MAA FOCUS The Newsmagazine of the Mathematical Association of America November 2008 | Volume 28 Number 8
WHAT’S INSIDE 4 ...... A Window on the Fifth Dimension 10 ...... Preparing Students for a Life in Math or Computer Science 14 ...... An Intuitive Approach to the Borsuk-Ulam Theorem 20 ...... Write About Mathematicians in Non-Major Courses
FOCUS_Nov_08FINAL.indd 1 10/21/08 10:39:46 AM MAA FOCUS November 2008
MAA FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, MAA FOCUS August/September, October, November, and December. Volume 28 Issue 8 Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA [email protected] 4 A Window on the Fifth Dimension Senior Writer: Harry Waldman, MAA By Frank A. Farris [email protected] Please address advertising inquiries to: 8 Marcia P. Sward (1939-2008) [email protected] By Linda Rosen : President Joseph Gallian 10 Preparing Students for a Life in Math or Computer Science First Vice President: Elizabeth Mayfield, By Donna Pierce and Peter A. Tucker Second Vice President: Daniel J. Teague, Secretary: Martha J. Siegel, Associate 12 Teaching Time Savers:
Secretary: James J. Tattersall, Treasurer: The Microphone is Mightier Than the Pen John W. Kenelly By Emily Dryden Executive Director: Tina H. Straley Director of Publications for Journals and 14 An Intuitive Approach to the Borsuk-Ulam Theorem Communications: Ivars Peterson By Alex Bishop, Adam Cimpeanu, Kyle Flood, Bianca Homberg, Steven The Mathematical Association of America Homberg, Eric Marriott, Jeffrey Roth, Linus Schultz, William Sherman, Alex intends to change the name of its newsmagazine Smith, Geoffrey Smith and James Tanton to MAA FOCUS. MAA FOCUS Editorial Board: Donald 16 The Courants and I J. Albers; Robert Bradley; Joseph Gallian; By Edwin Rosenberg Jacqueline Giles; Colm Mulcahy; Michael Orrison; Peter Renz; Sharon Cutler Ross; An- 20 Write About Mathematicians in Non-Major Courses nie Selden; Hortensia Soto-Johnson; Peter Stanek; Ravi Vakil. By Karl-Dieter Crisman Letters to the editor should be addressed to 22 Archives of the American Mathematics Spotlight: Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by The Lawrence Biedenharn Papers email to [email protected]. By Carol Mead Subscription and membership questions 24 Reflections on Montclair State University-Beijing Connection should be directed to the MAA Customer By Mika Munakata and Aihua Li Service Center, 800-331-1622; email: [email protected]; (301) 617-7800 (outside 26 Mathematicians Playing a Role in Math Education: U.S. and Canada); fax: (301) 206-9789. MAA Headquarters: (202) 387-5200. What We Learned at the IME/MIME Workshop By Anna Bargagliotti, Rama Chidambaram, and Gizem Karaali Copyright © 2008 by the Mathematical Association of America (Incorporated). Educational institutions may reproduce 28 Employment Opportunities articles for their own use, but not for sale, provided that the following citation is used: “Reprinted with permission of MAA FOCUS, On the cover: Frank Farris’s “5D Window,” created to his specifications by Hans the newsmagazine of the Mathematical Schepker. See the article on page 4. (Photo by Frank Farris.) Association of America (Incorporated).” Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: MAA FOCUS Deadlines Send address changes to MAA FOCUS, February March April Mathematical Association of America, P.O. Editorial Copy December 10 January 14 February 9 Box 90973, Washington, DC 20090-0973. Display Ads December22 January 28 February 23 ISSN: 0731-2040; Printed in the United States Employment Ads December 10 January 14 February 9 of America. 2 November 2008 MAA FOCUS
Cross-Cultural Study About Math Attitudes a Media Hit
On Friday, October 10, 2008 the story were media hits. By Saturday Math Whizzes;” the Calgary Herald used Notices of the American Mathematical morning, Rimer’s article was the second “Negative stereotyping robbing US of Society published an online version of most emailed Times story, only behind an math talent.” “Cross-Cultural Analysis of Students election politics op-ed. Within one day, with Exceptional Talent in Mathemati- a Google® search located 30 US news The impetus for the study came in Janu- cal Problem Solving,” an article by Titu stories and 23 international ones related ary 2005, when then Harvard President Andreescu, Joseph A. Gallian, Jonathan to the study, including ones written in Lawrence Summers suggested that factors M. Kane, and Janet E. Mertz. The article Chinese, German, Hungarian, and Ital- other than socialization and discrimina- is a comprehensive analysis of decades ian as well as English language stories tion could be the primary reason there are of data on students identified as having published in India, Canada, Australia, many more men than women in high-end profound math ability. It suggests that Thailand, and Malaysia among others. science and engineering positions in the cultural attitudes put American leadership Among the outlets were the New York US. Summers’ remarks prompted Janet in the mathematical sciences and related Post, Denver Post, AOL News, ABC News Mertz, a biochemist at the University of fields at risk. (online), MSNBC.com, Yahoo News, and Wisconsin-Madison whose child excelled Smashit.com. in the IMO and Putnam, to initiate the Working with an advance copy, Sara study. Mertz had long suspected that Rimer of The New York Times and The Orlando Sentinel ran an edito- cultural attitudes are the prime reason Carolyn Y. Johnson of The Boston Globe rial agreeing with the recommendations for the under representation of women wrote lengthy stories about the study that given in the study for correcting the and minorities among the top finishers in included quotes from the authors, some problem. Numerous newspapers and these ultra-high-level math competitions, of the students mentioned in the study, websites in India posted the news releases but could not find hard data to support her and Boston-area academics. Rimer’s or their own stories. MyNews.in used the belief. Andreescu, former leader of the piece, news releases written by Allyn title “US kids are math duds, so reveals US Math Olympiad team, Gallian and Jackson of the AMS and Terry Devitt a study;” Science News used “Numbers Kane joined in the study. The Notices of University of Wisconson-Madison don’t add up for U.S. girls;” Science- article can be found at http://www.ams. together with the authors, and a Reuters Daily.com used “US Culture Derails Girl org/notices/200810/tx081001248p.pdf.
MAA to Host Open House During the Joint Mathematics Meetings
The selection of Washington, D.C. as former Presidents that home to the upcoming Joint Mathemat- line the staircase, or by ics Meetings presents MAA members thumbing through old a special opportunity to see a different volumes of the journals side of their beloved Association. MAA in the Begle Room. headquarters will host an open house that will give its members a chance to visit the Shuttle buses marked Dolciani Mathematical Center, the MAA with an “MAA Open Carriage House, and Halmos River of House” sign will depart Bricks on Wednesday, January 7th from from the Marriott Ward- 3 p.m. until 6 p.m. man Park Hotel’s 24th Street entrance every The open house will give members a half hour from 3:00 p.m. chance to see the things that make MAA to 5:30 p.m. and return headquarters so unique, such as the every half hour from The MAA Carriage House spiral staircase winding throughout the 4:00 p.m. to 6:30 p.m. Dolciani building, the newly renovated If meeting attendee’s and left onto Church Street to get to the Carriage House, and the way the River would rather metro to the headquarters Carriage House at 1781 Church Street. of Bricks duplicates the confluence of buildings, they can catch a red-line train MAA FOCUS Deadlines the Potomac and Anacostia rivers that at the Woodley Park Station headed Refreshments will be available during the open house. Additional information February March April outline the nation’s capital. Those who toward Glenmont and get off at Dupont will be available during the meetings at Editorial Copy December 10 January 14 February 9 participate in the open house will also be Circle. Leave through the Dupont Circle the MAA booth in the exhibit hall at the Display Ads December22 January 28 February 23 able to take a peek into the Association’s North exit and walk east on Q Street to Marriott Wardman Park Hotel. Employment Ads December 10 January 14 February 9 past by checking out the portraits of 18th Street. Take a right on 18th Street
MAA FOCUS November 2008 A Window on the Fifth Dimension By Frank A. Farris Is there enough mathematics in your home? What visual aids across the bay at the eastern foot of the Dumbarton Bridge. do you keep on hand for that inevitable moment when guests We spent more hours sorting through possibilities, which after want to know why you spend your life on mathematics? Feeling a time ceased to appear finite. The goal was to implement cer- a lack in this area, I commissioned glass artist Hans Schepker to tain rules from the mathematical original: Crossing one of the produce a window — from the fifth dimension? — based on an circular boundaries leads to a neighboring color; moving from image that came up in my research. It turned out splendidly, and the center outward should lead from white through pastels to you can see it on the cover of this issue of MAA FOCUS. vivid saturated colors and then to darkness at the outside. (The outer darkness was replaced by clear glass in order to help the The story of the design involves complex functions, color as window appear to float in its frame.) a visualization tool, and five-fold symmetry. I cannot tell it to every guest who walks in the door, but mathematicians will find In addition to finding colors for each of the four rings of five it a strange combination of the familiar and the unlikely. Can congruent shapes, we thought about the balance of textures. this window make the fifth dimension transparent? In some places, the window is not entirely symmetrical. We decided that mathematical precision could give way to aes- The Human Story thetic considerations, given that the glass choices were finite. The bluish sector was the easiest part; there were more than At the 2007 JMM in New Orleans, I met Hans Schepker, who enough choices. We spent more time on the sector where greens was exhibiting his glass art. You may have seen his booth or become oranges and then reds. I especially like the gold crown visited his web site, http://glassgeometry.com. A rainbow pen- at the top of the window. Overall I very much appreciate how tagon design caught my eye and I asked whether he might be Kitty’s advice led to harmonious colors that honor the spirit of able to make me a custom window for my home. Hans was the mathematical design. enthusiastic, but I did nothing about the project until I saw him again a year later at the JMM in San Diego. Once Hans had all this information, he faced the engineering challenge of making the window strong enough. A typical glass It turned out that Hans was to spend several weeks that winter window has at least some straight lines — an obvious source of in my neighborhood, giving a geometry course at a Waldorf strength. This window has only curves. Despite the challenges School, using glass art as the hook to interest students. We of the unique design, Hans sent the finished window to me after met at my house and talked about possibilities, settling on a only six weeks’ work. It arrived in a custom-made plywood computed image — approximately the one in Figure 1 —as crate and has delighted me from my first view. the pattern for a window. The Mathematical Story
The mathematics behind the design started with my desire to find a mathematically correct depiction of a color wheel, something I have been trying to do for years. My need for a good color wheel arose in the mid-90s, when I proposed a particular way to use color to depict complex-valued functions on the complex plane [2]. The first step is to color the complex plane in such a way that, theoretically at least, each point has a different color. I like to use the primary colors red, green, and blue to color the cube roots of unity, then fill in hues around the unit circle, and fade to white at 0 and black at infinity. To create adomain coloring for a function f(z), at each z-value in the domain, paint the color corresponding to f(z). More realistically, for the z-value of each Figure 1: The original schematic pixel in the picture, set the color value of that pixel to f(z). design The next, rather difficult, step was selecting the actual glass for For instance, using the rather crude color wheel on the bot- the project. I spent a couple of hours with Hans at the Palo Alto tom in Figure 2 to indicate the color scheme, I produced the showroom of Franciscan Glass — enough to learn the difference domain coloring of a sixth-degree analytic polynomial beneath between pointing to a color on a screen and having a piece of the color wheel. The five white areas indicate the zeroes of the glass of just that color. polynomial, which might suggest that we are one zero short. Around the largest white area, note that the colors cycle twice A week or so later, I asked my college friend Kitty Kameon, around the edge: This is a double zero — just one example of who has taught color theory at the San Francisco Academy of the many phenomena revealed by domain colorings. Art University, to meet me at the Franciscan Glass warehouse,
November 2008 MAA FOCUS
Readers may recognize that the coefficients of the vectors arise from stereographic projection. It is conceivable that someone might recognize the three vectors: They are unit eigenvectors of the cyclic permutation of three variables. The first one points along the main diagonal of the cube, toward the vertex that will represent white. The second and third span the plane of the celebrated regular hexagonal cross-section of the cube.
