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
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
3/1/17
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
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
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
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
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
Math 381 Exam2 Spring 2915
Problem 1 (lUpts). Let E = cfw_a,b,c and P(E) be its power set. The function
f : P(E) > N is dened by
VA g E; 1%) = [Al
(Here lAl designates the cardinality of A).
(ad Find m.
M) :- Ll : 2
(b) Find f(P(E). ,
Irma): cfw_are m, Mi
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
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
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
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:
2/22/17
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
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
2/1/17
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 (
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
2/16/17
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
Math 381
Exam1
Spring 2014
Name:
Grade:
/ 100
Problem 1. True of False? Circle the correct answer.
(a) = cfw_x R : x2 + 1 = 0
T
F
(b) cfw_u, n, c, t, a, r, h, e, e, l, s = cfw_a, t, l, u, n, c, h, e, a, t, a, r, a, r, e, c, h, e, e, s, e
T
F
T
F
T
F
T
F
Math 381 Test I, Shrawan Kumar
Sept. 29, 2017
NAME:
PID Number:
Attempt all the problems 1-5. They carry 20 points each.
1.
2. $\ 31
1. Explain, without using a truth table, why (p V ~1q /\ q V -I7"
93
TVIp)
) ( )/\(
is true when p, (1,? have the sa
Math 381 - Discrete Math
Due: September 11, 2017
Solutions
Assignment 2
1.8.2 Prove that there are no positive perfect cubes less than 1000 that are the sum of the cubes
of two positive integers.
Solution: Note that 103 = 1000. The positive perfect cubes
Math 381 - Discrete Math
Due: September 18, 2017
Solutions
Assignment 3
2.2.4
Solution:
cfw_a, b, c, d, e, f, g, h
cfw_a, b, c, d, e
cfw_f, g, h
2.2.8
Solution:
By definition, A A A. Conversely, suppose x A A. Then either x A or x A. Thus,
A A A. Si
Problems: Descriptive Statistics
(Solutions to Even Questions)
2. Suppose a dataset has values of Xi and Yi in the table below.
a. Calculate 0 and 1 : 0 = 0.7639 , 1 = 0.7017
b. Calculate Yi for each individual: 9.19, 6.38, 7.78, 2.87, 9.19
c. Calculate u
Problems: Descriptive Statistics
Solutions
You may use a calculator for simple arithmetic calculations like adding and
dividing, for functions like logarithms and exponentials and roots. Otherwise,
you should do these problems by hand. You should submit y
Math 381 - Discrete Math
Due: September 6, 2017
Solutions
Assignment 1
1.1.4
Solution:
Jennifer is not Teja's friend OR Teja is not Jennifer's friend. Alternatively, Jennifer and Teja
are not friends.
There are not 13 items in a baker's dozen.
Abby sen
Probability Theory
An experiment leads to a random outcome. (For example, the experiment can be
pulling a card from a deck, and the outcome can be the number and suit of the
car.) The space describes all possible outcomes. (In a standard 52-card deck, the
Math 381 - Discrete Math
Due: September 25, 2017
Solutions
Assignment 5
2.3.2
Solution:
This is not a function. f (2) = 2 so the function is not well defined.
This is a function. For all integers, n2 + 1 is a real number.
This is not a function with th
Problems: Probability and Random Variables
Due Tuesday, Oct. 24, 2017
You may use a calculator for simple arithmetic calculations like adding and
dividing, for functions like logarithms and exponentials and roots. Otherwise,
you should do these problems b
Math 381 - Discrete Math
Due: October 2nd, 2017
Solutions
Assignment 5
4.2.2
Solution:
101000001
1111111111 (210 1)
11000100100011000
4.2.4
Solution:
27
693
958
31807
4.2.8
Solution: For each digit in hex, we can write down the binary string (4 bit