CSC/MTH 447  Discrete Mathematics
Fall 2012
Instructor:
Dr. Lutz Hamel
Tyler, Rm 251
Office Hours: Wed 3:304:40, Fri 10:0011:00
email: hamel@cs.uri.edu
TA:
Seonjoo Lim
office hours: Mon 1:00  2:00, Wed 12:00 2:00
email : seonjoolim@my.uri.edu
room : Tyler hall 136
** The takehome final exam is posted here.
The exam is due in my office no later than 12/18/12 @ noon.
NO LATE SUBMISSION WILL BE ACCEPTED. **
Announcements:
[12/19/12] Posted solutions to the fnal.
[12/10/12] version 2 of final posted...corrected some typos.
[12/10/12] posted solutions for assignment #7
[12/6/12] posted assignment #8
[12/5/12] posted midterm 2 solutions
[11/28/12] posted assignment #7
[11/19/12] ** The Midterm 2 exam is available now. Due date is Wednesday 11/28 in class. **
[11/15/12] the 2nd midterm is coming...
[11/15/12] Posted solutions assignment #6
[11/1/12] Posted assignment #6
[10/17/12] Posted solutions to midterm #1
[10/15/12] Posted solutions to assignment #5 and for class exercise 10/15
[10/13/12] Posted solutions for class exercise 10/10
[10/12/12] Posted solutions for assignment #4
[10/11/12] Posted assignment #5
[10/5/12] Posted solution for assignment #3 and for class exercise 10/3
[10/4/12] Posted assignment #4
[9/27/12] Posted solutions to assignment #2
[9/27/12] Posted assignment #3, see below
[9/27/12] posted an updated version to the class exercise of 9/26, it now also has formal
proofs in addition to the solution from the book, the formal proofs can be seen as templates
for some of the proofs in HW#3.
[9/26/12] posted solutions to class exercise 9/26
[9/24/12] Posted solutions to today's, 9/24, class exercise.
[9/20/12] Posted solutions to all class exercises up to now.
[9/20/12] Posted assignment #2
[9/19/12] Posted solutions for assignment #1
[9/14/12] Please read the directions for the homework problems carefully before attempting to
solve them!
[9/14/12] Posted solutions for class exercises 9/9 and 9/12.
[9/12/12] Posted assignment #1, see below.
[9/1/12] Welcome!
Description
This course is an introduction to the mathematical study of discrete objects. In it, you will learn how to construct proofs, as well as read and write formal mathematics. You will also become familiar with a range of standard mathematics concepts commonly used in computer science and particular areas of mathematics.
Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects:
 Examples of discrete objects: integers, steps taken by a computer program, distinct paths to travel from point A to point B on a map along a road network, ways to pick a winning set of numbers in a lottery.
 On the other hand, calculus deals with continuous objects and is not part of discrete mathematics.
The kinds of problems that can be solved using discrete mathematics include:
 How many ways can a password be chosen following specific rules?
 How many valid Internet addresses are there?
 What is the probability of winning a particular lottery?
 Is there a link between two computers in a network?
 How can I identify spam email messages?
 How can I encrypt a message so that no unintended recipient can read it?
 What is the shortest path between two cities using a transportation system?
 And many others...
The goals of the course are:
 Mathematical Reasoning: Ability to read, understand, and construct mathematical arguments and proofs.
 Combinatorial Analysis: Techniques for counting objects of different kinds.
 Discrete Structures: Abstract mathematical structures that represent objects and the relationships between them. Examples are sets, permutations, relations, graphs, trees, and finite state machines.
Documents of Interest:
Assignments:
Email submissions of homework are not
acceptable.

Assignment #1: Due in class Mon. September 17th. Do the following:
pg 13: 10 a,e,h
pg 14: 22 a,b,c
pg 15: 36 a, b, e
pg 34: 2; 4 a,b
pg 35: 18

Assignment #2: Due in class Mon. September 24th. Do the following:
Sec. 1.4
pg 53: 12 d,e,f
pg 53: 14
pg 54: 22
pg 56: 44
Sec. 1.5
pg 67: 30 a,c
Sec. 1.6
pg 78: 6
pg 80: 20 a

Assignment #3: Due in class Mon. October 1st. Do the following:
Sec. 1.7
pg 91: 6
pg 91: 16
pg 91: 22
Sec. 1.8
pg 108: 4
Sec. 2.1
pg 125: 10 a thru g
pg 126: 30
Sec. 2.2
pg 136: 18 d
pg 136: 22

Assignment #4: Due in class Wed. October 10th. Do the following:
sec. 2.3
pg 152: 2 a,b,c
pg 153: 22 a through d
pg 154: 38
pg 154: 48
sec. 2.4
pg 167: 4 a,c
pg 167: 6 d
pg 168: 10 a,b
pg 168: 12 a,d
pg 168: 16 c

Assignment #5: Due in class Mon. October 15th. Do the following:
sec. 2.5
pg 176: 2 d,e,f
pg 176: 12
pg 177: 22

Assignment #6: Due in class Wed. Nov 7th. Do the following:
sec. 5.1
pg 329: 6
pg 331: 40
sec 5.3
pg 359: 34 a,b,c
pg 359: 35
pg 359: 36
sec 6.1
pg 397: 26 a,b,c
pg 399: 72
sec 6.2
pg 405: 4 a,b
pg 441: 14

Assignment #7: Due in class Mon. Dec. 3rd. Do the following:
sec. 10.2
pg 665: 18
pg 665: 20 a,b,e
pg 665: 22
pg 666: 34
sec. 10.3
pg 676: 34
pg 676: 40
sec. 10.4
pg 691: 42

Assignment #8: Due in class Mon. Dec. 10th. Do the following:
sec. 11.1
pg 756: 14
sec. 11.3
pg 784: 18 a,b,c
sec. 11.4
pg 796: 34