All that remains is to map this 2 x 2 x 2 cube to the color cube: 1+XZ1 + 1+ Y XY,, Z → ,, . () 2 2 2
This is so theoretically lovely that it should yield beautiful pictures. Unfortunately, this mathematical color wheel looks terribly bland.
Figure 2: A choice of color wheel and the corresponding domain coloring of a sixth degree polynomial.
I have worked with several color wheels, each one a kludge. Then, in the summer of 2007, I prepared a talk for the MAA Silver and Gold Banquet at the San Jose MathFest. The new color wheel was mathematical! Figure 3: A color wheel derived by stereographic projection of the com- Most of my computed images have been coded in a file format plex plane into the color cube. called PPM. It is rather an antique file format, but it is extremely simple and portable. For each pixel, the file lists three values This is where my pragmatic nature took over, happily leading from 0 to 255 to indicate how much red, green, and blue light me to unexpected consequences: I decided 3to take the cube root should shine from that pixel. These are called RGB values and, XY,, Z –,1 1 of each component of () ∈ .Why? This would independent of file format, most screens you view are being ad- drive points outward toward the edges of the cube; brights would dressed via RGB values. The set of possible RGB values forms become brighter, darks darker. Before you read on, ponder the a rather obvious cube, with black at one corner, as (0,0,0) and resulting color wheel. What is Figure 4 a picture of? white, as (255, 255, 255), at the opposite corner. This cube was the inspiration for my next steps.
New Idea: Use stereographic projection to map the complex plane to the unit sphere. Map the unit sphere inside the RGB cube, tilted so that the pole corresponding to 0 is nearest to (255, 255, 255) and the equator point that came from 1 is near the red corner. Then read off the colors.
It takes a little computation to get white in the right place, and to pursue my intention that 1 should be colored red. Here is the formula that takes complex numbers to a correctly-tilted sphere inside a cube: z= u + iv → ()XY,, Z = 1––u2 v 2 ()1,, 1 1 2u ()2,– 1,–1 2 2 + 2 2 + Figure 4: A color wheel derived from 1+u + v 3 1+u + v 6 the previous by taking cube roots 2v 0,, 1 –1 3 coordinate by coordinate, for no () –,1 1 2 2 ∈ good reason. 1+u + v 2 5 MAA FOCUS November 2008
5 If you are discretely minded, you might recognize the graph The most fruitful idea was to put the 2 x 2 x 2 cube into ° of a regular octahedron, viewed by stereographic projection. so that it sits in a three-dimensional eigenspace of the cyclic A continuously minded mathematician might focus on the permutation of five variables. I had observed in the past that this circular boundaries, which are unstable sets of the cube root is a good source of five-fold symmetry. I used the components map, the traces of the coordinate planes. Let’s explain each of stereographic projection as coefficients of normalizations point of view. of the vectors
Picture what the cube root map does to the interval [–1,1] . It 1,,,, 1 1 1 1 ,,1cos( 2π/)5,cos(/ 4 π 5),cos( 6π /)5 ,,cos(8π /) 5 , moves positive values toward 1 and negative values toward () ( ) –1; these points are stable attractors. The origin is unstable; and (0,sin(2π/5),sin(4 π /5),sin(66π /5).sin(8 π /5)). points on either side, though they may be very close, are moved toward different endpoints. Now observe that I applied this 5 map to each coordinate of a triple inside the cube. This moves Once the cube was placed in ° , I took cube roots of each points away from the coordinate planes and toward the vertices component, moving each point toward the nearest vertex of the of the cube. 5-cube. This pulls points off the 3-plane spanned by the three given vectors, so I simply projected them back. It was then easy The reason we see eight regions of almost constant color is to read off colors, in the same manner as before. The resulting that all points in one of those regions have been pulled toward color wheel is shown in Figure 6; actually, this one uses fifth the same vertex of the cube, of which there are eight. The roots instead of cube roots, which gives a more distinct color- reason we see dividing circles is that color changes rapidly ation. Now that you know that a regular octahedron lurked in when we cross a place where one of the (X,Y,Z) coordinates is the previous color wheel, you might enjoy figuring out which zero; these three loci are the intersections of the tilted sphere polyhedron this represents. with coordinate planes. Appearances notwithstanding, this is indeed a continuous assignment of colors, and were it not for the discretization in RGB space, there would be a unique color assigned to each point in the complex plane. If we flatten the image to eight colors (my software says it contains more than 184 thousand), since each region corresponds to a vertex of the cube, we get a stereographic view of the polyhedron dual to the cube, namely the octahedron.
Using this color wheel in domain colorings gives a pleasantly art deco effect, as in Figure 5.
Figure 6: A color wheel with 5-fold symmetry, the source of the window design There are 22 faces — two pentagons, ten triangles, and ten quadrilaterals. This is the dual of the 5-fold zonohedron. Given that there are 32 vertices of the 5-cube, why do points on the sphere inherit colors from only 22 of them? Computation shows that 10 of those vertices have small projection onto this 3-space; they are not sufficiently near to draw points. Figure 5: The cube-root color wheel used for a domain coloring of a cubic I undid the stereographic projection and constructed this poly- polynomial. hedron in Maple, with the pentagonal faces missing so that you can look through. The faces are colored in only approximately And now, the fifth dimension: The three-fold rotational sym- the correct way. Figure 7 shows three views, from the top, the metry of the cube-root color wheel is beautiful, and consistent bottom, and along one of the great circles that corresponds to with my original intention to place red, green, and blue around rings in Figure 6. that unit circle at the cube roots of unity. Still, I wondered what other polyhedra might turn up as the result of more-or-less Figure 6 is the source of the window design, rotated for aesthetic natural maps of the plane into the color cube. I wondered if effect. It is a window on the fifth dimension in this sense: Look- I could produce the MAA logo, a regular icosahedron, in this ing into the center, we are looking up into the portion of °5 manner. My first goal was to produce a color wheel with five- where all coordinates are positive, along the vector (1,1,1,1,1). fold symmetry. 6 November 2008 MAA FOCUS
Figure 7: Three views of the dual of the 5-fold zonohedron
From there, crossing any of the five large rings takes us past a (Supplementary materials, including color versions of the pub- coordinate hyperplane, and one of the variables turns negative. lished images, appear at http://www.maa.org/pubs/amm_comple- When we have crossed all five rings, by any of the curious paths ments/complex.html.) our eye can trace, we are looking back the other way, along (–1,–1,–1,–1,–1), toward darkness. Frank A. Farris, Vibrating Wallpaper, Communications in Visual Mathematics, vol. 1 (later vol. 0 of JOMA). References Frank Farris teaches at Santa Clara University. He is currently Frank A. Farris, Review of Tristam Needham’s Visual Complex interim editor of Mathematics Magazine. His home page is Analysis in Amer. Math. Monthly, 105:6 (1998), 570–576. http://math.scu.edu/~ffarris/.
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7 MAA FOCUS November 2008
Marcia P. Sward (1939–2008)
By Linda Rosen The mathematics community lost a discussions with Marcia about the pos- champion and a friend with the death of sible inclusion of letters to the editor in Marcia Peterson Sward on September 21, the newsletter. Should they be encour- 2008. She died with dignity and grace aged? Should they be limited to MAA from kidney cancer that was diagnosed issues or to responses to FOCUS issues? just weeks before her death. There were no MAA precedents; her groundbreaking work on letters to the Marcia served as the first Associate editor and other FOCUS features persist Executive Director of the Mathemati- to this day. Marcia served as editor of cal Association of American (MAA) FOCUS until September 1985, when she between 1980 and 1985. She returned to left the MAA. the MAA as Executive Director in 1989. Between her two periods at the MAA, As her next professional venture, Marcia she served as the Executive Director of agreed to become the first Executive the Mathematical Sciences Education Director of the MSEB, which was estab- Board (MSEB) at the National Research lished by the National Research Council Council of the National Academy of in response to the David report, “Renew- Sciences. ing U.S. Mathematics: Critical Resource for the Future.” This was a risky venture. Marcia graduated summa cum laude and the possibility of combining her love of There was seed money from the National first in her class at Vassar College with mathematics, her dedication to helping Research Council (NRC) to keep the a degree in mathematics. She and her young people learn, and her leadership organization afloat for only a year, and husband of one year, Gil Sward, each skills, Marcia applied for the job. To get its mandate was proactive, unlike other pursued graduate study in mathemat- a feel for the place, Marcia decided to groups within the NRC. Working with ics at University of Illinois at Urbana- hand-deliver a cover letter for her ap- Kenneth Hoffman (then the director of Champaign. Although she was one of plication early on the morning of her in- the Joint Policy Board for Mathematics the few females in the program, Marcia terview. To her surprise, there was a man Office of Governmental and Public Af- approached her work with zest and dedi- sitting alone on the doorstep, waiting for fairs) and Shirley Hill (Past-President cation. Under Edward Scott, Marcia was the building to open. She had to explain of the National Council of Teachers of awarded her Ph.D. in 1967 for her dis- her somewhat unorthodox behavior, only Mathematics), Marcia convened a stel- sertation on The Mixed Boundary Value to learn that she was talking to Don Kre- lar advisory board and raised sufficient Problem Along the Line of Parabolicity ider, the chair of the search committee for funds to see the MSEB grow enormously for a Certain Class of Hyperbolic Partial her position! It was no surprise that her in influence. The seminal report, “Every- Differential Equations. drive, talent and contagious enthusiasm body Counts: A Report to the Nation on led to a job offer as the first MAA Associ- the Future of Mathematics Education” After graduation, Marcia spent a year at ate Executive Director. remains to this day a key resource for Catholic University in Washington, DC K–12 mathematics education. Always as a housemother while job hunting. She Employing paper, red pencil, and a persuasive and cheerful, she recruited began her academic career at Trinity Col- typewriter, she managed to bring out the Lynn Steen, just finishing his last meeting lege, also in Washington, DC. Although first issue of FOCUS in March 1981. The as Past-President of the MAA, to serve she loved teaching, Marcia was always debut of FOCUS “was worth waiting as author of that report. looking for new causes to wrestle and for,” Ralph Boas (Northwestern Uni- new heights to scale. She accepted a one- versity) later wrote. “You are setting a Under Marcia’s tutelage, the MSEB year visiting appointment at the National high standard for yourself.” Ivan Niven served as a focal point for the mathemati- Highway Traffic Safety Administration, (University of Oregon) hailed “the bal- cal community on issues related to K–12 where she began to hone her executive ance of articles and announcements, of teaching and learning of mathematics. and management skills. ideas on the one hand and facts on the I was then Director of Policy Studies other.” And Don Albers, then Editor at MSEB, and remember that Marcia At that time, the MAA was creating a of the Two-Year College Mathematics displayed acumen, an incredible work new position for an Associate Executive Journal, exclaimed, “FOCUS is terrific… ethic, talent for collaboration, passion for Director that would, among other tasks, Finally, something that I can say I’ve read the cause, and an unwillingness to seize direct publication of the organization’s from cover to cover.” Lynn Steen, who personal glory. Ken Hoffman noted that, three journals and create a newsletter co-chaired the FOCUS editorial board “Beyond her intellect, Marcia’s special to serve members’ needs. Intrigued by at that time, recalls many substantive gifts were her warmth and vitality. They
November 2008 MAA FOCUS were infectious, impacting every pating in the winter meetings, project and every person she special events at the Carriage worked with.” House, and MAA study tours. MAA staff member Lisa Marcia returned to lead the Kolbe treasures her memories MAA in 1989 on the occasion of time spent with Marcia of Alfred Willcox’s retirement. on the MAA’s first tour to Although many people tried to Greece. “I remember her persuade her to stay with MSEB, dancing high in the mountain citing her unique skill set and village of Vourliotes in the record of success, she admitted lovely white Greek outfit that her heart belonged to the she bought on the island of MAA. Samos.”
