Directions for Mathematics Research Experience for Undergraduates 9342_9789814630313_tp.indd 1 8/9/15 3:26 pm May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blank Directions for Mathematics Research Experience for Undergraduates Editors Mark A Peterson Mount Holyoke College, USA Yanir A Rubinstein University of Maryland, USA World Scientifc NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO 9342_9789814630313_tp.indd 2 8/9/15 3:26 pm Published by World Scientifc Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA offce: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK offce: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. DIRECTIONS FOR MATHEMATICS RESEARCH EXPERIENCE FOR UNDERGRADUATES Copyright © 2016 by World Scientifc Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-4630-31-3 In-house Editors: V. Vishnu Mohan/Tan Rok Ting Typeset by Stallion Press Email: September 8, 2015 13:49 Directions for Mathematics Research Experience 9in x 6in b2206-fm page v Contents Introduction ix Chapter 1: Undergraduate Research and the Mathematics Profession 1 by Donal O’Shea Chapter 2: FURST — A Symbiotic Approach to Research at Primarily Undergraduate Institutions 17 by Tama´s Forga´cs Chapter 3: A Laboratory Course in Mathematics 33 by Kathy Lin and Haynes Miller Chapter 4: REUs with Limited Faculty Involvement, “Underrepresented” Subjects in the Undergraduate Curriculum, and the Culture of Mathematics 53 by Yanir A. Rubinstein and Ravi Vakil v September 8, 2015 13:49 Directions for Mathematics Research Experience 9in x 6in b2206-fm page vi vi Contents Chapter 5: The Berkeley Summer Research Program for Undergraduates: One Model for an Undergraduate Summer Research Program at a Doctorate-Granting University 73 by Daniel Cristofaro-Gardiner Chapter 6: Fifteen Years of the REU and DRP at the University of Chicago 99 by J. Peter May Chapter 7: Why REUs Matter 125 by Carlos Castillo-Garsow and Carlos Castillo-Chavez Chapter 8: Integrating Mathematics Majors into the Scientific Life of the Country 147 by William Yslas V´elez Chapter 9: The Gemstone Honors Program: Maximizing Learning Through Team-based Interdisciplinary Research 167 by Frank J. Coale, Kristan Skendall, Leah Kreimer Tobin and Vickie Hill Chapter 10: The Freshman Research Initiative as a Model for Addressing Shortages and Disparities in STEM Engagement 181 by Josh T. Beckham, Sarah L. Simmons, and Gwendolyn M. Stovall September 8, 2015 13:49 Directions for Mathematics Research Experience 9in x 6in b2206-fm page vii Contents vii Chapter 11: Determining the Impact of REU Sites in the Mathematical Sciences 213 by Jennifer Slimowitz Pearl Chapter 12: The Mathematics REU, New Directions: A Conference at Mount Holyoke College, June, 2013 221 by Giuliana Davidoff, Mark Peterson, Margaret Robinson and Yanir A. Rubinstein May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blank September 8, 2015 13:49 Directions for Mathematics Research Experience 9in x 6in b2206-fm page ix Introduction This volume stems from the conference called “New Directions for Mathematics Research Experiences for Undergraduates,” held at Mount Holyoke College in June, 2013, celebrating 25 years of the Research Experience for Undergraduates (REU) program of the NSF. The majority of the articles reflect talks given at the conference. The conference itself is described by the organizers in the last article. The main impression left by the conference, documented and explored in these articles, is that the REU program in mathematics has stimu- lated innovations in mathematics education that go far beyond the original intent of the program. It is even possible to imagine that the sustained support of this program by the NSF over such a long period has begun to transform US mathematics itself. The idea that undergraduates might do mathematical research as a part of their education has a long history, but in the early years it was a lonely position to take. A conference on this topic was held in the summer of 1961 at Carleton College, documented in Undergradu- ate research in mathematics; report of a conference held at Carleton College, Northfield, Minnesota, June 19 to 23, 1961, edited by May and Schuster [4]. A second conference on undergraduate research in mathematics, held in July of 1988, also at Carleton College, gave rise to a second volume, Models for Undergraduate Research, edited by MSC 2010: 01A67, 01A80 ix