## CS 441  Discrete Mathematics for Computer Science

Time:  TH 11:00am-12:15pm   205 LAWRN

Instructor:

• Milos Hauskrecht
5329 Sennott Square, x4-8845
e-mail: milos at cs pitt edu
office hours: Monday 1:00-3:00pm

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, x4-0513
e-mail: ztliu at cs pitt edu
office hours: Monday 3:30-5:00pm, Tuesday 2:00-5:00pm, Wednesday 10:00-11:00am

Announcements (check often):

• The final exam for the course is on Saturday, April 26, 2014 at 10:00-11:50am 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.

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: one-to-one, 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 1.1-3. Homework assigment 1
January 14 Predicate logic. Sections 1.4. .
January 16 Predicate logic. Sections 1.4-5. Homework assigment 2
January 21 Predicate logic. Formal and informal proofs Sections 1.5-6. .
January 23 Informal proofs Sections 1.5-7. Homework assigment 3
January 28 Sets and set operations Sections 2.1-2. .
January 30 Sets and set operations (cont.), Functions Sections 2.1-3. Homework assigment 4
February 4 Functions II. Sections 2.1-3. .
February 6 Sequences and summations Sections 2.4. Homework assigment 5
February 11 Countable and uncountable sets. Matrices. Sections 2.5-6. .
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 6.1-2. 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 6.3-5; 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 7,9.1-3. .
April 3 Relations II. Chapter 9.1-3. Homework assigment 11
April 8 Relations III Chapters 9.1-3. .
April 10 Relations IV. Graphs Chapter 9.1-6. Homework assigment 12
April 15 Graphs: graph types, graph properties Chapter 10. .
April 17 Graphs: Connectivity, Trees Chapter 10. .
April 26 Final exam .

• 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.

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) 648-7890/(412) 383-7355 (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