The following presidents ben- After her retirement, Marcia efited directly from Marcia’s Marcia with Mary Kay Abbey and Tina Straley on the ferry went sailing for a year in the support — Lida Barrett, Debbie to Samos, May 2003. Photograph by Liz Teles. Bahamas, a sport she had Haimo, Don Kreider, Ken Ross, grown to love as a child. Gerald Alexanderson, and Tom Upon her return, she found Banchoff. Ken Ross remembers, for the progress of Project NExT, even after that she was not quite ready to retire. Her example, attending a workshop put on she retired from the MAA. pioneering spirit and her love of nature by the American Society of Association led her first to the National Environmen- Executives with Marcia. Its express goal Another project that benefited from tal Education and Training Foundation, was to help them analyze their own and Marcia’s leadership and dedication was whose mission is to provide objective each other’s working style. He notes that SUMMA (Supporting Undergraduate Mi- environmental information to help Amer- the workshop was “…a good idea and got nority Mathematics Achievement). Steen icans improve their quality of life. us off to a good start.” It meant enough wrote that “She was a perfect example, in to Marcia that she fondly mentioned the Robert Kennedy’s memorable image, of Until her death, Marcia was Deputy Ex- workshop in her last conversation with a person who dreams of things that never ecutive Director of Environmental Edu- Ken this summer. Lida Barrett had similar were and asks why not? MAA programs cation at the Audubon Naturalist Society. impressions of Marcia. “Because of her such as SUMMA and Project NExT are She helped design programs to reach past role at MAA, she offered wonderful living memorials to her energy, effort and over 8,000 children through preschool, support to me in my role as President. commitment.” school, camp, scout and family programs. Her wide contacts in the mathematics Among many other programs, Marcia profession, many from her time at MSEB, Her collaboration with Ed Dubinsky to provided the inspiration and leadership helped expand MAA’s interactions and develop special interest groups within to establish a preschool where children influence with other organizations and MAA came to fruition in 1999 with unravel the wonders of the natural world activities,” Barrett noted. SIGMAA-RUME. Dubinsky said that through a balance of self- and teacher- “First and foremost, Marcia was for me, directed activities. Under Marcia’s leadership, the MAA during the many years of her work with increased its membership, programs and the MAA and after, the “face” of the or- Marcia is survived by two sons, Douglas revenue. She was instrumental in initiat- ganization. Aside from her many concrete and David Sward and their wives, Honey ing new programs, many of which were accomplishments; she made the MAA a and Erika as well as her former husband, grant-supported. Chris Stevens recalls warm, humane, professional society. It Gil Sward. She is also survived by two that when she and Jim Leitzel were was a pleasure to interact with her and older brothers, Walt and Reeve Peterson, developing the idea for Project NExT, she created a very positive atmosphere their wives, Judy and Georgia, as well they wondered where they might secure in all aspects of the organization.” as many nieces and nephews. Her first outside funding. Marcia interested the grandchild, a boy, is due in October. De- ExxonMobil Foundation in the concept; “It is time for me to move on to new spite her many professional accomplish- in fact, Marcia was so persuasive that the challenges,” Marcia said on the occasion ments, what mattered most to Marcia was Foundation indicated their willingness to of her retirement in 1999. “I have had her family. provide support and requested a formal wonderful opportunities at the MAA.” proposal primarily for recordkeeping Gerald Alexanderson observed, “It is Marcia’s family has requested that dona- purposes. Stevens said that “Without difficult to imagine the MAA without tions in her memory be made to: her successful sales pitch, Project NExT Marcia at the helm.” Marcia Sward Tribute Fund might never have become a reality.” Audubon Naturalist Society Marcia’s support did not end with her Nonetheless, Marcia continued her asso- 8940 Jones Mill Road fundraising; she took a keen interest in ciation with the MAA, regularly partici- Chevy Chase, MD 20815.
MAA FOCUS November 2008 Preparing Students for a Life in Math or Computer Science
By Donna Pierce and Peter A. Tucker
“I like math, I just don’t know what • Guest speakers for them. Interacting with people in their I would do with a math degree.” We’ve • Ethical investigation field on a day-to-day basis gives students all heard this statement from undergradu- • Final paper booklet opportunities to ask questions that help ates. Students may be aware of a few them think more holistically about ca- vocational directions, but are largely The target audience for this course is reer choices, considering such things as unaware of other opportunities. They sophomores, for two reasons. They have personal satisfaction, personal values, are even more unaware of how those just decided on this major and we want and contribution to society. Through this vocational directions will influence their them to be thinking ahead. At this point, assignment students learn more about op- lives. We have found that students need they might be thinking about their plan portunities available to Math/CS students more than to be referred to web sites; for the next four years, but we want and the background skills required for they need to find out that there are bigger them to see why each piece of that plan qualifying for these opportunities. issues involved. Each student will require is important and how certain choices can different answers to vocational questions. help them as they consider future direc- Informational interviews and the field Thus, we realized that students need more tions. Sophomores aren’t always ready trip are one of the most eye-opening ex- complete guidance to help them do the for internships/REUs, but they need to periences for students, especially when exploration. We decided to develop a start thinking about and preparing for it comes to learning about the day-to- one-credit course on career preparation them. The course should be informal, day characteristics of a career. For the for Math/CS students. and therefore we made it a one-credit informational interview, students have to course. The seminar style, with weekly find their own interviewees. They choose Certainly, not all careers are the same cookies, also helps. We encourage dis- someone in a career of interest to them, — a course that simply tells students what cussion, both in small groups and with find out about the day-to-day facets of career they should pursue won’t work. the whole class. Finally, students each the interviewee’s job, specific issues that Students need experience in researching write a five-page paper on a particular might arise, and gather valuable career careers, and they need time to consider career path, incorporating all that they advice. We find that our alumni are a these careers in all their detail. The course have learned throughout the course. We great resource, as they are personally had to guide students toward learning collect these papers and bind them into invested in the school and show interest and understanding their own specific a booklet. Each student receives a copy in helping the next generation of gradu- strengths and values, so that they could of that booklet, as do the faculty in math ates do well. see what kinds of vocational opportuni- and computer science. ties are consistent with those strengths The field trips are always the highlight of and values. We wanted each student to Two components are critical to the our course. We try to include interaction consider the life they are looking toward success of this course: internships or with research and with industry on these and how their career fits into that life. In REUs, and field trips and informational trips. Students interact with research other words, we wanted students to be interviews. through a visit to a graduate school or to a concerned with their entire career, and not research conference, and with industry by just with landing the first job. We wanted One of the best ways for our students to visiting a workplace. In both cases, we try them to think beyond their potential sala- learn what they can do with a math degree to set up panels for open, informal discus- ry, and to consider environment, personal is to have them participate in an REU or sion. We find that it is very worthwhile values, ethics, contribution to society, and internship. Thus, we have the students re- to have a lot of diversity on these panels, personal satisfaction as well. search REUs. Many students do not know including gender and experience. what an REU is or how to apply. We ask Toward those goals, we set up the follow- them to find three different internships or We have offered this course for the past ing components for our course: REU opportunities using a worksheet to four years and have noticed the following guide their investigation. The worksheet benefits: Students have started thinking • Individual strength and value re- asks students to find such things as: title more about careers, and preparing for search (e.g. Meyers-Brigg) and description of internship, skills and those careers, before their senior year. • Career and opportunity research background required, stipend, and the ap- They know some of the questions they • Internship/REUs and graduate plication process. Additionally, students need to ask and how to find answers inde- school research who have done REUs in the past come pendently. The research assignments, in- • Career profiles, “day in the life” and discuss their experiences with the formational interviews and field trips give articles class, describing their experience and students a wider and more complete view • Field trips and informational inter- sharing what they have learned about of what’s out there and what working in views career opportunities and how to prepare their field looks like. More students are
10 November 2008 MAA FOCUS applying and participating in REUs and internships. Students report more interest in, and less fear about, graduate school. The course is also an asset in our re- cruiting efforts. Now when students say, “What would I do with a math degree?” we point them to this course. Finally, this course serves as a model for other depart- ments whose goal is to integrate career preparation into a student’s major. Dean of the College
One challenge we have run into is a dis- connect between student expectations for of Arts and Sciences this course and our own. Students would Embry-Riddle Aeronautical University invites applications and nominations for like us to tell them what career path they the position of Dean of the College of Arts and Sciences in Daytona Beach, should take and walk them through the Florida. Poised to expand its academic programs and to enhance its reputation process until they get the job. We want for excellence, the University seeks a dynamic, nationally/internationally students to think more holistically about recognized leader who will partner with faculty in maintaining and enhancing the career choices, but students tend to focus quality and national prominence of our educational and research programs. more on details. Course evaluations tend Reporting to the provost, the dean is the senior academic and administrative to say: “More help with resume writing officer of the college, responsible for strategic, operational, and financial and interviewing techniques.” In our leadership. The college comprises departments of Human Factors; view, this is training available at the Humanities and Social Sciences; Mathematics; Physical Sciences; and three career center and our course should go ROTC programs, and employs more than 90 full-time faculty who deliver courses beyond that. Another evaluation senti- in General Education, as well as teaching and mentoring 350 undergraduates ment echoes that disconnect: “Don’t majoring in Aerospace Studies, Communication, Engineering Physics, Space spend as much time on ethics.” We Physics, and Human Factors Psychology. The college additionally offers MS understand the students’ needs for practi- programs in Engineering Physics and Human Factors Psychology and is cal help. We have made adjustments to preparing to launch a Ph.D. in Engineering Physics. the course schedule to address some of those needs. However, on some course Candidates must have a doctorate in a discipline represented within the College objectives (ethics, holistic informed ca- of Arts and Sciences, or closely related field, and must have demonstrated reer choice, fostering independence) we effective leadership in an academic administrative position, preferably at remain stubborn. the department head, or higher, level. Candidates must also have achieved national/international recognition for scholarship, as well as offering evidence of As we consider future course offerings, excellence in service and teaching, including work with graduate students. we want to make our course expectations In addition, candidates must have the ability to achieve strategic educational clearer throughout the semester. We have and research goals; demonstrate success in resource development and financial two specific strategies for the next time: management; recruit and retain faculty committed to excellence in teaching and First, we will invite alumni of our course scholarship; maintain the quality and viability of the curricula; partner with other to return as guest speakers, to express colleges in delivering academic programs and attracting students, particularly how (we hope) the course has helped those from underrepresented groups; promote diversity, shared governance, and them. Second, we want to reconsider the uses of technology; and develop relationships with alumni, the industry and the homework assignments. Rather than have community. Candidates must have exceptional communication and interpersonal students simply report on what they find, skills, the ability to work collaboratively and productively in a culturally diverse we want students to be more reflective on environment, and a commitment to an open and participatory leadership style. how this information corresponds to their personal skills and values. We think these Consideration of applications will begin in October 2008 and will continue until the position is filled; the expected start date is July 2009. strategies will improve a course we are Applications should include a detailed letter discussing qualifications and already proud of. background that demonstrate a fit with the college mission and vision (http://www.erau.edu/dbcoas/); and current curriculum vita. Applicants Donna Pierce ([email protected]) BAYARD should reference IRC28443, and apply to http://www.erau.edu/jobs or is an associate professor of mathematics ADVERTISING AGENCY, INC e-mail to [email protected]. Applications can also be mailed or JOB #: B004832200 at Whitworth University. Peter A. Tucker faxed to Human Resources, Embry-Riddle Aeronautical University, ([email protected]) is an associate 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114; Fax: 386-323-5060. EOE CLIENT: Embry Riddle professor of computer science, also at PUBS: FOCUS Whitworth University. SIZE: 4.8125” x 9” DATE: 10-02-08 11 COST: mn ARTIST: Bz COMP: Oz REV. 0 OK to Release MAA FOCUS November 2008
