FOCUS December 2001

FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and December. Editor: Fernando Gouvêa, Colby College; December 2001 [email protected] Volume 21, Number 9 Managing Editor: Carol Baxter, MAA [email protected] Senior Writer: Harry Waldman, MAA [email protected] Please address advertising inquiries to: Inside Carol Baxter, MAA; [email protected] President: Ann E. Watkins, California State University, Northridge 4I’d Rather Go to Mathcamp First Vice-President: Barbara L. Osofsky, By Brenda Fine Second Vice-President: Frank Morgan, Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 7Mathematics and Democracy in Nigeria Gerald J. Porter Executive Director: Tina H. Straley 8 MAA Awarded Half Million Dollar NSF Grant to Support Assessment Associate Executive Director and Director of Publications and Electronic Services: Donald J. Albers 9Short Takes FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin 10 San Diego Program Updates Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Peter Renz; Annie Selden; Jon Scott; 13 Read This! Ravi Vakil. Letters to the editor should be addressed to 14 Reshaping Graduate Education: Looking Back at the Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by Wisdom of Mina Rees email to [email protected]. By Amy Shell Subscription and membership questions should be directed to the MAA Customer 18 Employment Opportunities Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. Copyright © 2001 by the Mathematical Association of America (Incorporated). Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is used: On the cover: Megan Guichard, a junior counselor at Mathcamp (see “Reprinted with permission of FOCUS, the page 4) displays her mathematically-interesting hair. Photograph by newsletter of the Mathematical Association of America (Incorporated).” Chris Tuffley. Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. FOCUS Deadlines Box 90973, Washington, DC 20090-0973. February March April ISSN: 0731-2040; Printed in the United States Editorial Copy December 14 January 15 February 4 of America. Display Ads December 21 January 29 February 25 Employment Ads December 10 January 15 February 11

2 December 2001 FOCUS JSTOR to Include Mathematics Magazine and Reforming Math College Mathematics Journal Teaching in Houston

The JSTOR Board of Directors ap- proved, in its October 2001 meeting, the addition of Mathematics Magazine and the College Mathematics Journal to their web-based electronic archive. JSTOR (the name stands for “Journal Storage”) offers its subscribers access to the complete runs of many scholarly journals, including the American Mathematical Monthly. The journals archived at the JSTOR site are fully searchable and give access to high- quality page images that produce beauti- Governor-at -large Jacqueline Brannon ful printout. Giles, seen above with Dr. Llayron L. Clarkson and Mrs. Charlotte Haynes , It is expected that the two MAA journals attended the HU-LINC meeting on Oc- will be added to JSTOR by early 2002, tober 12, 2001 to learn more about the implementation stage of the urban sys- making it possible for JSTOR subscrib- Members of institutions that are JSTOR ers to access electronic archives of the temic initiative in Houston. The Hous- subscribers can access the archive at http:/ ton Community College System Central three main MAA journals from their in- /www.jstor.org. Those individuals who do ception through 1997. (A five-year “mov- College has initiated a proposal to join not have JSTOR access through their in- the coalition of colleges, universities, ing wall” is maintained to preserve the stitutions can obtain annual subscrip- subscriber base of each journal.) schools and other entities that provide tions through the MAA. technology-integrated mathematics and science professional development for el- ementary, middle, and high school teach- ers. Other schools in the coalition include the University of Houston-Downtown, MAA to Host Meeting Have You Seen the Texas Southern University, Prairie View A and M University, Rice University, and for NSF PIs BIG SIGMAA Web many others. For more information on Site? HU-LINC, contact Charlotte Haynes at [email protected]. The Mathematical Association of America has been awarded a grant of The BIG SIGMAA is the special inter- From the Editor $168,548 by the National Science Foun- est group within the MAA devoted to dation to host a meeting of Principal In- mathematics and mathematicians in vestigators of NSF-funded mathematics Business, Industry, and Government. BIG In a forthcoming issue, we hope to pub- projects in the Division of Undergradu- was the second SIGMAA to be approved lish in FOCUS a set of articles discussing ate Education. The meeting will take place by the Board (the other two SIGMAAs mathematics on the internet: what is March 14-16, 2002 in Washington, DC. Focus on Research on Undergraduate available, how it is (or can be) used, who The focus of the meeting will be on dis- Education and Statistics Teaching). The uses it, how good it is. I would like to in- semination of project materials. Within BIG SIGMAA web site, at http:// vite our readers to contribute to that is- the meeting there will be two workshops: www.math.unt.edu/bigsigmaa/, has infor- sue. If you have observed or studied stu- one on writing learning materials and the mation about the SIGMAA and its offic- dents’ use of the internet, have partici- other on preparing learning materials for ers, announcements of program items at pated in the process of creating a math- the Joint Mathematics Meetings in San interactive, online use. Lang Moore, Vis- ematically-oriented web site, or just have Diego, a technical questions discussion iting Mathematician at MAA, is the prin- a site you would like to review, consider board, and lots of information about cipal investigator for this project; Tina submitting an article to us. You can reach non-academic careers in mathematics. Straley, Executive Director of MAA, is a me by email at [email protected] (this co-PI. The site is maintained by Peter DeLong; he can be reached by email at is by far the best way) or at Department [email protected]. of Mathematics, Colby College, May- flower Hill 5836, Waterville, ME 04901.

