Service Learning Coursebook in Mathematics

Chapter 10 : Individual Course Projects

 Math 3370 : Combinatorial Mathematics

Project I : Transportation and Network Flow
 Using maps provided from the MN Department of Transportation and the City of Morris, students will analyze the transportation networks in and about the City of Morris. This includes source and destination problems, using zoning as a basis for flow.

 In particular, four main issues looked into are :

• Where (optimal locations) to construct new "Welcome to Morris" signs.
• Possible routes to by-pass the city using Highway 28.
• General traffic flow diagram In/Out of the city.
• Zoning issues, as consequences of the aforementioned items.

Project II : Congestion
 Using population estimates and land use characteristics, traffic patterns will be viewed within both the City of Morris and the region as a whole. Usage estimates are provided at the regional level only by the MN DOT regional coordinator Al Wolffe. These results will then be used as baseline data for Project III : Network Design.

Project III : Network Design
 This project will examine past, present, and future road constructions to examine feasibility, benefits, and recommendations. Through contact with Dean Olson at the Minnesota Department of Transportation, students will discover and discuss factors which play in to expansion and location decisions.

 Projects II & III were combined. In particular, three main issues looked into are :

• Parking on main streets and around the city center.
• Relation of by-passes to traffic flow within the city.
• Reconstruction of main street, Atlantic Avenue, to alleviate congestion between the 5th and 7th street blocks.

Project IV : Snow Plowing Routes
 The current routes are provided by Bill Storck, the City of Morris Public Works Director, and will be examined using distances and intersections as indicators and represented as a network flow problem.

 The main objective of this project is to design a mechanism and a cost-effective way for the City of Morris to complete its snow-plowing routes around the city limit areas. These routes include the main streets (with the exception of Atlantic Avenue which is taken care of by Stevens County) and the alleys.

Project V : Expansion
 Through meeting with various local officials from the Department of Transportation and the City of Morris Planning Commission, the students will examine estimated future growth of the area, and formulate efficient networks to accommodate transportation needs.

Coordinator Notes
 This course was extremely surprising, as the various applications of theory gave rise to many opportunities. Dr. Ng must be commended for her personal involvement and commitment to the project. Her knowledge and applications of the subject matter was found to be vast and appealing. This course has taken on all levels of transportation analysis - examining regional, county and local data.

Faculty Notes
 Objectives of Projects : This project assignment is to give Math 3370 students the opportunity to work on real world applications of the modeling and analysis approaches we study in the course. In particular, we will see how some of the ideas that we used could actually be applied to the development and infrastructure of the communities surrounding Morris, Minnesota.

 Overall, the integration of service learning into Combinatorial Mathematics was a success, notwithstanding the obstacles that the students encountered. The results and proposals recommended by the students were very thorough, meticulously thought out, and well-organized. Hopefully, the City of Morris will find their proposals useful, and this experience will be the beginning of a collaborative partnership between the City of Morris and the University of Minnesota, Morris.

Problems Encountered :

• Time constraints, i.e. 10 weeks is quite restrictive in terms of trying to learn the material and then to apply the concepts to applications. Hopefully, when UMM goes into the semester system, it will alleviate this problem a little.
• Difficulties in getting some pertinent data or information, and in setting up meetings with a few city officials.

Texts Used :
Discrete and Combinatorial Mathematics by Ralph Grimaldi, 3rd Edition, Addison-Wesley.
Applied Combinatorics by Alan Tucker, 3rd Edition, John-Wiley.
Network Flows : Theory, Algorithms, and Applications, by R.K. Ahuja; T.L. Magnanti; J.B. Orlin, 1st Edition, Prentice-Hall.

 Mathematical Concepts

• Euler tours and circuits
• Network flows and design
• Maximal flow and minimal cut problems
• Basic graph theory concepts

Additional Sources
 Morris Police Department - Data related to parking citations and accidents were used to examine congestion in the City of Morris. Contact : Cindy Swenson (320) 589-1155.

This page was created and maintained by Benjamin S. Winchester. If you have any questions or comments, feel free to contact me.