This is a course in applied combinatorics - the study of arrangements
of finite sets of objects and the development and use of models
derived from that study.
The questions studied in combinatorics may be grouped under four
headings:
1. Is a specified arrangement possible (if not always, then when is it possible)?
2. How many ways are there to achieve a specified arrangement, and how can we classify them (to facilitate counting)?
3. What different properties can we identify in specific arrangements?
4. What is the "best" way to arrange the objects, how can we "best" achieve the arrangement?
Approximately half of the course focuses on graph theory - modeling of relationships among finite sets of objects (more closely related to questions 1, 3, and 4) - and half on enumerative combinatorics - determining the number of arrangements of specified types (more closely related to questions 1 and 2).
The course is considered an applied mathematics elective within the major, since it is built around use of the methods to model and solve problems; most of the work of the course is organized around solving problems and seeing what general results can be developed from the solutions.
The course fulfills a requirement for students intending to achieve secondary teacher certification. The models (especially many of the graph theory models) are widely used in computer science, and the problem-solving focus is useful in many areas both in mathematics and elsewhere.
This page will be occasionally updated to provide access to documents for the course, but most access will be through the Blackboard site(Students enrolled in the class login with own ID & password - others may login as "guest" with password "guest" but will not have access to all feaures)
For dates, course requirements, etc. see the current/most recent syllabus (Spring 2007)
Other pages with resources for the course:
Guidelines for advanced writing proficiency in mathematics
Maintained by cpeltier@saintmarys.edu
Last update 1/18/08