Fernando Q. Gouvêa

3 FOCUS December 2001 I’d Rather Go to Mathcamp By Brenda Fine

Last winter, Wellesley assistant profes- Mathcamp was founded in 1993 on a exciting mathematics and people who can sor Mira Bernstein, then a postdoctoral wing and a prayer by Dr. George Rubin relate to that excitement. Indeed, the en- fellow at Berkeley and a co-worker of Thomas, who recognized that teenagers ergy and enthusiasm for mathematics mine during the previous summer, interested in mathematics often lacked that staff and campers alike bring to the brought to my attention a series of ad- the resources — and the camaraderie — camp environment is palpable. For five vertisements that were running in the necessary for them to thrive as mathema- days a week during the five-week camp, popular teen magazine Seventeen as part ticians. Under the direction of Dr. Tho- students can choose courses tailored to of an aggressive anti-drug campaign. One mas, Dr. Mira Bernstein, McGill their backgrounds and interests from a of them featured a photograph of a teen- postdoctoral researcher Dr. David Savitt, packed schedule that includes classes on aged girl whose crush had just offered her and a host of dedicated counselors and all sorts of subjects. Some courses, includ- some (unspecified) sort of illicit sub- instructors who thrive on hundred-hour, ing linear algebra, number theory, stance. The full- fractals, real analysis, page ad suggested a projective geometry, variety of ways for and topology, are the girl, and others taught over the in her position, to course of several express indignation weeks, and intro- regarding this offer, duce students to the but one stood out rigors of university as particularly level mathematics damning: “I’d while incorporating rather go to fun applications that Mathcamp than students aren’t likely smoke a joint!” to see as under- graduates. Other Although the ad classes are one-time was soon pulled, affairs that cover there is no denying more whimsical top- that it reflected a ics such as False popular mindset Proofs (students are among its audience challenged to find of teenagers — and, the flaws), Van der indeed, among the Camper Pradeep Mouli peers out from George Hart puts the finishing touches on Waerden’s Theorem public at large. Ad- a Zometool Cage. Photo by Chris a camper’s makeshift Zome home. Photo (whose instructor, vertisers can hardly Tuffley. by Chris Tuffley. Mathcamp mentor be blamed for capi- Julian Gilbey cau- talizing on this phenomenon. When a math-filled workweeks, every year enthu- tioned, “If you are afraid of big numbers, million ads fail to quell the argument that siastic young mathematicians can inter- don’t take this class!”), and Hats and marijuana has its therapeutic uses, one act with spirited university math students Codes — Mira Bernstein’s presentation of might as well take advantage of the fact and professors from around the world. an unexpected synthesis of Hamming that mathematics is all but universally re- The camp itself migrates from summer codes with a problem about guessing the garded as bad medicine. to summer, and over the years has found color of one’s hat. (See the November is- temporary homes in Vancouver, BC, Se- sue of FOCUS.) Nevertheless, one particular segment of attle, WA; Toronto, ON; Wellesley, MA; the market was conspicuously overlooked and, most recently, in Waterville, ME, Mathcamp’s goal isn’t to give students the by the designers of this advertising cam- where Colby College hosted 115 gifted credits (or even the knowledge) that paign: the participants and staff (gradu- high school students and nearly three they’d otherwise obtain in their high ate student “mentors,” who teach, and dozen staff and visiting speakers. school classes — after all, most of our undergraduate “junior counselors,” who campers aren’t any more interested in handle nonacademic work) at the real- Far from being a chore for the staff and a doing even more high school mathemat- life Mathcamp, where Mira Bernstein and punishment (or a pretense for turning ics than are any of their less-mathemati- I spend our summers. down joint-smoking potential dates) for cally-geared classmates. Instead, the campers, Mathcamp is an oasis of Mathcamp aims to show campers awe-

4 December 2001 FOCUS inspiring results, connections between Professor Lang is but one of dozens of ers who didn’t mind getting tied up in seemingly unrelated branches of math- visiting professors who have enjoyed a knots — literally) to the mathematics of ematics, and overall “cool math”. symbiotic relationship with the many rainbows — and that’s without even get- budding mathematicians at the camp. ting into the dozens of topics that came By and large, students seem to think that This past summer, full-time mathemati- up while campers had lunch with the we’ve succeeded. Even though attendance cal sculptor and Zometool expert George camp’s celebrity mathematician. in classes is not mandatory and the at- Hart spent a week with the campers, stay- mosphere at the camp is very informal ing up until all hours to help them con- Other visitors shared their expertise in and relaxed, every hour of every day is a struct elaborate “Zome homes”. Dr. John fields indirectly related to mathematics. flurry of mathematical activity. Much of University of Cambridge physics this activity takes the form of problem postdoctoral fellow Sanjoy Mahajan sets and class notes, but a large propor- taught a handful of classes about ap- tion of it involves solving Rubik’s Cubes proaching physics problems through and building structures out of Zometool, order of magnitude analysis. His other a geometrical construction tool. More- classes, on analysis of data, will ensure over, mathematics permeates nearly ev- that a few dozen students will never read ery aspect of the camp. One might not the newspaper in quite the same way think that an a cappela group could pos- again. And Assistant Professor Hany sibly have much to do with math, but in Farid from Dartmouth shared his re- the hands of counselor Ari Nieh, the search and knowledge of image process- Mathcamp Contrapositones — whose ing and computer vision to some camp- repertoire included the song ers who now have reason to wonder “Nonabelian”, written by mentors Chris what’s behind that digital photograph Tuffley and Mary Pat Campbell and sung of Albert Einstein. to the tune of Simon and Garfunkel’s “Cecilia” — produced the quintessential But that’s just what goes on during the marriage of mathematics and music. week — and it’s not even the half of it: a myriad of impromptu games ranging At the end of the camp, our students’ from Capture the Flag to bridge to most common complaint about their Scrabble to Ultimate Frisbee peppered five-week stay isn’t “too much math,” as Junior Counselor Megan Guichard makes a the Colby campus for the duration of might be the case with most teenagers, mathematical fashion statement. Photo by the camp. Weekends (Sunday and Mon- but rather “scheduling conflicts” — that Chris Tuffley. day at Mathcamp) are reserved for is, too much cool math for nonmathematical fun, and them to experience all at this year we took full ad- once. When I polled the vantage of the beauty of Mathcamp alumni for ideas Maine. One Monday found for this article, one camper, us whitewater rafting (and, high school senior Tracy in some cases, swimming) Lau from Burnaby, British in the Kennebec river, and Columbia, enthused about another was spent at Acadia two of her favorite aspects National Park, where of the camp: “freedom” and campers could choose to go “math all day long without kayaking, hiking, or biking. ridicule.” The juxtaposition One camper, Jennifer of those two items speaks Sheppard of Beaumont, volumes about the level of Texas, commented to me at motivation and love of their the Kennebec: “I’ve spent subject that our campers more time outdoors this bring with them. Even pro- summer than I ever have fessional mathematicians before.” Indeed, this ain’t are struck by the camp en- Junior counselor Dan Zaharopol accompanies a crew of campers down your parents’ math class — vironment: after visiting the the Kennebec River. Photo by Chris Tuffley. or even yours. camp in 2000, Yale Profes- sor Serge Lang declared Mathcamp to be Conway joined us for a week from Sadly, all good things must come to an “the largest concentration of intelligence Princeton to talk about...well, all things end. (Some, however, beg to differ — at and math freaks” he had ever seen — and mathematical. His morning lectures cov- one of Julian Gilbey’s classes, a course that’s in some five decades of work in the ered everything from tangles (demon- dealing with methods of thinking, stu- field. strated visually by some volunteer camp- dents brainstormed over the pros and 5 FOCUS December 2001 cons of having a year-long Mathcamp.) math, but even then we can’t resist. This Personally, I’ve experienced no greater The final days of the camp are a high- year, a posse of campers presented a de- high than talking about conics in the pro- adrenaline variant upon what the camp- lightful skit about the camp, and I opted jective plane to teenagers who can catch ers have come to experience during the for the second year to take advantage of my enthusiasm — and I’ll be returning first several weeks. Far from tiring of the only audience that would ever appre- in 2002 to get my yearly fix. math, they do even more of it during the ciate The House With Too Many Perpen- entire last night of camp, which features diculars, a skit I wrote about a family liv- Brenda Fine is a graduate student in alge- showings of math movies (this year’s fare ing in a four-dimensional house. braic geometry at the University of British was the off-Broadway musical Fermat’s Columbia, and is counting the days until Last Tango), additional math talks (in- Indeed, I, like the girl in the Seventeen ad, next year’s Mathcamp. cluding one on David Savitt’s thesis, would rather go to Mathcamp than which he presented in response to some smoke a joint. But regardless of how well students’ requests for “math talks [we] that anti-drug tack resonated with most don’t understand at all!” — rumour has young adults, I’m afraid that it sells it these students weren’t let down), and a Mathcamp woefully short. Camper For more information about Mathcamp tradition — 30 proofs in 30 Chintan Hossain of Wilmington, Dela- Mathcamp, visit their web site at http:/ minutes (we managed 36, one of which ware, described the camp as “by far the /www.mathcamp.org or contact the was a thorough — modulo a couple of best five weeks” of his life — and it’s a organizers by email at lemmas — proof of Fermat’s Last Theo- sentiment echoed year after year by [email protected]. rem). There’s no requirement that the an- campers who insist that there’s nothing nual end of camp talent show involve they’d rather do than go to Mathcamp.

