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Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs Joseph A. Gallian Editor Cover photographs courtesy of Penn State Erie, The Behrend College, Erie, PA, and AU Photos, Auburn University, AL. This material is based upon work supported by the National Security Agency under Grant MDA 904-99-1-0063. Library of Congress Cataloging-in-Publication Data Conference on Summer Undergraduate Mathematics Research Programs (1999 : Crystal City, Arlington, Va.) Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs / Joseph A. Gallian, editor. p. cm. ISBN 0-8218-2137-7 (alk. paper) 1. Mathematics—Study and teaching (Higher)—United States—Congresses. 2. Mathematics— Research—United States—Congresses. I. Gallian, Joseph A. II. Title. QA13 .C6523 1999 510.72073—dc21 00-029329 Copyright c 2000 American Mathematical Society Printed in the United States of America. All rights reserved. 10987654321 050403020100 Table of Contents Preface ......................................................ix Part I. Descriptions of Summer Research Programs Auburn University . ..........................................3 CaliforniaStateUniversityFullerton..........................9 CarnegieMellonUniversity..................................13 College of William and Mary . .............................19 CollegeofWooster...........................................31 CornellUniversity...........................................37 CornellUniversity...........................................41 DavidsonCollege............................................51 DrewUniversity.............................................55 HopeCollege................................................59 IndianaUniversity...........................................69 LouisianaStateUniversity...................................77 MiamiUniversity............................................87 MichiganTechnologicalUniversity...........................93 MountHolyokeCollege.....................................105 NationalSecurityAgency...................................117 NationalSecurityAgency ..................................121 v vi CONTENTS NorthernArizonaUniversity................................123 OregonStateUniversity....................................127 PennsylvaniaStateUniversity..............................133 Rose-HulmanInstituteofTechnology.......................139 SUNYPotsdam-ClarksonUniversity........................147 TulaneUniversity.......................................... 151 UniversityofMarylandEasternShore......................155 UniversityofMinnesota,Duluth............................163 UniversityofPuertoRico-Humacao.........................169 UniversityofTennessee.....................................181 UnivesityofVirgina........................................189 UniversityofWashington...................................193 Williams College ...........................................203 WorcesterPolytechicInstitute..............................213 Part II. Descriptions of Summer Enrichment Programs CarletonCollegeandSt. OlafCollege...................... 223 CollegeofCharleston.......................................231 GeorgeWashingtonUniverity...............................237 Mills College and Berkeley. ..............................245 CONTENTS vii Part III. Student Evaluations of Summer Programs “Cornell 1999 REU program evaluation summary” by Nora L. Balfour.....................................................259 “TheSCAMPsummerprogram”byBlairBradley..........265 “Mathematics research experiences” by Stephen G. Hartke. .267 “Research Experience at the University of Maryland Eastern Shore”byAndreaHeight...................................273 “REU and the nontraditional student” by Laura E. Johnson 275 “Theexperienceofa lifetime”byDarrenA.Narayan.......279 “Reflections on the NSF/REU program” by Johnnell Parrish 281 “Experience in faculty mentored research” by Suzanne Sindi and GareguinMikaelian ........................................285 Part IV. Articles “Helping students present their research” by Joseph A. Gallian andAparnaHiggins........................................289 “Multi-faceted undergraduate research in mathematics at the Uni- versityofDayton”byAparnaHiggins......................297 “MASS Program at Penn State” by Anatole Katok and Svetlana Katok......................................................307 “How program design and implementation leads to achieving goals” by Herbert A. Medina . ..............................315 “Evaluatingsummermathprograms”byDeborahNolan....323 “Scholarly experiences for all students” by Lynn A. Steen . 331 viii CONTENTS “e-REU”byRobbyRobson.................................337 “Opportunities for Undergraduates at the University of Arizona” byEliasToubassi ..........................................341 Part V. Summary of Conference Sessions SummaryPlenarySessions................................. 347 SummariesofSmallGroupDiscussions.....................363 Part VI. Surveys of Summer Programs SummaryofSummerProgramSurveys.....................377 SummerProgramSurveys..................................379 Preface During a chance meeting in 1998 between John Ewing of the AMS and Barbara Deuink of the National Security Agency (NSA), John made the comment that it was his belief that there were many pro- fessional mathematicians whose careers had been positively influenced by their participation in a summer undergraduate research program. Barbara asked John if he knew of any attempt to document the impact of such programs. Out of this exchange came the idea for the AMS to organize a three day conference with the sponsorship of the NSA that would bring together mathematicians from across the country who have been involved in summer mathematics programs for undergraduates. An organizing committee consisting of Barbara Deuink, John Ewing, Joe Gallian, Jim Maxwell, Herbert Medina and Deb Nolan planned the conference. Diane Mack of the AMS served as the coordinator. Among those invited to participate in the conference were current and recent directors of the National Science Foundation Research Expe- rience for Undergraduates (REU) programs, directors of summer pro- grams for women and minorities, representatives from the NSF and NSA, and people active in promoting undergraduate research. The meeting took place on September 30 - October 2, 1999 at the Hilton Hotel in Crystal City, Virginia. The purpose of the conference was to exchange ideas, discuss is- sues of common concern, establish contacts, and gather information that would be of use to those in the mathematics community who are interested in establishing summer mathematics programs for un- dergraduates. The proceedings of the conference provides a wealth of information about the structure and philosophy of successful summer programs. This volume includes detailed descriptions of the programs run by the conference participants, expanded versions of some of the presentations given at the conference, an article about helping students present their research, an article about establishing an online REU, sur- veys completed by summer program directors, a summary of the survey data from the program directors, articles and statements solicited from students who have participated in summer programs, and summaries ix xPREFACE of the plenary sessions, panel discussions, and break-out sessions. The AMS has also committed to an effort to track participants in summer programs over a long period. I wish to thank the following people for their contributions to mak- ing the conference and these proceedings possible: Barbara Deuink, John Ewing, Diane Mack, Jim Maxwell, Herbert Medina, Deb Nolan, and Jim Schatz. I am grateful to Vickie Ancona, Ed Dunne, Gil Poulin, and Janet Simoneau from the AMS for their excellent work in produc- ing the volume. Robby Robson generously volunteered to take the notes of the plenary sessions that appear here. And, of course, the conference could have never taken place without funding from the Na- tional Security Agency and the cooperation of the summer program directors who participated in the conference. December 17, 1999 Joseph A. Gallian, University of Minnesota, Duluth E-mail address: [email protected] PartI DESCRIPTIONS OF SUMMER RESEARCH PROGRAMS Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs The Research Experience for Undergraduates in Discrete Mathematics at Auburn University, Summer, 1999 Peter D. Johnson Jr. Our program ran for eight weeks. We had 7participants. There were only two of us (Overtoun Jenda and Peter Johnson), but we en- joyed the generous support of our colleagues, of our graduate students, and of several visitors during the summer. These supporters gave talks (three colleagues gave two-talk sequences), and were available for dis- cussion and consultation. One of our graduate students, Michelle Fos- ter, gave a talk that struck the fancy of one of the participants, and sub- sequently Michelle directed her inquiry for the duration, in Michelle’s area (information theory). Two of our colleagues, Doug Leonard and Kevin Phelps, donated a significant amount of unpaid time in deliver- ing concentrated introductions to computer algebra and coding theory, and to the software available in our computer laboratory. The collegial, cooperative spirit of our department, and the fact that we are a noted research center in some areas of discrete mathe- matics, and can count on a steady stream of visitors, and also on the aid of graduate students of high quality

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