CS 441  Discrete Mathematics for Computer Science

Time:  MW 16:30-17:45pm   5129 Sennott Square

Instructor:  Milos Hauskrecht
5329 Sennott Square, x4-8845
e-mail: milos-at-cs.pitt.edu
office hours: MW 2:00-3:00pm

6504 Sennott Square, 4-9955
office hours: Tuesday, Thursday 11:00am --1:00pm

Announcements (check often)

• Final exam is scheduled for Tuesday, April 26, 2005, at 4:00-5:50pm, in Room 5129 (the same room as lectures).
The exam is:
• closed book and
• comprehensive (all material covered during the course)

• The course review sessions will be held on:
• Wednesday, April 20, 2005 during regular recitation
• Monday, April 25, 2005 at 6:00pm in SNSQ 6110

• Solutions for homework assignments:

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:

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
• Relations: properties, Combining relations, Closures, Equivalence, partial ordering
• Counting: basic rules, Pigeon hall principle, Permutations and combinations, Binomial coefficients and Pascal triangle.
• Probability: Discrete probability. Expected values and variance.

Lectures

Lectures  Topic(s)  Assignments
January 5 Administrivia and course overview ( Course description.)

January 10 Propositional logic

Homework 1
January 12 Logical equivalences

Homework 2
January 17 No class .
January 19 Predicates and Quantifiers

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January 24 Predicate logic

Homework 3
January 26 Methods of Proof

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February 2 Methods of Proof

Homework 4
February 7 Sets and set operations

Homework 5
February 9 Set operations, Functions

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February 14 Functions

Homework 6
February 16 Integers and divisibility

Readings: Chapter 2.4 and Euclidean algorithm (in Section 2.5).

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February 21 Midterm exam 1

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February 23 Integers and Division (cont)

Readings: Chapter 2.4 and Euclidean algorithm (in Section 2.5)

Homework 7
February 28 Sequences

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March 2 Summations

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March 7,9 Spring break .
March 14 Mathematical induction, Recursion

Homework 8
March 16 Counting. Basic counting rules.

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March 21 Counting. Pigeonhole principle. Permutations. Combinations.

Homework 9
March 23 Counting. Binomial coefficients. Pascal triangle. Counting with repetitions

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March 28 Probabilities

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March 30 Probabilities.

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April 4 Midterm 2

Homework 10
April 6 Relations. Properties.

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April 11 Relations. Combined operations.

Homework 11
April 13 Relations. Closures

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April 18 Relations. Equivalence relations and classes.

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April 20 Relations. Partial orders.

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April 26 Final exam

Readings: Material from Chapters 1,2,3,4,5 and 7

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• Lectures                          15 %
• Homework assignments   20%
• Exams                             65%

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