6 December 2001 FOCUS

Mathematics and Democracy in Nigeria

On July 20, 2001, Profes- United States. She believes that sor Jacqueline Brannon Giles programs in quantitative lit- visited Nigeria to present a eracy offer opportunities to de- paper entitled Mathematics velop human resources and to and Democracy: the Case for demonstrate commitment and Quantitative Literacy in the compassion for all sectors of our United States and Nigeria (A communities. Comparative Study). As a member of the MAA Quan- While in Nigeria in July 2001, titative Literacy Committee she revisited Ushafa Land in and MAA Board Member for Abuja, Nigeria and was named Minority Affairs, she received Gimbiya (Princess) of Ushafa a copy of Mathematics and Land, by the Chief of the village. Democracy, published by the Professor Giles had visited National Council on Educa- Ushafa earlier, at the time of tion and the Disciplines’. She former President Clinton’s visit immediately recognized the to the region in August 2000. importance of extending the Having been named Gimbiya, discussion of quantitative lit- she was asked to serve as a liai- eracy to the global commu- son to former President Clinton nity, especially in Nigeria. Professor Giles with Dr. Jerry Kolo (left), president of the Council to pursue the opportunity to es- of Nigerian People and Organizations (CONPO), headquartered tablish an Institute of Math- Nigeria was targeted in her in Florida, and Chief (Prof.) Adebayo Mokuolu, member of Council ematics and Technology in the discussion because of the of Obafemi Awolowo University, Ile-Ife, Nigeria. Nigerian village. On October 5, large number of Nigerians in 2001, Clinton’s office indicated the United States who regularly travel that he was incredibly busy now, back and forth to Nigeria to contribute and that Professor Giles should contact to the nascent democracy established in his office in January to make an appoint- May, 1999 under the administration of ment to see him to discuss the Chief’s Nigeria’s current President Olusegun proposal. Obasanjo. Professor Giles had attended the “Handover to Democracy” ceremony The International Guardian, a journal for and the inauguration of President Africa and America, published a large Obasanjo in 1999, and so was familiar portion of Professor Giles’s talk. The re- with the Nigerian situation. sponse to the article in the mathematics community has been extensive and favor- Professor Giles emphasized issues that able, indicating our interest in not only should be discussed nationally and inter- national but also international concerns. nationally. These included the impor- tance of sensitivity to the cultural and contextual situations arising in Nigeria (and other countries) in the process of constructing a sound definition of “lit- Have You Moved? eracy” and “quantitative literacy” in Ni- geria (and other countries.) The MAA makes it easy to change your Professor Giles with Mrs. Pauline K. Tallen, address. Please inform the MAA Ser- She further stated in her presentation that Honorable Minister of State, Federal Min- vice Center about your change of ad- more student exchange programs should istry of Science and Technology, Nigeria. dress by using the electronic combined be established and that workshops, fo- Mrs. Tallen arranged for the CONPO del- membership list at MAA Online rums, and conferences on quantitative lit- egates to attend church with President (www.maa.org) or call (800) 331-1622, eracy should be implemented in the Obasanjo and to have a two-hour dinner fax (301) 206-9789, email: United States and other countries who meeting with him to discuss educational is- [email protected], or mail to MAA, PO Box 90973, Washington, DC 20090. are in cooperative relationships with the sues.