Teaching Time Savers: The Microphone Is Mightier than the Pen
By Emily Dryden
In my upper-level courses for math used for work that is expository or Time Saved: At least 10 minutes per majors, I am fond of assigning projects. includes substantial abstract arguments. student per assignment. These multi-stage assignments include You can read a student’s submission and a brief proposal, a written report, and an write numbers in the margin at spots Emily Dryden is an assistant professor oral presentation. While these projects where you have a question or comment, at Bucknell University in Lewisburg, create an excellent opportunity for then simply refer to those numbered spots PA. Technology has not yet invaded all students to explore new mathematical in your recorded feedback. For the more aspects of her life, as she prefers to cycle topics and take ownership of their technologically inclined, Microsoft Word to work and exist without a cell phone. learning, they also add significantly to my and Adobe Acrobat Professional allow grading pile. On the written components you to embed audio files throughout of the project the bulk of my feedback a document; if students submit their takes the form of end comments, in which assignments electronically in one of these Teaching Time Savers are articles I try to point out both strengths of the formats, you can directly replace written designed to share easy-to-implement document and areas for improvement. I margin comments with audio clips. activities for streamlining the day-to- am extremely careful, almost obsessive, day tasks of faculty members every- when I write these comments. After all, How do students respond to this change? where. If you would like to share your if I want my students’ writing to improve, Well, my students are already used to favorite time savers with the readers I should model good writing. Each set of being bombarded by audio, and they of FOCUS, then send a separate email end comments takes about 20 minutes to haven’t reported any problems with description of each activity to Michael compose. listening to my comments. I can tell that Orrison at [email protected]. Make sure they do listen, because later submissions to include a comment on “time spent” Technology to the rescue! Using standard in the process incorporate my suggestions. and “time saved” for each activity, and recording software (see below for Since students are frequently asked to to include pictures and/or figures if at details), I find that I am able to say my submit work electronically, it seems all possible. end comments in two to three minutes. It natural to receive electronic feedback. takes me a few minutes to compose my thoughts, and I sometimes listen to my Okay, so how can you do this? First you comments to make sure that I struck the need to check whether your computer has right tone. But I now spend at most ten recording software and a microphone. I MAA Online minutes producing substantially the same use Audacity, which is available for free feedback as before, just in a different download for various operating systems Introduces medium. And the medium makes all the including Mac OS X, Windows, and NumberADay and difference — my speaking isn’t perfect, Linux; go to http://audacity.sourceforge. but I’m less obsessive about it. Also, net. Your computer may have a built-in MinuteMath I find it easier to convey criticism in microphone; otherwise, a basic plug-in the oral format without the harshness microphone will cost you about $15. Plug The MAA has added two new fea- that a written comment can sometimes in the microphone, open the software, and tures to its web site; NumberADay carry. While I am no longer explicitly you’re ready to record. I usually export (http://maanumberaday.blogspot. modeling the mechanics of good writing, my comments as MP3 files, since my com) and MinuteMath (http:// I am still emphasizing the importance of students are accustomed to listening to maaminutemath.blogspot.com). formulating thoughts clearly and in an these. Then you can either e-mail the files Every workday, the NumberADay audience-appropriate manner, which is to students, or place them in students’ blog spotlights a different number the guidance my students seem to need personal directories if there is a “drop and some of its interesting proper- most. box” system in place at your institution. ties, while MinuteMath will exer- cise your mind with a new problem Of course, this dose of grading relief is Time Spent: A one-time investment of selected from the American Math- applicable to more than just comments on 10–30 minutes to find/download recording ematics Competition’s bank of papers. While probably not appropriate software and get comfortable using it, contest problems. Your comments, for offering feedback on computationally- plus at most 10 minutes per student per suggestions, and additions are wel- heavy problem sets, the method can be assignment to provide feedback. come.
12 November 2008 MAA FOCUS
A Book on PhDs in Notice of MAA Policy for Interviews at the Mathematics National Meetings Education
The presentations from the recent Na- The MAA recognizes the important Board of Governors has adopted the fol- tional Conference on Doctoral Programs role that our national meetings play in lowing policy: in Mathematics Education have been the hiring process, both for those seeking published by the Conference Board of jobs and for departments. Especially for “The MAA strongly discourages the the Mathematical Sciences. The book is those on the job market, the application use of personal hotel sleeping rooms as entitled U. S. Doctorates in Mathematics and interview process can be a stressful the site for professional interviews of Education: Developing Stewards of the time, and it may be awkward for appli- prospective employees. This practice is Discipline. It was edited by Robert Reys cants to express their desire to modify intimidating for some job-seekers, par- and John Dossey and is in the Issues in the setting in a situation that they feel ticularly those who find the situation Mathematics Education series co-pub- is less than ideal. Therefore, the MAA uncomfortable and possibly unsafe.” lished by the American Mathematical Society and the Mathematical Association of America. A review is forthcoming on MAA Reviews. Found Math
…And as N increases, the value of 2N rises exponentially.
From “Quantum Computing with Ions,” Scientific American, August 2008, p. 67. Thanks to Jonathan Sondow
MAA Math Classifieds Pairing Mathematicians and Employers
The Mathematical Association of America can help you find mathematicians at the bachelor’s, master’s, or PhD levels.
At MAA Math Classifieds you can: • Post a job, • Update and edit job announcements, • Search for candidates, • View resumes, • Contact potential candidates
Be sure to visit www.mathclassifieds.org to launch your search for the best candidate.
Mathematical Association of America
13 MAA FOCUS November 2008 An Intuitive Approach to the Borsuk-Ulam Theorem By Alex Bishop, Adam Cimpeanu, Kyle Flood, Bianca Homberg, Steven Homberg, Eric Marriott, Jeffrey Roth, Linus Schultz, William Sherman, Alex Smith, Geoffrey Smith and James Tanton
Each semester I (Tanton) offer extra-curricular mathemat- circle (along all the antipodes of the first half) gives the rota- ics courses for math-interested students, ages 11–18, keen to tional image of this path in the image set. We now have a loop experience mathematics as a creative and organic enterprise. in the image set starting and ending at g(Q). These courses, dubbed research classes, introduce students to the joys — and frustrations — of the research experience, of not Holding the point Q fixed, shrink (that is, contract) the great knowing, of “feeling around in the dark” and of finding the for- circle over the surface of the sphere down to the point Q. The titude of mind to dwell on complex issues for sustained periods image loop starting and ending at g(Q) shrinks to the point (weeks, not just minutes). This semester the co-authors of this g(Q). Some intermediate loop during this contraction must pass paper established the classic Borsuk-Ulam Theorem in a way through the origin so, despite what the diagram suggests, there that is slick, intuitive, and completely accessible. Their success must be a point R for which g(R) = (0,0). qed speaks to the joy and value that can be found for all in allowing mathematical creativity to bubble forth, no matter the age and Down a Dimension the background experience of the mathematical artists! The one-dimensional version of the theorem states that for The Theorem any continuous map on a circle there exists antipodal points adopting the same value. As my students discovered, this can Informally, the Borsuk-Ulam theorem states: be generalized. Their approach is novel.
At any instant there exist two antipodal points on the Earth’s For any continuous map f: S1 → ° and any value k there surface with identical air temperature and air pressure. exists a value q such that f (q) = f ( q + k).
Here we are assuming that air temperature and air pressure (Here, a real value q corresponds to the point (cos q, sin q) on vary continuously over the surface of the Earth. A more formal the unit circle.) statement of the theorem would be that any continuous map 2 2 f: S → ° identifies a pair of antipodal points, but the above To see why this must be true, think of the function f as the height interpretation with f = (temperature, pressure) is usually offered function of a fence built along a circle and let q* correspond to in texts as an appealing and quirky consequence. the location of the maximum height of the fence. Attach a rod to the top of the fence at position q* and at position q* + k. Here is the students’ proof:
For a point P on the surface of the Earth let P* denote its an- tipodal point (and so P** = P), and for a continuous tempera- 2 2 ture/pressure map f=(, f1f 2 ): S → ° consider the map 2 2 g: S → ° given by the differences of temperatures and pressures for pairs of antipodal points:
g P = f P –,f P* f P – f P* () ( 1 () 1 () 2 () 2 ()) Notice that for any point P we have that g(P*) = –g(P), so if 2 we plot the set of all values of g(P) in the plane ° we obtain o a set that is rotationally symmetric 180 about the origin.
Figure 2 Now slide the rod around the fence, keeping the pivot points of the rod at positions q and q + k until the second end of the rod reaches position q* . The slope of the rod has changed sign and so the rod must, at some position, have been horizontal. Figure 1 Pick a particular point Q on the sphere and walk along a great (Question: Is there a two-dimensional analog of this result?) circle to its antipode Q*. This gives a path in the image set. Walking back from Q* to Q along the second half of the great
14 November 2008 MAA FOCUS
Ham-Sandwiches very easy as an educator to fall into the trap of answering questions that have not been asked. Playing with ideas first and A famous consequence of the (two-dimensional) Borsuk-Ulam setting technicalities aside can provide fodder for real questions theorem states, somewhat informally: and give context and meaning to technicalities that, in the end, cannot be ignored. Having a context is key to developing true At any instant there exists a plane that divides the volume of understanding and I sincerely hope as an educator that I more Pluto, of the Eiffel Tower, and of this magazine each exactly in often than not have the means to help students create a context. half simultaneously. My young high-schoolers, in a real sense, are now ready for a course on algebraic topology. Given that they are now also won- This result is known as the Ham-Sandwich theorem for it can dering what continuity really means and whether it is possible also be phrased in terms of slicing two pieces of bread and a to say that a fence will always have, somewhere, a maximum slab of ham each exactly in half. height they are clearly ready for a course on real analysis too! I hope never to underestimate the value of intellectual play.
To see why this it is true, imagine that we have three sets S1, S2, and S3, in space each with a well-defined volume. Note (By the way, the students achieved the results outlined in this that each upointuu r P on a fixed sphere with center O determinesuuu r paper in four one-hour sessions. The first four sessions of the a vector OP and that there certainly exists a plane with OP semester were devoted to studying Sperner’s lemma. My hunch as its normal that divides the volume of S3 in half. Let f1 (P) was that this combinatorial result could be used to prove the be the volume of the uportionuu r of S1 that lies on the side of this Borsuk-Ulam theorem, but my hunch, as it turned out, was plane that contains OP and f (P) the volume of S on this irrelevant!) 2 2 2 2 same side. We have defined a function f: S → ° and, by the Borsuk-Ulam theorem, there exists a point R such that James Tanton teaches at the St. Mark’s School in Southborough, f (R) = f (R*). But note that the planes corresponding to the MA, and is the founding director of the St. Mark’s Institute of points R and R*are the same but with opposite orientation. This Mathematics; see the web site at http://www.stmarksschool. common plane is the one that does the slicing trick. org/math.
Although this argument for proving the ham-sandwich theorem is the standard one, it was also developed by the students.
A Context for Technicalities
To experienced mathematicians Saint Louis University it is clear that many fundamental offers assumptions of continuity were master’s and doctoral programs of study in brought into play here: the interme- mathematics. The M.A. program provides a diate-value theorem, the extreme- strong foundation in algebra, analysis, and value theorem, an interplay between connectedness, path connectedness topology preparing graduates for continued and simple connectedness, the use study and careers in teaching and industry. of continuous images of connected The Ph.D. program brings students to the 2 sets, of compact sets f (S ) and the forefront of mathematical research and pre- like. And many of these issues were up for discussion during the pares graduates for research and teaching ca- course. For example, in exploring reers. the Borsuk-Ulam theorem students The Department of Mathematics and Computer Science continues a long- at first contemplated the image set and were wondering if it can have standing tradition as a national leader in the number of masters and “holes?” In math-speak, they were doctoral degrees granted to African-Americans and women. Small class really asking: Can the continuous size, personal attention and a learning environment that promotes stu- image of a simply-connected com- dent engagement provides collaboration between students and faculty. pact set fail to be simply connected? If this were a college course I would Assistantships and fellowships are available to students who qualify. have been wildly grateful for this opportunity to leap in and begin For more information visit http://math.slu.edu/ or email [email protected] a speech on beginning homotopy theory: a burning question has just provided a context and a need for a theory.
15 MAA FOCUS November 2008
The Courants and I
By Edwin Rosenberg It was years before I realized I had piano that Papa played while around him missed the greatest opportunity of my gathered other members of chamber en- life: to become a protégé of Richard Cou- sembles, some family, some visitors often rant. In 1940 a hand had been extended to famous beyond New Rochelle. Nina was me, perhaps tentatively; but .... a violist whose specialty was the viola da gamba, an obscure Renaissance instru- In 1935, my parents bought a house in ment. (In 1997, at my 50th reunion at MIT, New Rochelle, a short train trip from I sat next to Professor Victor Weisskopf, New York, where my father worked. who had come close to a Nobel Prize in My older brother Fred and I commuted physics. He had been Ernst’s PhD advisor by car to the Ethical Culture-Fieldston in physics at the University of Rochester, School in the West Bronx, a 40 minute and recalled being at and in some of the drive — then. A kilometer from us lived Courants’ musical gatherings.) the Richard Courants. He had founded, and from 1920 to 1933 directed, the Göt- Performances were held at the Courants’ tingen Mathematics Institute in Germany, and friends’ homes. My mother, invited the acme of European mathematics. to hear Mrs. Courant play the viola da gamba, arrived late and rushed in. Just Because of his Jewish background, Pro- Richard Courant and one of his sons. as Mama’s presentation began, a police- fessor Courant was expelled from Göttin- man entered and asked whose car, with a gen by the Nazis. He, his wife Nina, and twenty-three: J. Robert Oppenheimer. specified license plate, was blocking the their elder son went to England in 1934, “In 1934, ... [my father] remembered driveway. My mother’s, of course: by the and briefly considered settling there. this ..., and promptly enrolled Ernst in time she got her coat, exited, moved the The other three children were planted that school,” says Hans Courant (email, car to a legal but distant location, and re- with friends of the family, the younger March 14, 2008). Gertrud and then Hans turned, Mama’s performance had ended. son living in Copenhagen with the fam- followed at Fieldston; Lori went to public No further opportunities arose. ily of Harald Bohr, younger brother of school in New Rochelle. Niels Bohr. Soon, however, Courant was Once, when I wandered into the house, a invited to New York University and the However the connection was made battered but serviceable French horn was family came to the United States. Richard between the Courant and Rosenberg sitting bell down on the piano. “Whose became a professor and again established parents, two person commuting became is that?” I asked Hans. “Oh,” he proudly a mathematical institute, modeled after four person. My brother and I, studying said. “It’s mine. Papa just got it, and it’s the one at Göttingen and named for him German at school, enjoyed practicing my turn to learn a new instrument.” What when he retired in 1958. with, or on, the Courants. Our standard an attitude! inquiry to Ernst was: “Ein schöner Tag, The Courants, Papa and Mama [accents nicht wahr?” (“A lovely day, not so?”) In Occasionally I was invited upstairs to on the second syllables], settled in New return, the Courants used us to improve Papa’s study. A high point was his show- Rochelle in a sprawling house on Calton their English. ing me how to physically determine the Road. Mama monitored a vegetable and surface of minimum area bounded by an flower garden far behind the house, which Ernst also used these trips to practice a irregular curve. He started simply, mak- became a center of refugee and musical wooden musical instrument new to my ing a circle with easily malleable wire and activity. Mama also monitored their chil- brother and me: a Blockflöte, or recorder. dipping it into a soap solution. When he dren: Ernst, Gertrud, Hans, and Leonore Holding the instrument vertically to the removed the wire frame from the soap, (called Lori ). lips, its player could not avoid introduc- a bubble remained which, as it dripped, ing into it saliva that brass players deli- soon reduced itself to just one surface: Professor Courant already knew where cately dump from valves. Here there was the thin disc inside the wire. Surface ten- his children should go to school. He no valve, and much was the ribbing Ernst sion, he pointed out, forced that surface had heard about a “wonderful school, took as liquid dripped onto whatever to be the one of minimum area for the Fieldston ... [with] a really great science protection he put beneath it. boundary. Then he twisted the frame into teacher, Augustus Klock.” This informa- increasingly complicated three dimen- tion came from an American who, in This was my introduction to a musical sional closed curves, and showed me that 1926–1927, studied under Max Born at family far above my background. In their the principle still prevailed. Though the Göttingen, obtaining a doctorate when living room was rooted a massive grand shapes seemed weird, the bubbles always
16 November 2008 MAA FOCUS contracted to the minimal area for their boundaries. I was fascinated. His aim was to mathematically obtain minimal areas for any boundaries. A nice problem that, like many mathematical problems, is easy to comprehend; but not easy to solve! Decades later, I learned that some of his work was based on the Problem of Plateau. (Cf. Constance Reid, Courant in Göttingen and New York, Springer-Ver- lag, 1976, pp. 189–191, 263.)
On the floor, near and partially obstruct- ing the living room entrance, was an eight-foot long, sixteen inches square wooden crate. When I inquired, its top was removed, revealing a refractor tele- scope, which on the next clear evening was taken outside. With Ernst now at Swarthmore, Gertrude and Hans instruct- Ernst, Hans, Mama, and Gertrud, probably in 1927. ed me. The main tube was mounted on a tripod and a small sighting scope attached atop the tube. That was my introduction to astronomy: planets were discs, stars remained points, and galaxies fuzzily swam into view. If care were taken to align the mount with north, one could pull gently on a cord that rotated the telescope so it stayed focused on objects such as the moon and planets, which otherwise moved rapidly across the field of view. I was hooked: I wanted to become an astronomer.
In winter, when observing was best, though cold, we sometimes built igloos large and stable enough for non-watch- ers to crawl in together for warmth. How nice, I learned, to snuggle against Richard Courant in his first car, a Rohr, in 1927. a female close to my age. were walking or sitting on a log.” To me, been narrowed one year by the recent The years passed. Gradually we went in the atmosphere in the auditorium was pal- loss of the family ensemble’s cello player. different directions. In 1943 Hans, like pably electric, reflecting the tremendous Jürgen Moser, who, imprisoned by the I, came to MIT, but by then I was in the intellectual powers of those assembled. Russians after World War II, had main- Army. My parents moved into New York I was awed. tained sanity and honed mental skills by in 1947; after that I was in but intermittent constructing logarithm tables in his head, touch with the Courants. A few years later we were asked to the not only filled both requirements but, in family retreat on Loon Lake, in far north- time, married Gertrud and became head When his father died in early 1972, Hans ern New York State. It was a delightful of the Institute. considerately invited my wife and me occasion to reminisce in a good-sized to the memorial service, fittingly held cottage on the shore, perhaps a third of a Nina passed away some six months short at the Courant Institute. We listened to mile across an inlet to the far shore. There of her 100th birthday. At her memorial speakers from many countries, starting we heard stories about Papa’s repeated service, also at the Institute, speakers with Richard’s first doctoral student in trips to Germany following World War included her children and grandchildren. Germany and continuing, by order of age, II, where he had gone to assist mathemat- Gertrud mentioned a visit to the vacation to a grandson, who told of his grandfather ics departments’ redevelopment, and to home when her mother was more than taking him walks into the neighboring recruit promising young mathematicians ninety. While making coffee early one woods “and always teaching, whether we for the NYU Institute. The search had morning, Gertrud looked out the kitchen
17 MAA FOCUS November 2008 window and noticed a small dark speck in the water, two-thirds of the way across the lake. “What is a seal doing here?” she wondered, and then realized it was a person swimming. She ran down to the dock, got into a rowboat, and caught up to the swimmer near the far shore. Mama, of course.
Alarmed that her mother was alone and unsupervised, the daughter asked her how she was going to get back to the cottage. “Swim, of course,” answered Mama. The daughter urged her to get in the boat and return, at which suggestion Mama became incensed, and told her daughter The four Courant siblings at a family wedding in 1998. From left to right: Gertrud, that she swam over and back every morn- Hans, Ernst, and Lori. ing, intended to complete her swim this morning, and wanted to be left alone. The service ended with a moving perfor- of some math book he was co-authoring. mance by Lori, a professional violist, of a I took a sheaf of papers home, but I was The eldest grandson, who had been fre- favorite piece of her mother’s, which Lori too busy with other things such as: the quently cared for by his grandparents, had played for her mother during her last school newspaper, girls, friends, sports, said that when he was a little kid, Mama days. Part of Bach’s Violin Sonata #3 in even my high school courses. had put a stick into the ground near the C major, on Lori’s viola it was in F ma- back of the house and another one out jor. How many recollections the service, Perhaps you have heard of the book What by the garden. Then she raced him from and that music, brought back. Tears of Is Mathematics? Still, despite that major one stick to the other and back, running laughter turned to tears of reminiscences. missed opportunity, I did teach math- sideways or backwards, always exhorting Youth had fled, but not memories. ematics. Yet how often have I wondered: him to go faster, faster. This continued what if...? for years. Clearly, Papa’s genes have not receded. His two sons became physicists; Ger- Edwin Rosenberg taught mathematics “You know,” concluded the grandson, “I trud obtained a PhD in biology; Lori, over thirty years, at Western Connecticut became a fairly good athlete and played who married two mathematicians, ed- State University in Danbury, CT, and lots of sports: team sports, individual ited mathematical papers. A daughter for two years (1976–78) at Community sports. Naturally, I won some and I lost of Gertrud’s is a mathematician at the School in Tehran, Iran. He has had ar- some. But I’ll tell you one thing: never University in Dijon, France; one of Hans’ ticles published about mathematics, his- again in my life did I experience the has a PhD in mathematics. Now for the tory, and sports. He expresses his grateful thrill I got the first time I beat my grand- next generation. appreciation to the Courant siblings for mother!” their suggestions and assistance: in par- Oh, yes, that missed opportunity. When I ticular to Lori for the loan of photographs Another grandson recited his embar- was a high school junior, Professor Cou- and permission to use them. rassment as a teenager when one day he rant asked me to comment on a chapter asked his grandmother, then well in her eighties, what it was like to be an old lady. “As soon as I said it, I realized it was rude and started to apologize. But it didn’t faze her.
“Her face lit up and her eyes shone. ‘Oh,’ she replied, ‘I’m very, very busy. There are lots of things I used to do that I can’t do any more, and those I still can do take me so much longer that I’m very, very busy.’”
Such stories brought down the house. Sitting in the back of the sloping audi- torium, I watched heads nodding at the tales. “Just like her,” all agreed. 18 November 2008 MAA FOCUS
19 MAA FOCUS November 2008 Write About Mathematicians in Non-Major Courses By Karl-Dieter Crisman In recent years we’ve (rightly) empha- about the individual they chose. More to benefit that, since there is often not as sized writing skills in math major cur- our purposes, since most of the people in much easily accessible documentation ricula. Isn’t this just as natural in service question are closely linked to their work, about these mathematicians, the students courses or so-called ‘core’ courses? Of students often learn about some truly new were forced to try to understand the math. course! mathematical idea. Most gratifying to As one might expect, students finding me was that many students also seemed topics close to their interests improved Attempting this (especially in truly low- to gain real perspective about their own the outcome. In one class of a pre-sci- level classes) encounters the usual com- studies and future from learning about the ence track, a number of women found plaints and fears about content, or flowery challenges these real people faced in life, real role models in Julia Robinson and responses on now-discredited topics like which promoted a better attitude toward other female mathematicians who faced the universality of the golden ratio in art. mathematics in general by the end. I’ll great challenges. It’s difficult to bridge the gap between our give a few of my favorite examples. goal of giving students a broader perspec- As with all assignments, there are practi- tive of what math is (and is useful for) Archimedes is almost always a top cal suggestions. Students take more own- and students’ persistence in viewing it as choice, and notions of notation from ership of their thinking when the paper a collection of formulas to be memorized “The Sand-Reckoner” and his amazing is connected to sharing it with peers, and used under controlled conditions. So applied side consistently wow students. whether a group presentation on related instead of having the students write about (You should limit how many students in figures or just a quick blurb from their math, I’ve done a ‘bait-and-switch’ to one section get to pick him, because he seats. Timing is crucial too, so that there encourage learning. There is still a paper is so popular!) I’ve had students from is enough time to do it, but not enough to to write, but it’s about a mathematician, non-European backgrounds discover forget about it — I like assigning it over a not about mathematics per se. (See the significant mathematics from the history break if I know they will have little other handout on page 21.) of their own cultures; this had the extra homework, since it isn’t too onerous.
The assignment is to write a paper about a mathematician and then to describe (ac- Research topic: A three-week summer program for curately and with detail) what the student Arithmetic of L-functions graduate students finds compelling and/or interesting about undergraduate students mathematics researchers that mathematician. To get students start- Education Theme: undergraduate faculty ed, I provide a list of common possibili- Making Mathematical secondary school teachers ties organized into rubrics like “Female Connections math education researchers Mathematicians” or “Mathematicians who Died Young.” Usually students find at least one of the topics intriguing, and IAS/Park City Mathematics Institute (PCMI) search through several possibilities to June 28 – July 18, 2009 find one they will enjoy; I’m always sure Park City, Utah to provide explicit (and reliable) library Organizers: Cristian Popescu, University of California, San Diego; Karl or web starting points. Rubin, University of California, Irvine; and Alice Silverberg, University of California, Irvine. Graduate Summer School Lecturers: David Burns, Kings College, The point isn’t that the assignment is London; Benedict Gross, Harvard University; Guido Kings, Regensburg hard — indeed, it isn’t. Instead, the idea University; Manfred Kolster, McMaster University; Cristian Popescu, is to build a bridge between students’ University of California, San Diego; David Rohrlich, Boston University; conceptions and the reality of mathemat- Karl Rubin, University of California, Irvine; John Tate, University of Texas at Austin; Doug Ulmer, University of Arizona; and Vinayak ics. The assignment is not much affected Vatsal, University of British Columbia. by ‘math anxiety,’ since the topic is the Clay Senior Scholars in Residence: Benedict Gross, Harvard person, not the math. Students typically University; and John Tate, University of Texas at Austin. end up doing quality work. Finally, since Other Organizers: Undergraduate Summer School and Undergraduate Faculty Program: Aaron Bertram, University of Utah; and Andrew it focuses on their thoughts, I have fewer Bernoff, Harvey Mudd College. Secondary School Teachers Program: worries (though still some) about simple Gail Burrill, Michigan State University; Carol Hattan, Vancouver, WA; internet plagiarism. and James King, University of Washington.
Applications: pcmi.ias.edu My experience is that essentially all stu- Deadline: January 28, 2009 dents (often to their surprise) report that IAS/Park City Mathematics Institute they learned something quite interesting Institute for Advanced Study, Princeton, NJ 08540 Financial Support Available
20 November 2008 MAA FOCUS
Have them submit early samples if you I’ve used this assignment at colleges Karl-Dieter Crisman (karl.crisman@ think they might have difficulty using real ranging from open admission to highly gordon.edu) is Assistant Professor of arguments to express their preference; if selective, and consistently found it to Mathematics at Gordon College in Wen- you do use a draft system, then online have very high impact for its length. The ham, MA. A version of this appeared in submission is essential. only caveat is that students in a particular the Proceedings of the 16th Conference section must have at least a minimal in- of the Association of Christians in the A final key asset of this idea is that one terest in the class. If most students’ goal Mathematical Sciences, and this mate- can easily tailor the assignment to one’s is truly a gentleman’s D (I am not exag- rial has been presented at both MAA and needs. There are plenty of mathemati- gerating), this assignment won’t help. ACMS sessions in the past. cians out there to restrict the assignment, But the majority of students had plenty for example, to those who thought about of innate desire to do a decent job, which faith issues, or to a specific time period. led to learning irrespective of their back- One can also more explicitly require grounds. With a little bit of forethought, some description or understanding of the this assignment can open eyes and even math as opposed to just the person. change attitudes.
Write About a Mathematician You will do a three page essay on MacTutor site (http://www-groups.dcs. By the way, there are a few mathema- a historical mathematician. Note: this st-and.ac.uk:80/~history/) and MathWorld ticians who have appeared in popular does not necessarily have to be about (http://mathworld.wolfram.com). books recently, like Srinivasa Ramanu- math! It just has to be about what you jan, Paul Erdös, and John Nash. If find interesting/compelling about this Who on earth would you write about? you do a report on Nash, the movie A person. Here are ideas for you! Here is a very short and very incomplete Beautiful Mind has been fictionalized, list of some mathematicians and/or math- so don’t use it as a resource. The book You can go to the library and check out ematically minded people whom you the movie was based on is fine. Also, books about interesting mathematicians could write about: Euclid, Pythagoras, Good Will Hunting, Pi, the TV show – this would be in QA 21–31. Many Archimedes, the Bernoullis, Euler, Fibo- NUMB3RS, and others are fiction, so general history of math books will be nacci, Pascal, Fermat, Mersenne, Gauss, don’t use them! good. E. T. Bell’s Men of Mathematics, Abel, Galois, Dirichlet, Weierstrass, despite its dated (and unfortunately Fourier, Condorcet, Borda, Cauchy, Can- To help you get some ideas, here is a accurate) title, is a fun first resource; tor, Hilbert, Ramanujan, Hardy, Laplace, table with common names encountered some older books by Dirk Struik or under categories people often find in- Galileo, Newton, MacLane, Dickson, Ja- Howard Eves are good, too. There are teresting. Remember, find something cobson, Einstein, Noether, Grothendieck, several good websites, especially the interesting! Gromov, Wiles, Tao...
Category Some Famous Names (Old) Greek Mathematicicans Pappus, Archimedes, Apollonius, Euclid, Zeno, Democritus, Pythagoras Female Mathematicians Emmy Noether, Julia Robinson, Karen Uhlenbeck, Karen Smith, Sophie Germain, Fan Chung, Ingrid Daubechies Non-Western Ramanujan, Al-Khwarizimi, Omar Khayyam, Liu Hui, mathematicians/mathematical texts Brahmagupta, G. Shimura, H. Hironaka, the Rhind Papyrus, Plimpton 322 Mathematicians who died young or violently or may have Nash (not deceased yet), Ramanujan, Riemann, Erdos, had mental illness Boltzmann, Cantor, Galois
Mathematicians who thought (well or poorly) about God Pascal, Descartes, Galileo, Laplace, Kronecker, Kepler, Rus- sell, Hardy, Euler, Riemann, Ramanujan, Erdos, Cauchy “Mathematicians” primarily known for something else Pascal, Descartes, Mersenne, Galileo, Newton, Einstein, Pauli, Zeno, E.T. Bell, Stephen Wolfram Some recent Fields medalists of interest Gromov, Drinfeld, Thurston, Witten, McMullen, Voevodsky, Tao, Perelman
21 MAA FOCUS November 2008 Archives of American Mathematics Spotlight: The Lawrence Biedenharn Papers By Carol Mead
The Archives of American tivistic quantum mechanics, and Mathematics at the Center for Coulomb Excitation, about all American History has recently of which he wrote and published processed and made available extensively. Also included in the the papers of prominent physi- serial notes are printed material cist Lawrence Christian Bie- related to his teaching activities denharn, recognized worldwide and his participation in various as one of the leaders of modern conferences around the world. theoretical physics. The papers consist of Biedenharn’s notes, In addition to the serial notes, publications, conference talks, the collection contains copies of teaching materials from Duke hundreds of his research articles University, correspondence, and in the fields of nuclear physics personal documents. Bieden- and later mathematical physics harn’s wife, Sarah, donated the along with related notes, his papers to the University of Texas conference talks covering a span at Austin in 2007. of 40 years, and his teaching materials used at Duke Univer- Biedenharn was born in Vicks- sity. The personal series of the burg, Mississippi, in 1922. His papers includes his thesis from undergraduate studies at the MIT, military service documents, Massachusetts Institute of Tech- Fulbright and Guggenheim awards in personal correspondence, the nology (MIT) were interrupted by World 1958, and the Alexander von Humboldt proceedings of a symposium in honor War II, which he spent in the U.S. Army Foundation Senior Scientist Award in of Biedenharn, and the memorial issue Signal Corps. He received his Bachelor 1976 and 1987. Biedenharn’s 70th birth- of the Foundations of Physics journal of Science degree in absentia from MIT day was celebrated with a symposium dedicated to Biedenharn. in 1944 and applied for graduate stud- held in his honor in Bregenz, Austria. ies at MIT while stationed in Tokyo in The journal Foundations of Physics A digital version of Lawrence Bieden- 1946. He returned to MIT in 1946 and published a memorial edition dedicated harn’s Biography, including photographs completed his PhD in theoretical nuclear to Biedenharn in 1997. The University of and a publication list, can be found physics in 1950. Texas at Austin established the Lawrence online on Duke University’s website at C. Biedenharn Endowed Chair in Physics http://www.phy.duke.edu/about/Lawrence- After graduation, Biedenharn worked for with a gift by Sarah Biedenharn to honor Biedenharn. two years as a research assistant at the her husband’s contributions to theoretical Oak Ridge National Laboratory in Ten- physics. The finding aid for the Lawrence Bieden- nessee. His teaching career began in 1952 harn Papers is available online at http:// when Yale University hired him as an as- Biedenharn’s colleagues and his many www.lib.utexas.edu/taro/utcah/01016/ sistant professor. He joined the faculty at students knew him as an intelligent, cah-01016.html. Rice University in 1954, becoming an as- cultured man with varied interests. In sistant professor there in 1956. Five years addition to his extensive scientific work, The Archives of American Mathematics later, he moved to Duke University where which continued unabated throughout is located at the Research and Collections he became the youngest full professor on the years, and even increased towards the division of the Center for American His- the Duke faculty at age 38. He worked at end of his life, Biedenharn pursued many tory on the University of Texas at Austin Duke, supervising 24 PhD students, until other interests. Among other things, he campus. Persons interested in conducting becoming Emeritus in 1992. At that time, had a great love for music, particularly research or donating materials or who Biedenharn moved to the University of chamber music. have general questions about the Ar- Texas at Austin where he continued to chives of American Mathematics should teach as an adjunct professor until his The highlight of the Biedenharn papers contact Carol Mead, Archivist: carol- death from cancer in 1996. is his serial notes. Over the course of al- [email protected], (512) 495-4539. most 50 years, Biedenharn kept research The Archives web page is at http://www. Throughout his life, Biedenharn received notes related to his work on symmetries cah.utexas.edu/collections/math.php. many honors and awards, including the in nuclear physics, time reversal, rela-
22 November 2008 MAA FOCUS
Page from Biedenharn’s serial notes “I,” 1962.
23 MAA FOCUS November 2008 Reflections on Montclair State University–Beijing Connection
By Mika Munakata and Aihua Li At this year’s national meeting for the NSF GK–12 graduate fellows program, NSF Director Arden Bement cited inter- national collaborations as a focal point of NSF efforts. Scientists and mathemati- cians must be able to function within the global setting and must seek opportunities to engage in cross-cultural partnerships. In particular, there is an urgent need to ex- pose undergraduate and graduate students to international research opportunities. NSF’s commitment to international col- laborations is demonstrated by funding for international projects. Recently, our GK–12 Fellows in the Middle program at Montclair State University (NSF Award #0638708) received a supplement to establish an international component to our existing project.
Supported by the supplement and by con- Welcome banner to US-Sino Workshop in Xi’an siderable contributions from the univer- sity, in January 2008 17 GK–12 project presenting their research to small groups. entire research career.” participants spent two weeks in Beijing, One mathematics Fellow commented China. The group included four graduate that “it was very interesting for me to see The teachers visited several middle and students (Fellows), three middle school the types of problems the math graduate high schools. There, they met teachers teachers, two university faculty members, students were working on. For example, and students, observed classes, and gave four project staff, and the superintendent they were working on optimization prob- sample lessons to the students. We were of a local school district. The main goal lems involving traffic — which they can all intrigued by some of the differences of our visit was to form international part- really use.” The Chinese students were we saw. The Chinese teachers we met nerships for all of our participant groups. particularly interested in presenting their teach just two classes each day, but teach Less tangible goals included deepening research and to practice their English about 60 students in each class, which the participants’ understanding of cultural communication skills. Aside from the means that the total number of students differences and having them practice research experiences they gained, the taught by one teacher per day is not too effective cross-cultural communications US Fellows established some important different between the two countries. But and collaborations. contacts. As one Fellow put it, “meeting having only two teaching periods means with fellow researchers at Beijing Normal that the teachers are able to meet more During our stay in Beijing, the Fellows, University was a tremendous experience often with their colleagues. They col- teachers, and university faculty often where I was able to develop international laborate on lesson planning, assessment, moved in different circles. The Fellows collaborations that I hope will last my and reflection on lessons. They visit each each spent about four days at a univer- sity in Beijing. Our partner universities were University of Science and Technol- ogy Beijing, Beijing Normal University, Beijing Jiaotong University, and China University of Geoscience. Each Fellow was paired with a member of the research faculty at one of these universities and was introduced through him/her to graduate student partners. The science Fellows learned new techniques of bio- logical research and saw state-of-the art laboratories. The mathematics Fellows worked with Chinese graduate students on reading and analyzing papers and Middle School students at Xisi Middle School in Beijing. 24 November 2008 MAA FOCUS other’s classes frequently and offer sented at various venues including a feedback. professional development workshop, an Optimist’s luncheon, and at our While the Chinese teachers seemed middle school Math and Science accustomed to working together Day; and met with us about possible outside the classroom, they were collaborative projects. They were also interested in learning about our able to visit tourist sites around New project’s models for co-teaching York City and were invited to many interdisciplinary lessons. In fact, barbecues. in keeping with the structure of the GK–12 program, one pair of US Next January, we will return to Beijing teachers team-taught an interdisci- with different participants to further plinary lesson on natural selection strengthen our partnership. It is the that relied on statistics. One of the US mathematics graduate student Daniela Kitanska hope that our partnership with the presenting teachers commented presenting her research to a Chinese mathematics four universities in Beijing will serve that “traveling to China and being graduate student. as a springboard for sustainable in- immersed in a culture so different ternational programs for our science to me was unforgettable. However, opportunities and challenges associated and mathematics graduate programs. as a teacher, visiting the schools and be- with international collaborations. Before In Years three and four of our funding ing invited to present a lesson to a class our visit, Aihua (who is originally from period, we will partner with colleagues of Chinese middle school students was Beijing) led four afternoon Chinese in another country in a different part of an experience I do not think I will ever language and culture workshops. While the world. equal.” these workshops helped all participants learn basic Chinese greetings, everyone Our experiences in Beijing were eye- The US university faculty members met was humbled by the difficulties associ- opening for all of our participants. (For with Chinese researchers and gave sev- ated with being immersed in a different several of the participants, this was their eral presentations. The topics included language. It is important for those unac- first experience abroad.) The teachers descriptions of our grant activities, customed to cross-cultural and cross- gained new insights into the teaching of mathematical problem solving, research linguistic interactions to be aware of mathematics and science. The graduate projects in Antarctica, and astronomy. We these challenges and to think about how students became exposed to the idea of also participated in several colloquia with to adjust to them. Similarly, we wanted international collaborations. The univer- Chinese educators. Of particular inter- the participants to think actively about sity faculty established connections that est to us was the panel discussion with how differences in culture can often will undoubtedly lead to collaborations in members of the Ministry of Education, the future. Regardless of the individual the Institute of Education at Beijing Nor- experience, however, all of us are very mal University, and several mathematics grateful to our Chinese hosts. From the textbook authors. These discussions lent graduate students who took our Fellows a new perspective to our observations of shopping, to the middle school teachers the Chinese mathematics classrooms. who shared their experiences with us, to our Chinese colleagues who helped us In addition to our professional activities, organize and coordinate the visit – every- Montclair State University’s GK–12 team where we went, we were met with a warm visited many historical sites such as the welcome. Their hospitality and common Great Wall, Forbidden City, and the Terra interests make us hopeful that this will be Cotta Warriors in Xi’an. We also visited a long-lasting partnership. mathematics and science-related sites including the Peking Man geological site Mika Munakata is an associate professor and the Beijing Planetarium. With the The group at the Wild Goose Pagoda in at Montclair State University, where she Beijing Summer Olympics fast approach- Xi’an. specializes in mathematics education. ing, it was fun to be able to see some of She received her PhD from Columbia’s the landscape and city life that later ar- impact how people learn, teach, conduct Teachers College in 2002. rived through our television sets. research, and communicate. Dr. Aihua Li received her PhD in math- While we were busy with research activi- This May, we hosted three colleagues ematics in 1994 from the University of ties, visits to schools, and sightseeing, the from Beijing: a physicist, a professor of Nebraska-Lincoln. Previously she taught most important element of the experiment mathematics education, and a biology at Loyola University New Orleans for was the cultural exchange. We wanted professor. During their 12 days in New nine years. She has been teaching at to expose the graduate students to the Jersey, they visited middle schools; pre- Montclair State University since 2004.
25 MAA FOCUS November 2008 Mathematicians Playing a Role in Math Education: What We Learned at the IME/MIME Workshop By Anna Bargagliotti, Rama Chidambaram, and Gizem Karaali
In Hollywood, some actors are regularly in playing many different roles in the eager to get involved and ready to begin cast as mean, others as sweet and endear- mathematics community. Our tale reflects exploring the world of mathematics ing, and some typically play innocent big- our experiences at the “Mathematicians education. eyed youths who inevitably succeed after in Mathematics Education” (MIME) awakening to the particular facts of life workshop at the Institute of Mathematics We started with a working dinner in that their producer wants them to awaken Education (IME), University of Arizona, which everyone had the chance to meet to. It is unusual and difficult for actors to which we attended March 20–22, 2008. informally. After dinner, we had the op- cross the bridge between different types portunity to listen to Roger Howe of Yale on a regular basis. However, there are Let us give some background and con- University, who has “worked diligently always exceptions to the rule. text: We were all intrigued by the MIME over the years to broaden and profes- workshop announcement that promised sionalize the involvement of a research In the seemingly unrelated world of to orient mathematicians to key issues mathematician in educational reform, to academics, mathematics faculty may of mathematics education. Each of us lead us towards the goal where involve- find themselves playing different roles. was convinced by the argument that “the ment of mathematicians in education is People with different skills and interests demand is increasing for mathematicians viewed as a well-informed professional strive to balance their careers in ways who can constructively contribute to activity by mathematicians and educators that will be uniquely fulfilling to them. work in mathematics education, such alike,” as the citation for his 2006 AMS Many choose to play multiple roles as standards development, validation of Award for Distinguished Public Service within their research fields and within tests, curriculum design, textbook review, says. Many mathematicians know him the mathematical community. However, and the preparation and professional for his work in representation theory, some typecasting naturally happens in development of teachers.” We found our and many others are familiar with his our midst as well, and switching roles separate ways to Tucson, AZ, hoping contributions to mathematics education. becomes difficult. Who knew mathema- that, with some guidance, we too could For us novices, his talk was inspiring, ticians and Hollywood celebrities had find our own unique ways to contribute not only because of his reputation as a anything in common? to the discussion and to work on current research mathematician, but also because issues in mathematics education. his message was very compelling. Typecasting among mathematicians is worth investigating. Looking at math- We were looking to make our first cross- Howe gave us several simple examples ematics departments across the country over. In graduate school, we were trained of how to approach problem solving in we see mathematicians making many dif- to be research mathematicians. We are of the context of mathematics education. ferent choices. Some choose to dedicate course grateful for our training and will He discussed the difference between most of their energy to the advancement continue to do research mathematics, but knowing the definition of number as of mathematics through research. This we would like also to have the chance a mathematician and actually coming kind of role can come in many distinct fla- to be involved with mathematics educa- up with a definition that an elementary vors: undergraduate research, historical tion research. We respect and admire the school student can understand and use research, subject area specific research, handful of mathematicians who have in a meaningful way. He also suggested etc. Others excel in classroom teaching taken this path ahead of us, and want to specific ways a mathematician could and focus their energy on developing follow in their footsteps. The philosophy become involved in mathematics educa- interesting coursework. Many dedicate of the workshop was precisely that this tion: collaborating in the development themselves to innovate and improve could be done: university mathematicians of various teacher preparation programs, the process of teaching mathematics. could contribute in meaningful ways to designing professional development op- Recently, there has been an emergence the work of mathematics educators while portunities for teachers, writing about of yet another group: a relatively small still maintaining their role as mathemati- mathematics to provide motivation and self-selected minority who successfully cians. insight to pre-service and in-service cross the bridge between mathematicians teachers, participating in various educa- and mathematics educators called “math- Three prominent mathematicians and tion-related program panels and commit- ematicians who also do mathematics edu- an accomplished mathematics educator tees of IES or NSF, reviewing or writing cation.” This group’s scholarly research organized the workshop. The participants educational materials such as textbooks, bridges and enriches both fields. were mathematicians at various stages of being a consultant on education proposals their careers. Many had dedicated years (such as NSF curriculum change propos- This is a story told by three junior to several key issues related to mathemat- als), etc. mathematicians who have not yet gone ics education. Others, like the three of us, through the Sorting Hat, but are interested were mostly new to the conversation, but The next morning, renowned mathemat- 26 November 2008 MAA FOCUS ics educator Deborah Ball led us through for teachers. They emphasized that this is rah Ball’s discussion of the landscape the present landscape of mathematics an area of education that mathematicians of mathematics education in the US. education in the US. Following her lead, are qualified to comment on, provided The workshop ended after a discussion we embarked on a discussion about they develop a keen sense of observation