Combinatorics and Graph Theory Courses at UCF
Discrete Mathematics is one of the fastest growing areas of mathematics. Its name is meant to distinguish it from the more common continuous mathematics as is found in calculus. The subject deals with objects, and the numbers involved are usually positive integers, with occasional daring forays into the rationals.
Combinatorics tends to deal with three main questions: (1) existence (does something occur?), (2) counting (if it does occur, how many of them are there?), and (3) optimization (if there are a lot of them, which one is the best?). Applications include counting the number of ways of assigning m objects to n boxes while obeying various rules, coding theory, statistical design of experiments, and solution of recurrence relations
Graph Theory studies the abstract mathematical model composed of objects formed by connecting points with lines in a manner which is not meant to be geometrical. Applications include methods for finding shortest paths between two points, efficient assignment of police or fire fighting personnel, scheduling of exams or assignment of radio/TV frequencies, matching two sets of objects in a one-to-one manner, design of compilers, optimum flow in transportation networks, and efficient design of computer networks.
UCF currently offers three courses in this area:
MAD 4203-Combinatorics and Graph Theory I. This is the introductory course and gives a thorough basic training in the two areas. It is usually offered in the fall semester. Although it is at the 4000 level, it still can be used for credit towards a masters degree since up to six hours of 4000 level work can be so counted.
MAD 5205-Combinatorics and Graph Theory II. This continues the first course. The subject matter is more or less independent of it and this course can be taken if the student has had a good discrete math course some place else. This course is normally offered in the spring semester. Anyone completing this course will be able to understand the majority of papers in a conference on these subjects and will be ready for original research.
MAD 6309-Advanced Graph Theory I. This is a seminar on graph theory in which students do projects and read and report on current literature. It is offered when there is sufficient interest, and then normally in the fall semester.