About MATH 2678 A
Introduction to basic combinatorial principles emphasizing problem-solving techniques. Enumeration, generating functions, Fibonacci numbers, pigeonhole principle, inclusion-exclusion, and graph theory. Prerequisites: MATH 2055 (preferred) or CS 1640.
Notes
Prereqs enforced by the system: MATH 2055 (preferred) or CS 1640; Open to Degree and PACE students
Section Description
Enumeration questions range from the easy (how many weeks are there in a year?) to the medium (how many ways can you make change for a dollar?) to the hard (how many configurations of a Rubik's Cube are there?) In this course we will learn various methods for approaching many of these problems. Most of the time the questions we ask will be phrased in terms of tidy little problems. And the methods we learn are quite beautiful on their own terms. But the ideas we examine will form the basis for important techniques for solving practical, applied problems in engineering, computer science, operations research and many other fields. The main topics covered will be Basic Counting, Inclusion/exclusion, Generating Functions, Recurrence relations and Pólya theory.
Section Expectation
Lecture and discussion. Students should expect to spend 6-8 hours outside of class reviewing notes and working on homework problems. There is no textbook, but readings and lecture notes will be provided as appropriate.
Evaluation
Grades are based on weekly assignments, midterm exam, final exam and in-class tests.
Important Dates
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