7 FOCUS December 2001 MAA Awarded Half Million Dollar NSF Grant to Support Assessment

The MAA has been awarded a $499,928 tor) will manage the project at the MAA grant by the National Science Foundation office. Peter Ewell, an internationally (NSF) for a three-year project entitled known authority on assessment and Supporting Assessment in Undergraduate evaluation, will serve as Project Evalua- Mathematics. The project’s products will tor. There is a sub-award to the Univer- include a workshop series, a volume of sity of Arkansas to support Madison’s case studies and syntheses of case studies work there. on assessment, and a web site for infor- mation about assessment. The award fits into the NSF program on Assessment of Student Achievement. This The objective of the project is to support new program is part of NSF’s Education faculty members and departments in ef- and Human Resources division, and this forts to assess student learning in at least was the first round of proposals. The so- one of the following: (1) Coherent blocks licitation attracted 144 proposals, of Bernard L. Madison of courses of undergraduate mathemati- which only 10 were funded. A second so- cal sciences, including entire degree pro- licitation is now in process. The MAA funds to support the senior personnel to grams; and (2) Individual courses, espe- proposal was strengthened by the conduct these forums. cially reform courses, using various as- organization’s record in supporting as- sessment tools across varieties of institu- sessment of student learning. MAA’s work Gold, Marion, and Keith will be gather- tions. began in 1990 with the appointment of ing additional case studies on assessment the CUPM Subcommittee on Assessment and updating some of those in Assessment The targeted blocks of courses are: (a) the (with Madison as Chair). Practices in Undergraduate Mathematics major in mathematics, (b) courses for to constitute part of a new volume to be future teachers; (c) school mathematics In 1995 the Subcommittee issued guide- submitted for publication in the MAA as a preparation for college mathemat- lines for departments to use in establish- Notes series. Steen and Madison will be ics, usually called college placement pro- ing a cycle of assessment aimed at pro- writing syntheses of various coherent grams; and (d) general education courses, gram improvement. Marion was a mem- groups of case studies for this same vol- including those aimed at quantitative lit- ber of the Subcommittee and joined with ume. Once the new volume is published, eracy. This latter block will include study Gold and Keith to edit Assessment Prac- it, too, will be mailed to every US math- of assessments of the mathematical and tices in Undergraduate Mathematics ematics department. quantitative literacy achieved in entire (MAA Notes #49), published in 1999. degree programs, recognizing that much This volume contains over seventy case Haver will have principal responsibility mathematics is learned outside math- studies of assessment at institutions for developing a workshop series to sup- ematics courses. across the US and includes the Subcom- port assessment efforts. The first work- mittee on Assessment’s 1995 report as an shop is already scheduled and will be sup- Assessing learning in individual courses appendix. Prefaces by Steen and Madison ported by the MAA PREP program, an- across a variety of institutions will focus give more history of the MAA’s support other NSF-funded activity. This work- on reform courses and include study of of assessment. (The book was reviewed shop is an extended version, aimed at classroom assessment. Cycles that use as- in MAA Online: see http://www.maa.org/ having 10 to 12 institutional teams work- sessment for program improvements will reviews/assess.html.) ing jointly on assessment efforts over two be of special interest, including those that years. use research in learning. As a part of the project, this MAA Notes volume will be sent to every US math- The workshop will begin with a two-day Bernard L. Madison (MAA Visiting ematics department within the next few session following the Joint Mathematics Mathematician from the University of months. The volume and other aspects Meetings at San Diego in January 2002 Arkansas), who wrote the proposal, is the of this project will be the focus of forums and end with a session at the close of the Project Director. Senior personnel are that will be scheduled at MAA Section Joint Mathematics Meetings in Baltimore Bonnie Gold (Monmouth College), Wil- and other meetings. in January 2003. Gold, Marion, Keith, and liam E. Haver (Virginia Commonwealth Madison will assist Haver in conducting University), Sandra Z. Keith (St. Cloud Sections wishing to schedule such a ses- this workshop. Support for travel, hous- State University), William A. Marion, Jr. sion to help support faculty who are ing, and food is available. More informa- (Valparaiso University), and Lynn A. working on assessment or planning work tion can be found at MAA Online under Steen (St. Olaf College). Thomas W. on assessment should contact Madison Professional Development (http:// Rishel (MAA Associate Executive Direc- ([email protected]). The project has www.maa.org/pfdev/prep/prep.html).

8 December 2001 FOCUS Assessment at the Short Takes Department Level Not Ready For College Functions, Models and Data William Haver, Bonnie Gold, Sandra Keith, William Marion A report released in October by the Na- This NSF summer institute, to be held on and Bernard Madison tional Commission on the High-School June 19-June 24, 2002 at Dickinson Col- January, 2002-November, 2003 Senior Year concludes that high schools lege in Carlisle PA, is based on the new are failing to prepare many of their stu- Workshop Precalculus materials developed This workshop has four components, dents for college. Only half of those stu- by Nancy Baxter Hastings (Dickinson spanning a time frame of 24 months. dents who enroll at four-year colleges College) and Allan Rossman (formerly of succeed in obtaining a degree, largely, Dickinson College, now at California January 10 & 11, 2002-Embassy according to the report, because these stu- Polytechnic State University San Luis Suites, San Diego, CA dents are inadequately prepared for the Obispo). Its goal is to prepare partici- rigors of college academics. The report, May 22-25, 2002-Virginia Common- pants to utilize the interactive teaching entitled “Raising Our Sights: No High wealth University, Richmond, VA techniques and innovative technology School Senior Left Behind,” recommends that characterize the workshop approach. a major restructuring of the high-school January 19 & 20, 2003-Convention It will provide them with the necessary curriculum and better coordination be- Hotel, Baltimore, MD background and support to adapt the tween high school and college. Copies of November 2001-2003-On-going, Workshop Precalculus materials for use the report are available online at http:// online consultation and communi- in their own environments. www.commissiononthesenioryear.org. cation Faculty from high schools, community This workshop series is a continu- colleges, four-year colleges, and univer- JOMA Panel Session in San Diego ing education program to help teams sities are encouraged to apply. An appli- of two faculty members lead their de- cation is available on the web at http:// partments in the conceptualization, calc.dickinson.edu/SummerInstitute, or The MAA’s new Journal of Online formulation, and implementation of contact Joanne R. Weissman at Mathematics and its Applications assessment of some component of [email protected]. Electronic sub- (JOMA) is now a year old. We will cel- their academic programs. Participants mission of applications is encouraged. ebrate this event at the Joint Meetings in will be provided with ongoing sup- San Diego with a panel session featuring port and consultation throughout the JOMA authors discussing their JOMA entire process. Carole Lacampagne Named Director materials and their work in general. of MSEB Members of the panel include: If you are interested in learning what is known about assessment in math- • Dennis DeTurck, University of ematics programs, carrying out an as- Carole Lacampagne has been chosen as Pennsylvania sessment program and then contrib- the new director of the Mathematical Sci- • John Kiltinen, Northern Michigan uting to the assessment knowledge ences Education Board (MSEB), which is University base of the mathematics community, affiliated with the Center for Education • Tom Leathrum, Jacksonville this workshop is for you. of the National Research Council. State University. Lacampagne comes to MSEB from the There is no fee to attend the workshop. RAND Corporation, where she was The session will be introduced and mod- All meals and workshop materials are working as a senior researcher on loan erated by JOMA editor David Smith paid for by the MAA with support from the U. S. Department of Education. (Duke University). The session will be from the NSF. Participants are respon- At the U.S. Department of Education, she held on Monday, January 7, 9:00 a.m.- sible for making their own travel ar- directed the National Institute for 10:30 a.m. The JOMA web site is http:// rangements and are asked to save Postsecondary Education. For more in- www.joma.org. This session has been or- original receipts for reimbursement. formation on MSEB, visit their website ganized by Lang Moore (MAA and Duke at http://www4.nationalacademies.org University), Executive Editor of the For questions about this workshop, dbasse/mseb.nsf/web/homepage? Mathematical Sciences Digital Library please contact Tom Rishel at OpenDocument. (MathDL). [email protected] or visit http:// www.maa.org/pfdev/prep/haver.html.

