Ellen Panofsky (Millersville University): Geometric Analysis of Distance Minimizing Paths Crossing the Same Rim of a Circular Can Twice

John Bryk (Williams College and Williams College REU Program): Completions of Unique Factorization Domains

Jarod Alper (Brown University and Lafayette College REU Program): The Number Theory of the Composition Algebra

Nicholas Leger (University of Texas at Austin and Williams College REU Program): Double Bubbles on Flat Two-dimensional Tori-Part I

D. Jacob Wildstrom (Massachusetts Institute of Technology and University of Idaho REU Program): On Pairs of Monochromatic and Zero-sum Hooked Sets

Also, a special research prize of $150.00 from the Council on Undergraduate Research was awarded to:

Paul Holt (Williams College and Williams College REU Program): Double Bubbles on Flat Two-dimensional Tori-Part II

MAA Student Lecture

Early August is a good time to start talking about college football, and Dr. Rhonda Hatcher of Texas Christian University entertained an audience of about sixty people with her MAA Student Lecture on ranking college football teams. Dr. Hatcher, a Harvard Ph.D. and 1998 winner of the MAA Deborah and Franklin Tepper Haimo Award for Distinguished College Teaching of Mathematics, provided some linear algebra based approaches to ranking college football teams. The first of these produced rankings based on the powers of the matrix used to represent division I college football teams and the outcomes of their games against one another. The first power of this matrix produced a ranking based on team winning percentages. The second power of the matrix gave a ranking based on the sum of the winning percentages of a team's opponents divided by the number of the team's wins. After thirty iterations this matrix produced a ranking based on strength of conference. This was evidenced by an entertaining top ten ranking of last year's college football teams which included six teams from the Big Ten Conference and three teams from the Pac Ten Conference.

A slight variation on this approach led after eight iterations to a top ten that was more similar to the final top ten of last year's college football season. This approach favored strength of schedule in producing the ranking.

As Dr. Hatcher noted, the method of ranking college football teams employed by the Bowl Championship Series, arbiters of the national college football championship, is not purely mathematical in nature but employs some very subjective components. Dr. Hatcher's purely mathematical approaches to ranking college football teams offered a very entertaining look at some alternatives to the BCS ranking system.

MAA Student Workshop

Dr. Jeffrey Weeks, freelance mathematician and MacArthur Fellow, guided a group of about fifty students through a very hands-on and highly entertaining MAA Student Workshop. Dr. Weeks, who received his Ph.D. from Princeton University, led the

students through an exploration that yielded a classification of the number of possible tilings of spherical, Euclidean, and hyperbolic space for dimensions three and higher using maximally symmetric tiles. The five maximally symmetric tiles consisted of tetrahedra, cubes, octahedra, icosahedra, and dodecahedra. The highly imaginative student workshop began with Dr. Weeks passing out small plastic triangles to several

groups of students and asking different groups of students to discover that joining the triangles with three, four, or five triangles per vertex yielded tilings of a sphere, while six triangles per vertex tiled a plane and seven or more triangles per vertex tiled hyperbolic space. This exercise was then repeated with squares, pentagons, hexagons, and septagons. The tetrahedra, cubes, octahedra, icosahedra, and dodecahedra assembled in these exercises were put to use in the exploration of possible tilings of spherical, Euclidean, and hyperbolic space in dimensions three and higher. The student workshop concluded with a question and answer session with Dr. Weeks.

Student Hospitality Center

The Student Hospitality Center was as busy as ever at MathFest 2001 in Madison, Wisconsin. Following the Student Reception, and for the duration of the meeting, it was a favorite place for students to congregate. The Student Hospitality Center has been a mainstay now for almost a decade for students attending the joint winter meetings as well as MathFest meetings. Some prepared and practiced their talks, some collaborated with others on solving some of the more difficult mathematical puzzles, and some perused the library of Math Horizons magazines. Some met with advisors, some formed new acquaintances, some came in to simply relax and enjoy refreshments. Most MAA Student Chapter Advisors dropped by for information about student talks. Advisors are always welcome in the Student Hospitality Center. Members of the MAA Committee on Undergraduate Student Activities and Chapters frequented the center in greeting visitors. Katarina Briedova of MAA headquarters saw to it that the Center was furnished with lots of different information for both students and their advisors.

Look for The Student Hospitality Center at the next national meeting. Everyone is welcome in The Student Hospitality Center.

New National Math Champion Crowned

The fourth annual U.S. National Collegiate Mathematics Championship was held following the MAA Student Lecture at MathFest 2001. The champion for the past two years, Greg Jones of the University of Missouri, was present along with twenty other students from across the country. Among them was Michael Khoury from Denison University who took first place this year, with Jones the runner-up. The competition, which lasted nearly an hour, began with an explanation of the rules. After this each competitor began working on the first in a series of seven problems. A competitor was not allowed to begin working on a subsequent problem until the immediate problem was finished. Khoury and Jones both finished all seven problems, with Khoury finishing first. First place prizes included a trophy in the shape of the U.S. , a TI 92 Calculator donated

by Texas Instruments, and a summer internship at the Lawrence Livermore National Research Laboratory. The internship is an outstanding opportunity for the top winner of the yearly championship to study among some of the finest researchers in the world, and has a monetary value of almost $10,000. All students received t-shirts and U.S.

Championship medallions. Jones also received a runner-up trophy to go along with his two national championship trophies from years past.

In order for a student from your campus to qualify for the national championship, the college must be registered in the monthly Problem Solving Competition, edited by Dr. Richard Neal. For information on the annual event and the monthly Problem Solving Competition contact Richard Neal, University of Oklahoma, Department of Mathematics, 601 Elm Avenue, Norman, OK 73019.