Proceedings of the Conference onPromoting Undergraduate Research in MathematicsMath 485: Seminar in Mathematical Problem SolvingSteven J. WintersMathematics majors at the University of Wisconsin Oshkosh are required to takea problem solving class. Math 485: Seminar in Mathematical Problem Solving is acourse that meets this requirement and is offered annually during the spring term.It is considered a capstone course for mathematics majors. I have taught this two-credit course twice in the last three years. It meets once per week for 14 weeks. Thefirst class had 11 students e nrolled and the second class had 17 students enrolled.This course is also taught by other faculty. Faculty have the option to teach thiscourse alone or to team teach the course. Additionally, faculty have the freedomto design the seminar using whatever problem solving methods they choose. Thetopics vary by the instructor. I have chosen to focus the design of the class with aresearch basis to achieve the problem solving outcome competency.My goal for the students is that each will discover within themselves their abilities,creativities, and desires to engage in mathematical research. The primary objectiveof the course is to introduce students to an area of mathematics that they may notbe familiar with and lead them to discover how problem solving can lead to research.In this case that area is graph theory.The first few class sess ions are spent learning general graph theory concepts. Oncethe students have an understanding of graph theory I begin to introduce my ownresearch topics to the students as a way of funneling them toward the actual researchproject they will work on as the final class project.Generally, three areas of my research interests are chosen as the direction for thecourse. The students work individually and in groups during class and on homeworkassignments. The topic areas are introduced one at a time and designed to buildstudents’ skills in both solving and designing research problems. As they progressthrough the homework assignments they learn how to introduce variations to theproblems and attempt to solve them as a means to learn how to come up with newresearch questions.Received by the editor December 18, 2006.c2007 American Mathematical Society355356 STEVEN J. WINTERSFor example: One topic covered is on distance related sub-graphs of graphs such as the center, median, and periphery. Awell known problem in this area is the fire station problem. Inclass we talk about recent results of the topic and think of newquestions. I give them a variation such as; changing the defini-tion of distance. The students try to solve the problem with thisvariation. They also try to introduce their own variations.These exercises build student confidence throughout to be able to introduce theirown variations and solve them or attempt to solve increasingly difficult variationsthat I create.For example: One student’s variation was based on a pizzadelivery restaurant where she worked. The restaurant manage-ment defined distance as delivering two pizzas and returning tothe restaurant. They call this the two-stop and return distance.The final research project is a group project based on one of the three topics thatthey have the most interest. Class time is used as a time for the groups to discusswhat they have been working on. I meet with the students individually or in groupsat least once per week outside of class to give individual attention on their researchproject. I use this time to check their work and guide them in the research. I maypresent them with additional questions based on the direction and progress theyare making.To date this course has resulted in one published paper, two papers submitted forpublication, and five papers in progress.Other research projects:In addition to this course I have had the opportunity to work with undergraduatestudents on research projects through various grant opportunities. The Universityof Wisconsin Oshkosh has a Student and Faculty Collaboration Research Programthat is funded through faculty development dollars. The purpose of the program isto develop s tudent researchers. The grant provides a monetary stipend of $2500 tothe student for participating in the project. The faculty receives a $500 stipend tobe used for supplies needed as part of the research.The University of Wisconsin System also has a research program called WiscAMP(Wisconsin Alliance for Minority Participation) which has also given me the op-portunity to work with undergraduate students on research. The program wasestablished in 2004 and one of the goals of the program is to increase the num-ber of baccalaureates awarded to underrepresented minority students in STEMdisciplines (science, technology, engineering, mathematics). The funding source isdifferent than the Student and Faculty Collaboration Research Program; however,the elements of the program for myself and the undergraduate student are verysimilar. The student receives the grant award of $3000 and we work together ona research project during the summer. I receive a $500 stipend for this project aswell, to be used for the purchase of supplies needed for the research.Mathematics Department, University of Wisconsin Oshkosh, Oshkosh WI, 54901E-mail address: