Summer Research Opportunities in Mathematics at CSB/SJU

            The Mathematics Department has funding for two continuing CSB/SJU students to engage in undergraduate mathematics research in cooperation with faculty here.  Each student interested in participating in this program should find a faculty sponsor in the Mathematics Department willing to work with the student.  The student and faculty sponsor will choose one of the topics given on the back of this sheet or propose another topic.  Then the student should fill out the application below and submit it with a supporting letter from the sponsoring mathematics professor to Phil Byrne by March 15, 2002.   The department will announce the students who will receive the funding by April 2, 2002.  Further questions should be directed to Tom Sibley.

Logistical Information

Students will be employed full time (40 hours per week) for 10 weeks.  Last summer students earned $7.60 per hour plus up to $2.06 per hour to defray room and board for a total of $3040 plus $824 for the room and board.  The pay for next summer hasn’t been announced, but it will probably increase approximately 3%.  Because only SJU provides a summer meal plan, housing will be on the SJU campus.  Students will meet regularly with their faculty advisors.  They will have access to computers and library resources.  They are encouraged and expected to participate in all activities organized for summer research students in other departments.  They are expected to share the results of their research in writing and at suitable forums, including the summer research seminar and, if appropriate, the national Pi Mu Epsilon Conference in Burlington, Vermont on August 2-4 or other conferences during the following school year.  Funding for traveling to any conferences would be arranged.

Descriptions of Research Topics

The Mathematics of War with Marc Brodie. Continue work by Marc and previous undergraduates concerning the mathematics involved in the card game War. Questions for consideration include the probabilities of matches, the patterns of games that go into infinite loops, etc.. Prerequisite: Math 345 would be helpful, but is not a necessity.

Counting Coverings of Groups with Marc Brodie. In how many ways can a given group be expressed as a set-theoretic union of proper subgroups? Prerequisite: Math 331.

Game Theory with Gary Brown.  The Nash Equilibrium Theorem shows non-constructively that every n-person finite non-zero sum game has at least one equilibrium point.  The student would look for constructive, graphical proofs for the two person 4x4 non-zero sum games and three person 2x2x2 non-zero sum games, starting with examples of various kinds of scenarios. 

Game Theory with Gary Brown.       The student would look for optimal strategies for variations of two well known games in game theory, "Divide the Dollar" and "The Dollar Auction" or other games.

 Numerical Analysis of Differential Equations with Bob Hesse.  Applying numerical integrators haphazardly to specific ODEs may lead to spurious solutions. We will look at specific differential equations and specific methods (Euler, Runge-Kutta, etc.) Prerequisites: Math 337. Math 343 (Recommended)

Mathematical Biology with Tom Sibley and a biology professor.  Develop and explore a mathematical model for some biological system of mutual interest.  Previous students have studied assortative mating, protein regulation, population interactions among three species, and meta-populations. The prerequisites depend on the particular project: MATH 239 in general, MATH 337 for some.  Biology courses are beneficial but not necessary.

Finite Geometric Structures with Tom Sibley.  Draw colorful pictures to find and test examples, look for general patterns, make and prove conjectures, build on prior students’ research.  The prerequisites depend on the project: MATH 239 for all projects, MATH 331 for some.  MATH 325 and 333 are beneficial but not necessary.

 (please cut and paste the application into Microsoft Word)

APPLICATION FORM

DUE: March 15, 2002 electronically or as a hard copy to Phil Byrne

NAME:_________________________          Phone number: ________________

SCHOOL:________________           YEAR: __________

NAME AND SIGNATURE OF SPONSORING PROFESSOR:

_______________________              _____________________________

DO YOU HAVE A WORK STUDY GRANT? ________

DO YOU WISH TO LIVE ON CAMPUS? ________

DO YOU WISH TO USE THE MEAL PLAN? _____

FOR EACH MATH COURSE YOU HAVE FINISHED HERE, LIST ITS NUMBER, PROFESSOR AND THE GRADES YOU RECEIVED:

LIST ALL MATH COURSES YOU ARE CURRENTLY ENROLLED IN HERE:

DESCRIBE THE PROJECT YOU WISH TO DO.  (If it is one of those described in the announcement, you may copy that description.  For your own proposal, consult with your sponsoring professor to develop a description.)

DESCRIBE WHY YOU WOULD LIKE TO DO THIS RESEARCH.