9 FOCUS December 2001 San Diego Program Updates MAA Sessions and among students all gathered in a of how to write a winning proposal and “classroom” on a virtual campus that re- contract essentials. He will cover the JOMA Authors Present sides on a server. It supports synchronous, tricks of the trade describing how to Monday, 9:00 a.m. – 10:30 a.m. collaborative use of common software present your textbook in its best possible Organized by David Smith packages including Mathematica, Maple light in the Proposal. You’ll learn tech- Duke University and Lang Moore and various commonly used software niques for selling your acquisitions edi- MAA and Duke University packages, such as word processors and tor with a clear description of the text, its spreadsheets via the Web. Control of a features, and ancillaries. After an introduction by the editor of the software package opened on one machine Journal of Online Mathematics and Its can be passed to a person at another ma- Michael Sullivan, Lemont, IL, will de- Applications (JOMA), authors who have chine in another room or even another scribe how to assure a successful review published in JOMA will talk about their geographic location. This campus sup- process and discuss the similar yet dis- materials and their work in general. Au- ports audio connectivity in a cooperative tinct pre-contract review, developmental thors include David Smith, Duke Univer- learning environment. Sessions can be review, and post-publication review from sity, Tom Leathrum, Jacksonville State recorded for review of the session by stu- the unique position of the mathematics University, and John Kiltinen, Northern dents or for study by students who missed author. Michigan University. the session. We will describe the Global Classroom project and demonstrate the Robert Christophererson, American interconnectivity and collaboration over River College, will discuss the discipline Course Portfolios and the Scholarship the internet. In addition, participants will of writing a textbook and what you must of Teaching and Learning learn how to develop their own online know about the publication process. He Sunday, 4:15 pm – 5:45 pm teaching material. will explain why setting up a “writing stu- Organized by Thomas Banchoff dio,” preparing the outline, style guides, Brown University and tracking logs are critical elements to The Mathematical Education creation of a successful manuscript. He A course portfolio is “a form of scholarly of Teachers will discuss research and writing, produc- inquiry and communication through Tuesday, 1:00 p.m.- 2:30 p.m. tion of manuscript and art, and the pub- which we can represent and exchange the Organized by Ron Rosier, CBMS lishing process, including developmental scholarship of teaching” (Shulman 1998). editing, book design, and marketing. In this session, panelists who have all been “The Mathematical Education of Teach- Each presentation will be followed by participants in the Carnegie Academy for ers,” published last August by the AMS questions and answers and will include Teaching and Learning will discuss how and the MAA, calls for mathematics fac- handouts. course portfolios might be most profit- ulty to take a more active role in the ably used in the discipline of mathemat- preparation of future teachers of math- ics. ematics at all levels. Two themes guide the AMS–MAA Joint Session MET document: 1) the intellectual sub- The presentations will be illustrated by stance in school mathematics, and 2) the Professors for the Future Programs portfolios in progress. Discussion will special nature of mathematical knowl- Wednesday, 9:00 a.m. – 10:30 a.m. follow. Panelists for the session include edge needed for teaching. Organized by Samuel M. Rankin, AMS Bruce Cooperstein, University of Califor- and Tom Rishel, MAA nia; Santa Cruz. Curtis Bennett, Bowling This session will focus upon how faculty Green State University; Anita Salem, can use the document to develop courses Various graduate student development Rockhurst University; and John that can provide future teachers with a and training programs, often described Holcomb, Cleveland State University deeper understanding. The speakers will as Professors for the Future, have come include: James Lewis, University of Ne- into existence at institutions across the braska; Alan Tucker, SUNY Stony Brook; country. One of these is funded by the The Global Classroom: Live E-Learning and Glenda Lappan, University of Michi- NSF and administered through the AMS Over the Web gan. and MAA. Tuesday, 9:00 a.m. – 10:30 a.m. Organized by Marcelle Bessman In this panel, directors of both the NSF- Jacksonville University and Douglas A. How to Successfully Publish a Textbook funded and some of the separately- Quinney, Keele University, UK Wednesday, 1:00 pm – 2:30 p.m. funded programs will discuss their activi- Organized by Michael R. Lennie ties, looking at what works and what The Global Classroom is a “classroom San Diego, CA doesn’t, and concentrating on the effects without walls” that supports interaction they are seeing on the continuing careers between students and a “visiting” scholar Michael Lennie will cover the essentials of their students.

