CS 441 Discrete
Mathematics for Computer Science
Time: TH 11:00am12:15pm 205 LAWRN
Instructor:
 Milos
Hauskrecht
5329 Sennott Square, x48845
email: milos at cs pitt edu
office hours: Monday 1:003:00pm
Recitations:
 Section 1: Thursday: 5:00  4:50 PM, 5313 SENSQ,
 Section 2: Friday: 11:00  11:50 AM, 5313 SENSQ
TA:
 Zitao Liu
5406 Sennot Square, x40513
email: ztliu at cs pitt edu
office hours: Monday 3:305:00pm, Tuesday 2:005:00pm, Wednesday 10:0011:00am
Links
Course
description
Lectures
Grading
Homeworks
Additional
Student Resources
Academic
Honesty
Announcements
(check often):
 The final exam for the course is on Saturday, April 26, 2014 at 10:0011:50am in 205 LAWRN. The exam is a closed book, cumulative exam. Please bring your own calculator. You may need it to complete the solution for some of the counting problems.
 The review will be held during the recitations on Thursday (04/17) and Friday (04/18).
 Please note that all problems in the homework assignments are from the 7th edition of the textbook.
 Homework assignment solutions:
Course description
The purpose of this course is to understand and use (abstract)
discrete structures that are backbones of computer science. In
particular, this class is meant to introduce logic, proofs, sets,
relations, functions, counting, and probability, with an emphasis on applications in computer science.
Prerequisites:
2 years of high school algebra.
Syllabus
Textbook:
Kenneth Rosen.
Discrete Mathematics and Its Applications, 7th Edition , McGraw Hill Publishing Co., 2012.
Tentative Syllabus
 Logic: propositional logic, logical equivalence, predicates &
quantifiers, and logical reasoning.
 Sets: basics, set operations
 Functions: onetoone, onto, inverse, composition, graphs
 Integers: greatest common divisor, Euclidean algorithm.
 Sequences and Summations
 Mathematical reasoning: Proof strategies, Mathematical Induction,
Recursive definitions, Structural Induction
 Counting: basic rules, Pigeon hall
principle, Permutations and combinations, Binomial coefficients and
Pascal triangle.
 Probability: Discrete probability. Expected values and variance.
 Relations: properties, Combining relations, Closures, Equivalence,
partial ordering
 Graphs , directed, undirected graphs.
Lectures
Lectures 
Topic(s) 
Readings 
Assignments 
January 7 
Administrivia, Propositional logic.

Section 1.1. 
. 
January 9 
Propositional logic.

Sections 1.13. 
Homework assigment 1 
January 14 
Predicate logic.

Sections 1.4. 
. 
January 16 
Predicate logic.

Sections 1.45. 
Homework assigment 2 
January 21 
Predicate logic. Formal and informal proofs

Sections 1.56. 
. 
January 23 
Informal proofs

Sections 1.57. 
Homework assigment 3 
January 28 
Sets and set operations

Sections 2.12. 
. 
January 30 
Sets and set operations (cont.), Functions

Sections 2.13. 
Homework assigment 4 
February 4 
Functions II.

Sections 2.13. 
. 
February 6 
Sequences and summations

Sections 2.4. 
Homework assigment 5 
February 11 
Countable and uncountable sets. Matrices.

Sections 2.56. 
. 
February 13 
Matrices. Integers and division

Sections 2.6., 4.3. 
Homework assigment 6 
February 18 
Integers and divisions. Congruency. CS applications.

Sections 4.3., 4.5. 
. 
February 20 
Integers: Applications, base conversions. Mathematical induction.

Section 4.2., 4.5. 
Homework assigment 7 
February 25 
Mathematical induction and recursion.

Chapter 5 
. 
February 27 
Counting: basic counting rules.

Sections 6.12. 
Homework assigment 8 
March 4 
Counting: permutations, combinations.

Chapter 6 
. 
March 6 
Midterm exam

Chapters 1,2,4,5 and 6.1. 
. 
March 18 
Midterm exam solutions

Chapters 1,2,4,5 and 6.1. 
. 
March 20 
Counting: advanced counting methods. Probability

Sections 6.35; Chpater 7 
Homework assigment 9 
March 25 
Probabilities.

Chapter 7 
. 
March 27 
Probabilities: Bayes theorem, Bernoulli trial, Random variables, Expected value.

Chapter 7 
Homework assigment 10 
April 1 
Probabilities: expected value
Relations

Chapters 7,9.13. 
. 
April 3 
Relations II.

Chapter 9.13. 
Homework assigment 11 
April 8 
Relations III

Chapters 9.13. 
. 
April 10 
Relations IV. Graphs

Chapter 9.16. 
Homework assigment 12 
April 15 
Graphs: graph types, graph properties

Chapter 10. 
. 
April 17 
Graphs: Connectivity, Trees

Chapter 10. 
. 
April 26 
Final exam


. 
Grading

Lectures 10 %
 Homework assignments 40%

Exams
50%
Homeworks
There will be weekly homework assignments. The
assignments are due at the beginning of the class on the day specified
on the assignment. In general, no extensions will be granted.
Additional Student Resources
Academic Honesty
All the work in this course should be done
independently. Collaborations on homeworks are not permitted. Cheating
and any other antiintellectual behavior, including giving your work to someone
else, will be dealt with severely. If you feel you may have violated
the rules speak to us as soon as possible.
Please make sure you read, understand and abide by the Academic
Integrity Code for the Faculty and College of Arts and Sciences.
Students With Disabilities
If you have a disability for which you are or may be requesting an
accommodation, you are encouraged to contact both your instructor and
Disability Resources and Services, 216 William Pitt Union, (412)
6487890/(412) 3837355 (TTY), as early as possible in the term. DRS
will verify your disability and determine reasonable accomodations for
this course.
The web page is maintained by milos