# Fall 2001

San Diego Site of

Joint Winter Meetings

The AMS/MAA Joint Winter Meetings will take place in San Diego from January 6 through January 9 of 2002. Activities for students and faculty advisors will begin with an opening reception (a first at the winter meetings). Other activities will include the Minority Student Initiative, Faculty Advisors Breakfast, MAA Student Lecture, and Mathematical Experiences for Students Outside of the Classroom. As always, the Student Hospitality Center will provide a place for students to gather and meet new friends. Further information can be found in Whassup in San Diego on page 5 and in the October issue of Focus.

MathFest 2001:

Math in America's Dairyland

Although MathFest 2001 took place in the heart of America 's Dairyland, Madison, Wisconsin, the opening weather was more reminiscent of a tropical monsoon. By the first afternoon, however, the torrential rains gave way to sunny, humid weather for the rest of the meeting. News about student activities at MathFest 2001 can be found in Madison Menu beginning on page 2.

What's inside?

Student Paper Sessions

MAA Student Lecture

MAA Student Workshop

Student Hospitality Center

Problem Solving Competition

Whassup in San Diego:

MAA Student Lecture

Minority Student Initiative

Mathematical Experiences Outside the Classroom

Contact Information

MAA Student Paper Sessions

at MathFest 2001

On Thursday and Friday, August 2-3, eight MAA Student Paper Sessions were held at the Madison MathFest. Sessions 1-4 were held from 1:00 to 5:00 p.m. on Thursday while sessions 5-8 took place from 1:00 to 5:00 p.m. on Friday.

The program included forty-six talks involving forty-nine students from thirty-two colleges and universities. There were twenty-seven student chapter members, of whom sixteen qualified for travel grants. Three students also spoke at previous MathFests and there were twenty-three students from six REU programs.

Cash awards of $150.00 from the MAA were presented to the following students for outstanding presentations: Aliyah Ali (Rutgers University and Rutgers University REU Program): Graphs and Matrices Eric Katerman (Williams College and Williams College REU Program): Knot Complements: the Hyperbolic Alter-ego of Out Twisted Friends Cody Patterson (Texas A&M University): Distinct Element Vectors Over Finite Groups John Meth (Indiana University): Idempotent Cocycles on Cyclic Groups Eva Kashat and Daniela Silva (jointly) (Wayne State University): Geometric Applications of a System of Congruences 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.

Whassup in San Diego

· MAA Student Lecture

Professor M. Elisabeth Pate¢-Cornell will give the MAA Student Lecture on the topic of Finding and Fixing Systems' Weaknesses: the Art and Science of Engineering Risk Analysis. Professor Pate¢-Cornell is the Burt and Deedee McMurtry Professor of Engineering and Chair of the Department of Engineering at Stanford University.

Methods of Engineering Risk Analysis are based on a functional analysis of engineered systems and on probabilities, most of the time, Bayesian. These methods allow identification of the system's failure modes and of the contribution of each element to the overall probability of failure. The model can then be extended to include human decisions and actions and the management factors that might be root causes of systems' failures. Because this approach allows considering rare events, even some that have never occurred yet, it can be particularly beneficial when trying to identify, in a proactive mode, a system's weaknesses and the least expensive way of fixing them. This is particularly critical in situations when decisions and policies need to be made before full information is available, when many other human needs are competing for the same resources, and therefore when priorities need to be set. In this talk Professor Pate¢-Cornell will describe the engineering risk analysis method and present illustrations ranging from the management of space systems (e.g., the tiles of the space shuttle) to medical problems (e.g., patient risk in anesthesia) and the mitigation of seismic risks. Some limitations of the method and ethical aspects of its application will also be discussed.

· Minority Student Initiative

There will be small grants available for faculty in California to help bring minority students to attend the MAA/AMS Joint Winter Meetings in San Diego in January of 2002. Interested faculty in California should write to Jean Bee Chan at jbchan1@attglobal.net. (Please note the "1" after jbchan)

· Mathematical Experiences for Students Outside the Classroom

Mathematics "happens" outside the classroom and, in fact, many math majors are drawn to the subject through an event sponsored by a Student Chapter or Math Club. This session seeks presentations by academic, industrial, business, or student mathematicians. Descriptions of non-classroom activities could include, but are not limited to, special lectures, workshops for students, Math Days, Math Fair, research projects for students, Career Days, recreational mathematics, problem solving activities, and student consultants. Applications should be submitted to Rick Poss (possrl@mail.snc.edu) of St. Norbert College by November 30, 2001. The application should include name, address, phone number, e-mail address, title of presentation, and a one-page description of the activity. Presentation time is limited and there is no guarantee that all submissions can be accepted. Applicants will be notified by December 14, whether or not their proposal has been accepted.

Contact Information

How to Reach the MAA

¨For Membership Information, Subscriptions,

and Publications orders contact:

The MAA Service Center

P.O. Box 9112

Washington, DC 20090-1622

800-331-1622 or (301) 617-9415

FAX: (301) 206-9789

The Mathematical Association of America

1529 Eighteenth Street, NW

Washington, DC 20036-1385

800-741-9415 or (202) 387-5200

FAX: (202) 265-2384

To Contact the Chapter News Editor

¨Suggestions, concerns, and/or contributions of articles for this newsletter may be sent to:

James P. Marshall

Illinois College

Department of Mathematics

1101 W. College Ave.

Jacksonville, IL 62650

(217) 245-3432FAX: (217) 245-3034

jmarshal@hilltop.ic.edu

May the MATH be with you!