10 December 2001 FOCUS Presentations by Recipients of tory of a small oral dose of caffeine, MAA Short Course the Haimo Teaching Awards equivalent to half a cup of regular coffee, as its concentration rises and falls in the A Sampler of Applica- Tuesday, 3:30 p.m. – 5:00 p.m. bloodstream. This will lead to the statis- Room 6C of the San Diego tions of Graph Theory tics of generic drug testing, planning a Convention Center dosing schedule to achieve steady-state level of a drug, and differential equations This short course, organized by Fred Rob- models, all of which are interesting, real- Polymath Teaching erts of Rutgers University, will survey a world applications of first and second Dennis DeTurck variety of applications of graph theory. year college mathematics. University of Pennsylvania Graph theory is an old subject which has found a vast number of exciting applica- College and Uni- tions in recent years. The speakers will in- Teaching Up and Down the versity teaching in troduce the graph-theoretical topics Mathematical Ladder general, and math- needed, describe both historical and cur- Paul J. Sally, Jr., University of Chicago ematics teaching in rent applications, and discuss current re- particular, faces search topics in graph theory related to We will talk about topics in mathematics many challenges the applications. Many of the topics to be which stretch through the K-16 curricu- and opportunities. covered will be amenable to discussion lum like ropes (not strands). Too often We teach indi- in the classroom as well as making for connections among different levels of vidual and small good research topics for both research- mathematics are missed. We discuss some groups of students Dennis DeTurck ers and students. No prior knowledge of of these connections. who share our en- graph theory will be required. thusiasm for our subject, larger groups of widely varying aptitude and inclina- tion, and a public that is increasingly con- SIGMAA on RUME Short Course Program: sumer-oriented, but largely ignorant Session Speaker about our subject and how it is practiced Applications to Network Visualization and taught. Information technology has How Can Mathematical Concepts Nathaniel Dean, Rice University changed both what we teach and how we Be Learned? interact with our students. Synthesizing APOS Theory and Graphs are commonly used to model sys- Mathematical Formalism to Get One tems of discrete objects and to visualize Given the range of tasks that faces the Possible Answer these systems by exploiting technology profession, our departments, and us as Ed Dubinsky, Cincinnati, OH and human visual psychology. We present individuals, and the pace at which the Tuesday, 5:00 p.m. -5:45 p.m. several approaches to drawing graphs, environment is changing, it is remarkable some computer tools for visualizing the how well the “tried and true” curricular How can a student, on hearing, reading graphs in the plane and higher dimen- and pedagogical strategies continue to or working with a mathematical concept, sions, and we explain some of the diffi- serve. We’ll examine many of these, and come to understand it? There seems to culties associated with constructing good see that some things never change, while be general agreement that whatever the drawings. others need only slight adjustment and answer, it involves some kind of idea or “dusting off” to be at least as effective as mental structure, an image that was not ever. previously present but must develop in Graph Structure on the World the student’s mind. There is considerably Wide Web Pharmacokinetics less agreement about the nature of such Sridhar Rajagopalan, IBM Almaden Edward L. Spitznagel, Jr. images and how they get into one’s mind. Washington University (St. Louis) In this talk I will consider some answers In this module, we will look at the web as to this question that have been proposed, a graph (pages are nodes, weblinks are Pharmacokinetics is such as metaphors, natural language, rep- edges) from three points of view. In the a wonderfully rich resentations and contrast them with first section, we will detail various experi- source of examples APOS Theory. Then I will describe how mental studies to estimate macroscopic for teaching calcu- APOS Theory can be combined with parameters of the web graph. We will lus, statistics, and mathematical formalism to not only de- compare our estimates to the parameter differential equa- scribe how difficult mathematical con- values expected in typical (random) tions, which I have cepts, such as uniform vs. pointwise con- graphs. In the second section, we will talk been using in my vergence of a sequence of functions, can about new random graph models for gen- courses for almost Edward L. be learned, but also to help students learn erating large random web like graphs. ten years. I will begin Spitznagel, Jr. such concepts. by showing the his-

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Finally, we will talk about algorithms Optimality depends on criteria usually of applicable combinatorics, rich in prob- which process the web graph for the pur- involving some idea of distance and var- lems, and offering an occasional surprise. pose of searching and data mining. The ies according to the application. Weighted module is meant to be an introduction graphs provide a context for studying Graph Theory and Social Networks to a new and emerging research area, but these types of problems, where vertices Fred S. Roberts , Rutgers University is not comprehensive. Therefore, we will and edges are assigned weights represent- conclude with some pointers to follow for ing certain parameters according to the Graph theory has many applications in information not covered in the talk. application. Usually, special sets of verti- the study of social networks, networks ces are sought that are either “central” or whose vertices are people and whose “peripheral.” Results range from the de- edges represent some relationships be- Applications of Graph Theory to scriptions of optimal locations to the tween individuals. Applications include Molecular Biology computational difficulty in actually de- graph coloring models to help define the R. Ravi, Carnegie Mellon University termining these optimal locations. Con- “social roles” of individuals; signed and siderable study has been focused on marked graph models to help define “bal- In this talk, we will survey key concepts weighted trees. These issues have moti- ance” and “social justice” in small group from graph theory that have found im- vated graph theorists to probe many dif- situations; models of the spread of opin- portant applications in algorithms for ferent notions of centrality and notions ions from person to person; and models problems arising in Molecular Biology. of the “outer fringes” in ordinary describing the structure of acquaintan- Key topics covered will include (1) ex- (unweighted) graphs, particularly trees. ces and the influence of some people on ploiting the graph structure in dynamic In such models, users and facility loca- others. Social networks are also increas- programming applications for optimal tions are thought to be restricted to ver- ingly important in the study of infectious alignment of DNA and RNA sequences, tices. However, the graph theoretical ori- diseases, like AIDS, that are spread (2) graph-theoretic ideas arising in the gins of centrality precede the advent of through social contact. We shall describe various formulations of multiple se- modern location theory as C. Jordan in- such applications of graph theory and the quence alignment problems, (3) the use troduced the concepts of the center of a fascinating graph-theoretical concepts of Interval graphs in applications to prob- tree and the branch weight centroid of a and problems that arise in such applica- lems in the Physical Mapping of genomes, tree in 1868. tions. (4) the importance of the notion of ad- ditive and ultrametrics in the realm of In the main part of this talk we will sug- Applications to Statistical Physics phylogenetic reconstruction, and time gest answers to the question: “Where is Peter Winkler, Bell Labs permitting (5) the use of sophisticated the center of a tree?” We will start with a graph-theoretic structures in deriving novel treatment of the two classical cen- Statistical physicists would like to under- polynomial-time algorithms for deci- tral sets, the center and the branch weight stand how local rules for a many-part sys- phering the minimum genome rear- centroid. Then we will treat in turn other tem can cause qualitative changes, called rangement distance between two organ- notions and their relationships including “phase transitions’’, in the global behav- isms. We will assume no prior knowledge the median, the security center, the tele- ior of the system. How can graph theory of Molecular Biology. phone center, the accretion center, the set help? of weight balanced vertices, and the la- Graphs in the Theory of Location tency center. In contrast to these notions, Sometimes the local rules are what we call of Facilities we will consider the distance balanced hard contraints, which might, for ex- K. Brooks Reid vertices. Several other central sets will be ample, forbid two particles to occupy California State University, San Marcos briefly mentioned, some of which make neighboring sites in a grid. Such rules can sense in the class of all (connected) be formulated graph-theoretically, and The theory of location of facilities in net- graphs. indeed the resulting systems often corre- works combines tools from graph theory, spond to familiar constructions like col- basic analysis, optimization, and com- Finally, we will mention some one-pa- orings and independent sets. plexity theory. The central issue is the rameter and two-parameter families of study of the optimal location(s) of a fa- central sets of vertices in trees. In some We will take a little tour through the cility such as emergency installation, a instances we will discuss these concepts graph theory of hard constraints, visit- supply depot, a switching center, a pump- for general networks where, in some in- ing fertile graphs and dismantlable ing station, an obnoxious dump, a com- stances, users and facility locations can graphs on the way to some combinato- munications center, or the like in a net- be placed not only at vertices but also at rial understanding of the notion of phase work such as a street or road network, an points along edges. transition. electrical network, a network of channels or pipes, a communications network or One goal of this talk is to convey the idea the like. that this subject is a very accessible branch

