Mathematics 213

Section X1 Spring 2010
Lecture: MWF at noon
Classroom: 142 Henry Admin Bldg

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Instructor Isidora Milin Office: 337 Illini Hall Email: imilin [at] illinois [dot] edu Office Hours Wednesdays 9:30-11AM 337 Illini Hall / Espresso Royale Course Information Syllabus Class Schedule Assignments Exam Information Handouts Official Course Listing from the course catalog

Math 213 - Basic Discrete Mathematics

In this course we will study problems with a discrete structure, which are particularly common in computer science and related fields. Discrete problems involve sets with finitely (or countably) many elements, relationships between such sets, and/or algorithms and processes with finitely many steps. Some examples are:

• What is the likelihood that a poker hand contains four cards of one kind?
• How many bit strings of length n without any consecutive zeros are there?
• How do we prove that a recursively defined sequence has a certain property?
• What is the shortest path between two cities using a transportation network?

Often, such questions (and their solutions) are best understood by introducing a particular discrete mathematical structure - for example, a graph or a tree. We’ll study objects such as sets, functions, relations, graphs and trees; We’ll introduce techniques for counting objects, computing probability of events and proving mathematical statements rigorously. In all of this, we will emphasize strategies/algorithms for solving discrete problems, and study how efficient these algorithms are.

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576

© 2011 Isidora Milin.