midterm I, Wednesday Feb. 8
need: scrap paper (not turned in), pen, calculator (not your phone)
closed book
starts 3:35 pm ends 4:50 pm (
3/20/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter (CLRS), 22.4
Homework 4, due Wednesday March 22nd, at class
time (3:35 pm)
2nd Midterm April 3rd
1
3/20/17
DEPTH-FIRST-SEARCH (DFS)
Explo
2/22/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
POLL EVERYWHERE
Will be using poll everywhere in class for responses and
attendance
Please register with poll everywhere (UNC specific
instructions are at: http:/help.unc.edu/help/polleve
2/6/17
COMP 550: ALGORITHMS AND
ANALYSIS
JAN-MICHAEL FRAHM
including slides from: Ming Lin and George Kollios
ANNOUNCEMENTS
Midterm I, Wednesday Feb. 8
need: scrap paper (not turned in), pen, calculator (not your phone)
closed book
starts 3:35 pm ends 4:
2/13/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin, A. Klappenecker
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 6, 7 (CLRS)
Assignment #3 released due Wed. Feb 22, 3:35 pm
1
2/13/17
QUICKSORT (A, P, R)
1. if p < r
2.
then q Partition
3/8/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter 22.1-22.3 (CLRS)
Homework 4 released, due Wednesday March 22nd,
at class time (3:35 pm)
Assignment 3 (soon to come out)
Friday office hou
STOR 415, Spring 2017
Solutions to Homework Assignment No. 1
1. Let us denote by x1 the number of desks and by x2 the number of chairs
produced by Furnco. Here, for simplicity, we accept x1 and x2 to be
real numbers and they can be rounded after solving t
Discrete Mathematics Chapter 4 Notes
I) Divisibility and Modular Arithmetic
1) The part of mathematics devoted to the study of the set of integers and their
properties is known as number theory.
2) When one integer is divided by a second nonzero integer,
Discrete Mathematics Chapter 1.1 Notes
I) Propositional Logic
1) The rules of logic give precise meaning to mathematical statements.
2) A proposition is a declarative sentence that is either true or false.
3) The truth value of a proposition is true, deno
MATH 381 (002,004) - FALL 2015
DISCRETE MATHEMATICS AND ITS APPLICATIONS
Contact
instructor: Xavier Mela
office: PH324K
office hours: MWF 10a-11a and by appointment
email: [email protected]
web page: sakai.unc.edu
Overview
Math 381 is a course designed to
Math 381
Divisibility
Fall 2015
Problem 1. Prove or disprove:
(i) (a | b) (c | d) (a + c) | (b + d)
(ii) (a | b) (b | c) a | c
(iii) a | (b + c) (a | b) (a | c)
(iv) (a | c) (b | c) ab | c2
Problem 2. Find all possible positive integers n such that n + 1
Exam1
Math 381
Fall 2014
Name:
Grade:
/ 100
Problem 1. Construct a truth table for the compound proposition (p q)(q r)
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
Problem 2. True of False? Circle the correct answer.
(a) cfw_1, , e
T
F
T
F
T
F
Test 1
Math 381
Spring 2008
Name:
Problem 1 (10pts). Construct a truth table for the compound proposition (p q)
(p q).
Problem 2 (10pts). Suppose p, q and r are true statements and that s and t are
false statements. Label the following compound statement
Math 381 . 7 Exam 1 m ' Fall 2013
Name: Han-5
Problem 1. Use logical equivalence to determine if the following statement is a
tautology
(WMP-WD-hq
E bl'lrle’lpvelg v 7‘) (and. 19—262 27F“? +‘*“"'3
"'5: [PVCP/ﬂ‘ﬂ] v 1% (W “35“”! h”)
( kssmakcdﬁ of “ V
Test 1
Math 381
Spring 2008
Name: Answer Key
Problem 1 (10pts). Construct a truth table for the compound proposition (p q)
(p q).
p
T
T
F
F
q pq pq
T
T
T
F
F
T
T
F
T
F
F
F
pq
T
T
T
T
Problem 2 (10pts). Suppose p, q and r are true statements and that s an
Math 381
Exam 1
Fall 2013
Name:
Problem 1. Use logical equivalence to determine if the following statement is a
tautology
(p (p q) q
Problem 2. Let B(x, y) be the statement y is the best friend of x. Express the
statement Everyone has exactly one best f
Math 381 — Examl —~ Fall 2014
Problem 1. Construct a truth table for the compound proposition (3? + 90th (~—> 7“)
Problem 2. True of False? Circle the correct answer.
(3.) {DE {1,7r,e}
Cr) - F
(b) {2} E {1:23}
(C) 06 P({1})
@ F
T @
(e) {1,7T, 6} ﬂ {7r
Test 1
Math 381
Spring 2010
Name:
Problem 1. Show that (p q) and p q are logically equivalent by using truth
tables.
Problem 2. Suppose p, q and r are True statements and that s and t are False
statements. Label the following compound statements as True
3/29/17
COMP 550
JAN-MICHAEL FRAHM
with some slides from Ming Lin
ANNOUNCEMENTS
Weekly Reading Assignment:
Chapter (CLRS), 16, 23
Homework 5, due Wednesday March 29, at class
time (3:35 pm)
2nd Midterm April 3rd (black pen, scrap paper, closed
book, ca
Warm Up Problem: 1/17
Compound propositions that have the same truth values in all
possible cases are called logically equivalent (denoted by ).
Show p q (p q) (q p) by using a truth table.
Warm Up Problem: 1/19
1) Let P(x) be a proposition. What are the