12 December 2001 FOCUS

Read This! Letter to the Editor Recently Reviewed on MAA Online As a believer in partial credit, I have The MAA Online book review column is still going strong. We now have over 200 never found a satisfactory way to grade book reviews and brief notices online. The latest reviews are featured at the main the student who makes an error at the Read This! page at http://www.maa.org/reviews/reviews.html. Recently reviewed books beginning of a problem that converts it include: to a much simpler problem.

Teaching First, by Thomas W. Rishel Suppose that the student has solved the When Topology Meets Chemistry, By Erica Flapan simpler problem correctly. In the inter- Symmetry, by Hans Walser est of fairness, what penalty if any should George Green: Mathematician and Physicist, 1793 - 1841, By D. M. Cannell be imposed on the solution by virtue of Misteaks, by Barry Cipra the student’s having escaped the problem Stamping Through Mathematics, By Robin Wilson that was intended? Mathematical Reminiscences, By Howard Eves Drawbridge Up, By Hans Magnus Enzensberger I would be interested in hearing readers’ Computers, Ltd. , By David Harel reactions. The Fermat Diary, By C. J. Mozzochi Mathematical Perspectives on Theoretical Physics, By Nirmala Prakash Sincerely, Identification Numbers and Check Digit Schemes, By Joseph Kirtland Jay Beder The Geometry of Numbers, By C. D. Olds, Anneli Lax, and Giuliana Davidoff Department of Mathematical Sciences The Mathematics of Soap Films, By John Oprea University of Wisconsin-Milwaukee Mathematical Olympiads 1998–1999, By Titu Andreescu and Zuming Feng [email protected] The Shape of the Great Pyramid, By Roger Herz-Fischler Flatterland, By Ian Stewart Chaotic Elections!, by Donald G. Saari The Math Gene, By Keith Devlin The Sand Reckoner, By Gillian Bradshaw

13 FOCUS December 2001 Reshaping Graduate Education: Looking Back at the Wisdom of Mina Rees

By Amy Shell Mina Rees (1902-1997) is most widely a doctorate in mathematics. At that time, known for her work on the development however, Columbia was not interested in of the computer in the early 1950s. As having female doctorial students. Thus, head of the Mathematical Sciences Divi- in 1925 she completed her master’s de- sion of the Office of Naval Research fol- gree at Columbia in mathematics educa- lowing World War II, Rees’ funding poli- tion and started lecturing at Hunter Col- cies helped guide research in computing, lege. Four years later, she took a leave of as well as research in mathematics and the absence from Hunter to pursue her Ph.D. mathematical sciences, at universities She headed to the University of Chicago across the country. What most people and completed her doctorate in Decem- outside of the City University of New ber 1931 with a thesis in associative divi- York (CUNY) system do not know is that sion algebras under the guidance of after leaving the high-powered world of . grant administration, Rees returned to academia to participate in launching Rees returned , where she CUNY. was promoted to Assistant Professor in 1932, and then to Associate Professor in As the founding president of the Gradu- 1940. At the start of World War II, Rich- Mina Rees ate School and University Center at ard Courant suggested to CUNY, Rees had a profound effect on of the government’s Applied Mathemat- and Governor Nelson Rockefeller ap- graduate work there. Her involvement in ics Panel that Rees be made Weaver’s as- proved the establishment of The City research and education as a member of sistant and Technical Aide to the Panel. University of New York. CUNY originally both the National Science Board and the Her role was to be the liaison between the consisted of the five senior colleges of National Science Foundation Board and government and the university research : City College, Hunter, her tenure as the first female president of groups contracted by the panel to do re- Brooklyn, Queens, and Lehman, along the American Association for the Ad- search related to the war. with three of the city’s junior colleges. The vancement of Science made her an expe- consortium style permitted greater flex- rienced and influential voice on educa- At the close of World War II, Rees was ibility, allowing CUNY to meet the tional policy in the 1960s and 1970s. appointed to head the Mathematics unique needs of the city. Branch of the newly formed Office of During those years Rees was an outspo- Naval Research (ONR) in Washington, The first chancellor of CUNY, John ken advocate for the reform of graduate D.C. Rees’ 1952 appointment as Deputy Everett, appointed Rees as the first Dean education. Thirty years after her 1972 re- Science Director of ONR allowed her to of Graduate Studies effective September tirement from the helm of the Graduate make policy and funding decisions that 1961. Rees comments that School and University Center, her wis- greatly influenced scientific and math- dom and insight into the policies and ematical research in the U.S. For example, The experience in Washington had given programs of graduate education deserve prior to the ONR, most funding went to me administrative and academic sophisti- a second look. the institution and then on to the re- cation that would have been hard to get searcher, with little or no money for elsewhere … the importance of the ONR A native New Yorker, Mina Rees attended graduate students. Rees changed this, experience was in the rather intimate Hunter College High School for girls and awarding grants to individual research- knowledge it gave me of the modus oper- Hunter College for women in Manhat- ers and supporting their students. From andi and of the ambience of virtually all of tan. When she graduated from Hunter the early 1950s through the 1960s, ONR the country’s leading research universities College in 1923, she was asked to join the was the largest source of funding for aca- and of many of the liberal arts colleges. 1 faculty. Believing she did not have the demic research in the sciences. mathematical background to be a good She was the first female dean of a co-edu- college instructor, she taught at Hunter In 1953, Rees left ONR to return to cational graduate school in the United High School while attending Columbia Hunter College as Professor of Math- States. Her challenge would be to bring University as a full-time graduate student ematics and Dean of Faculty. In the spring together a high quality faculty to serve in mathematics. Rees intended to pursue of 1961, the New York State Legislature both the new graduate programs and the

1 Rees, Mina, Biographical letter, Association for Women in Mathematics Newsletter, 9, July/August 1979, pp. 15-18.

14 December 2001 FOCUS undergraduate colleges, design the gradu- Can the university in the years ahead serve with overarching social as well as educa- ate programs, and create new facilities. the human needs of all our people in their tional and scholarly purposes. The program for the dedication of the search for human dignity? Can it main- Mina Rees Library at CUNY in 1985 tain our belief in the power of scholarship I would hold that a continuing major func- states that for the eleven years Rees was to improve our understanding of our neigh- tion of the university in the United States at CUNY, she “provided the leadership, bors and ourselves? Can it restore our con- is to support and strengthen the kind of inspiration, and guidance for the devel- fidence that the unbiased and competent inquiry into nature which can be pursued opment of doctoral work” at CUNY. study of society by trained and dedicated chiefly from a motivation to understand the men and women can fashion for us the tools world and the people in it. … Though I Rees went on to become provost of the that can assist us in improving society? Can subscribe to these statements as a formu- Graduate Division in 1968 and then the it provide a means for some students and lation of one of the major functions of the first president of the Graduate School and some members of the faculty to gain expe- university, it is important to recognize that University Center (GSUC) of CUNY in rience at the university with research on in this vast and varied country of ours there 1969. Originally the graduate school had outstanding social problems, with a view are many functions to be served and diverse only four programs. By the time of Rees’ not only to gaining greater insight but also clienteles to be educated, and it would serve retirement, 26 doctoral programs were in us ill if all our universities set for them- place and 477 Ph.D.s had been awarded. selves the same purpose, the same organi- zational patterns, and the same campus At the time Rees returned to academia in ambience. 1953, the nation was poised on the threshold of profound social, technologi- To answer her own questions, Rees ad- cal, industrial, and economic change. The vocated that graduate education be vi- technological advances made during tally linked to industry, tackling the prob- World War II, the need for scientists, en- lems of a modern society. She counseled gineers, and teachers, along with the birth educators to actively engage their stu- of the computer age, changed the focus dents in intellectual pursuits that would of undergraduate and graduate pro- further their profession and its relation- grams. The jump in enrollment in gen- ship to society. Above all, Rees envisioned eral, and of women and minorities in a future for academia in which the solv- particular, stressed a system that had been ing of social problems was of prime im- historically slow to change. As the 1950s portance to every student, faculty mem- led into the 1960s social and environmen- ber, and department. She hoped to bring tal issues grew in importance. All this academics out of the ‘ivory tower’ and caused educational norms to begin to into valuable contact with the issues of shift to reflect this new focus. the day.

Rees was keenly aware of the changes tak- If we are to address ourselves to some of ing place, and advocated educational re- our outstanding national problems such as form to meet not only new demands, but a drastic reordering of our patterns of pro- also new social concerns. duction, a redesign of our modes of con- sumptions, the rehabilitation of our core What, indeed, is graduate education for? cities and our ghettos, and the solution of Is it for getting a job? For providing the our myriad other urban and rural prob- understanding out of which criticism of our lems, there are opportunities for local spe- social goals and national actions can be Mina Rees with Ed Begle, 1960. cialization in thesis research and in design built? Is it for pushing back the boundaries of programs that can call on the resources of knowledge and decreasing the areas of to proposing possible solutions based on of the university and at the same time ex- ignorance? Or is it, perhaps, for the glory careful research and critical discussions? 3 ploit the interest and the vigor of our stu- of the human spirit? Is it for the student? dent population.4 For the faculty? Or for society?… 2 Rees held high expectations for the fu- ture of graduate education. She saw Rees faced these new issues squarely and graduate education in a larger context, posed tough questions to the educational community.

2 Rees, Mina, Graduate Education–A Long Look, Graduate Education Today and Tomorrow, University of New Mexico Press, 1972, 130-151. 3 Rees, Mina, The Ivory Tower and the Marketplace, On the Meaning of the University, University of Utah Press, 1976, pp. 81-101. 4 The remaining quotes are taken from footnote 1. 15 FOCUS December 2001

At CUNY Rees developed programs in For example, she set in place programs The graduate program at the City Uni- cooperation with industry, city govern- to help returning students, especially versity of New York was her testing ment, and cultural institutions to train women and minorities, back into aca- ground, and her efforts on the national CUNY’s students to effectively meet the demic life. level were practical, timely, and informed. needs of New York City. Though she be- Though thirty years have passed since lieved graduate education should be spe- As the president of GSUC, Rees set the Mina Rees left the City University of New cialized, she strongly protected the under- standards for the institution, which en- York, legacy remains. Through her words graduate curriculum from premature compassed all facets of the graduate pro- and presence, she forced her colleagues specialization. gram. One of Rees’ hallmarks was the to look to the future of education, not the implementation of non-traditional pro- past. “Can we have excellence and equal- Rees also worked to build graduate pro- grams with emphasis on internships and ity or must we chose between them?” grams that meet not only the needs of interdisciplinary work. Frances D. society, but of the student. Horowitz, President of GSUC at the time Amy E. Shell is Assistant Professor in the of Rees’ death, stated in a memorial that Department of Mathematical Sciences at Graduate education, in the American style, “Mina Rees’s understanding of what it the United States Military Academy, West embraces both course work that is aimed means to do quality graduate education Point, New York. She received her B.S.Ed. at bringing the student to an understand- set the founding base for the City Uni- form the University of Michigan in 1989, ing of the conceptual structure of his field versity Graduate School — a base upon her M.A. from Oakland University in 1995, at the frontier, and research that is aimed which it was possible to build to the emi- and her D.A. from the University of Illi- to push the frontier a little further. … We nence that the GSUC now enjoys.” nois at Chicago in 2000. Her dissertation need to distinguish between the role of the was a historical piece on mathematician graduate school vis-a-vis those students Rees’ work to better graduate education, Mina Rees, and her current research, con- whose immediate goals are concerned pri- along with her work in the Office of Na- ducted with Fred Rickey, focuses on the his- marily with pushing back the frontiers of val Research, earned her the Mathemati- tory of the Department of Mathematical knowledge, those whose concerns are with cal Association of America’s first Award Sciences at USMA. understanding and criticizing society from for Distinguished Service to Mathemat- the vantage point of the university, and ics in 1962, and the National Academy of those who aspire to enter society as practi- Sciences Public Welfare Medal in 1983. tioners preparing to address themselves im- mediately to pressing social problems.

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