regarding our future work as mathemati- mathematical subject knowledge and and listening to identify the problems cians in mathematics education. Mathematical Knowledge for Teaching involved in teaching. Collaborating with (MKT). Pretty soon we discovered that educators, we discovered, mathemati- We left Tucson full of excitement, hope, MKT is not just about knowing math- cians could use their knowledge about and promise that in the future we would ematics, but also includes everything mathematics to develop more effective be able to cross the bridge between teachers do to support student learning: ways to teach teachers. mathematicians and math educators lesson planning, choosing the right doing scholarly research in both fields. examples, asking good questions that At the end of the day we were assigned It was clear to us that doing research lead to classroom discussions, assessing homework! We were asked to examine in mathematics education is engaging, student work, etc. Each of these tasks and critique the treatment of the concept challenging, and requires skills substan- involves pedagogical skill as well as a of a function in various algebra text- tially different from just knowing and considerable amount of mathematical books. We were given sample materials successfully teaching mathematics at proficiency, skills of mathematical rea- from three textbooks and were asked to the university level. We also learned that soning and communication, and fluency review them overnight so that we could with a lot of motivation and keen sense with examples and terms. continue the discussion. of observation and listening, we could make significant contributions to the field To illustrate this point we watched a The action-packed day ended with a of mathematics education. video of students in an elementary school fantastic dinner at William McCallum’s classroom. Students in the video were house. As the beauty of the southwestern With mathematics educators like Debo- discussing which fraction is larger: 4/4 sunset came upon us, many informal rah Ball and mathematicians like Hyman or 4/8. While watching the class discus- conversations about mathematics edu- Bass, Roger Howe, and William McCal- sion, our task as mathematicians was cation took place. For example, one of lum, paving the way to make this transi- to observe the mathematics in a child’s us chatted with Deborah Ball about tion possible, we believe crossing over explanation. After an hour of delibera- education as a research field and more should be a lot easier for mathematicians tions, we had filled up a large whiteboard specifically about questions like: What than for Hollywood actors. However, in with mathematical ideas such as the should being a “mathematician who order for the work of a mathematician in knowledge of unit measure, relationship also does mathematics education work” mathematics education to be regarded as between divisor and dividend, equiva- really mean? How can this be defined valuable research, the end product must lence classes, etc. In the end, this turned in terms of scholarship? What is the meet the scholarly standards in two fields: out to be a surprisingly challenging and relevant research component? How can mathematics and mathematics education. undeniably exhilarating experience. We this research be incorporated into the Clearly, this is no small task. How it can enjoyed our task and came to appreci- more traditional research portfolio of an be done is an open question that we are ate the nuances and subtleties involved academic mathematician? Who is the au- eager to attempt to answer. in identifying mathematical ideas in a dience interested in this type of research? child’s work. Discussing these types of questions with For information on IME, check out: http:// Deborah Ball, Hyman Bass, and William ime.math.arizona.edu. For an introduc- That afternoon, Hyman Bass encouraged McCallum provided interesting perspec- tion to MKT see: Ball, D. L., Hill, H.C, us to think about how to help school tives about this vast territory, which & Bass, H., “Knowing mathematics for students understand the meaning of a remains largely uncharted. We felt lucky teaching: Who knows mathematics well standard procedural algorithm used in to be at this workshop and be led through enough to teach third grade, and how can performing mathematical operations. Our this geography by these pioneers. we decide?” American Educator, Fall task was to use pictures and manipula- 2005, pp.14–22, 43–46; also available tives to represent the standard procedures On Saturday morning at 8:30 am McCal- online at Deborah Ball’s home page at such as borrowing and carrying used to lum, a 2005 NSF distinguished teaching http://www-personal.umich.edu/~dball/. add, subtract, multiply, and divide in a scholar award winner and director of way elementary school students could IME, initiated a discussion on develop- Anna Bargagliotti is assistant profes- understand. This again proved to be ing a framework for evaluating school sor of mathematics at the University of challenging for a group of approximately textbooks. We learned to give construc- Memphis. Rama Chidambaram is as- twenty PhDs in mathematics. tive criticism to the authors in order sistant professor of mathematics at the to ensure correct mathematics is being University of Michigan-Dearborn. Gizem In their presentations, Bass and Ball il- taught throughout all grades. In addition, Karaali is assistant professor of math- lustrated to us the large amount of mathe- we also had a chance to view some state ematics at Pomona College. matical reasoning and skill that is needed high school curriculum standards, which to develop the necessary knowledge base touched on issues mentioned in Debo-
27 MAA FOCUS November 2008
Employment Opportunities campus is located on Long Island Sound years. This position carries a teaching in southwestern Connecticut, about 50 responsibility of one course per semester, CALIFORNIA miles from New York City. Fairfield is and the expectation that the incumbent play an Affirmative Action/Equal Opportunity a significant role in the research life of the California State University, Fresno Employer. For more information see the Department. The salary for AY 2008-2009 The Department of Mathematics at the department web page at http://www.fair- for this position is $54,500, the salary for California State University, Fresno, invites field.edu/macs_index.html AY 2009-2010 may be higher. Applicants applications for a tenure-track assistant must have a Ph.D. or equivalent degree in professor position beginning August Applicants should send a letter of ap- mathematics, computer science, statistics, 2009. A Ph.D. (or A.B.D) in mathematics plication, a curriculum vitae, teaching mathematics education or related field, and is a requirement. Exceptional faculty at a and research statements, and three letters evidence of outstanding research potential. higher rank may be considered. All appli- of recommendation commenting on the Preference will be given to candidates in cation materials will be processed through applicant’s experience and promise as a areas related to number theory or dynami- mathjobs.org. For full consideration, the teacher and scholar, to Matt Coleman, cal systems. application must be complete by January Chair of the Department of Mathematics 15, 2009. For more information about and Computer Science, Fairfield Univer- Send vita and at least three (3) letters of the position or institution, please visit: sity, 1073 N. Benson Rd., Fairfield CT recommendation, clearly indicating the po- http://www.csufresno.edu/aps/vacancy/sci- 06824-5195. Full consideration will be sition being applied for, to: Appointments ence_math.shtml given to complete interviewing at the Joint Committee; Dept. of Mathematics, Statis- Mathematics Meetings in Washington DC, tics, and Computer Science; University of CONNECTICUT January 5-8, 2009. Please let us know if you Illinois at Chicago; 851 S. Morgan (m/c will be attending. 249); Box R; Chicago, IL 60607. Applica- Fairfield University tions through mathjobs.org are encouraged. Assistant Professor WASHINGTON, DC No e-mail applications will be accepted. To Department of Mathematics and ensure full consideration, materials must be Computer Science American University received by December 31, 2008. However, The Department of Mathematics and Com- Two tenure-track positions in the Math- we will continue considering candidates puter Science at Fairfield University invites ematics/Statistics department at American until all positions have been filled. Minori- applications for one tenure track position in University at the rank of Assistant Pro- ties, persons with disabilities, and women mathematics, at the rank of assistant profes- fessor or Associate Professor, beginning are particularly encouraged to apply. UIC sor, to begin in September 2009. We seek a Fall 2009. Qualified candidates will have is an AA/EOE. highly qualified candidate with a commit- a strong background in mathematics or ment to and demonstrated excellence in statistics with a PhD, teaching experience University of Illinois at Chicago teaching, and strong evidence of research is required. American University is an Department of Mathematics, Statistics, and potential. A doctorate in mathematics is EEO/AA employer. Minority and women Computer Science required. The teaching load is 3 courses/9 candidates are encouraged to apply. See The Department has active research credit hours per semester and consists math.american.edu/positions, or contact the programs in a broad spectrum of cen- primarily of courses at the undergraduate Department of Mathematics and Statistics trally important areas of pure mathematics, level. The successful candidate will be at (202) 885-3120 for details. computational and applied mathematics, expected to teach a wide variety of courses combinatorics, mathematical computer sci- from elementary calculus and statistics ILLINOIS ence and scientific computing, probability to graduate level courses; in particular, and statistics, and mathematics education. Fairfield University’s core curriculum University of Illinois at Chicago See http://www.math.uic.edu for more includes two semesters of mathematics for Department of Mathematics, Statistics, and information. all undergraduates. Computer Science The Department has active research Applications are invited for the following Fairfield University, the Jesuit University of programs in a broad spectrum of cen- positions, effective August 16, 2009, sub- Southern New England, is a comprehensive trally important areas of pure mathematics, ject to budgetary approval. university with about 3,200 undergradu- computational and applied mathematics, ates and a strong emphasis on liberal arts combinatorics, mathematical computer sci- Tenure track positions. Candidates in all education. The department has an active ence and scientific computing, probability areas of interest to the Department will be faculty of 14 full-time tenured or tenure and statistics, and mathematics education. considered. The position is at the Assistant track members. We offer a BS and an MS See http://www.math.uic.edu for more Professor level. in mathematics, as well as a BS in computer information. science. The MS program is an evening Tenured position. Candidates in math- program and attracts students from various Applications are invited for the following ematical logic, with a preference for model walks of life secondary school teachers, position, effective August 16, 2009, subject theory or descriptive set theory, will be eventual Ph.D. candidates, and people to budgetary approval. considered. The position is at the Associate working in industry, among others. Professor or Professor level. Research Assistant Professorship. This Fairfield offers competitive salaries and is a non-tenure track position, normally Applicants must have a Ph.D. or equivalent compensation benefits. The picturesque renewable annually to a maximum of three degree in mathematics, computer science, 28 November 2008 MAA FOCUS statistics, mathematics education or related teaching (if applicable), and four letters 1st. Minority candidates are encouraged field, an outstanding research record, and of recommendation with at least one ad- to apply. evidence of strong teaching ability. The dressing teaching. Electronic applications salary is negotiable. will not be accepted. Please send hardcopy Berea College, in light of its mission in materials to: the tradition of impartial love and social Send vita and at least three (3) letters of equality, welcomes all people of the earth recommendation, clearly indicating the po- Search Committee to learn and work here. sition being applied for, to: Appointments Department of Mathematics Committee; Dept. of Mathematics, Statis- Pittsburg State University MAINE tics, and Computer Science; University of 1701 S Broadway Illinois at Chicago; 851 S. Morgan (m/c Pittsburg, KS 66762 University of New England 249); Box T; Chicago, IL 60607. Applica- Assistant Professor of Mathematics tions through mathjobs.org are encouraged. For full consideration, candidates should The Department of Mathematical Sciences No e-mail applications will be accepted. To submit complete applications by Decem- at the University of New England invites ensure full consideration, materials must be ber 1, 2008. Review of applications will applications for a tenure-track Assistant received by November 11, 2008. However, continue until the position is filled. For Professor beginning with the 2009-10 we will continue considering candidates additional information see the position academic year. Applicants should have until all positions have been filled. Minori- description at http://www.pittstate.edu/ an earned doctorate in Mathematics or ties, persons with disabilities, and women eoaa/jobs.html. Questions may be directed Applied Mathematics. The Mathematics are particularly encouraged to apply. UIC to Dr. Tim Flood at [email protected] or Department is developing new programs is an AA/EOE. 620-235-4400. Employment will require a focusing on mathematical applications in criminal background check. Pittsburg State the Biological, Marine, and Health Sciences KANSAS University is an Equal Opportunity/Affir- and candidates with applied concentra- mative Action Employer tions related to these areas are preferred. Pittsburg State University Additional qualifications include teaching MATHEMATICS ASSISTANT PROFES- KENTUCKY experience at the collegiate level, interest SOR - The Department of Mathematics at in teaching a variety of undergraduate Pittsburg State University invites applica- Berea College mathematics courses, experience using tions for a tenure-track position starting Berea College announces a full time, ten- technology in mathematics instruction, and August 2009 at the Assistant Professor ure-track position in the Mathematics and an active research program. level. The candidate must have an earned Computer Science Department, beginning doctorate in mathematics or a related dis- September, 2009. A Ph.D. in Computer To apply, send CV, cover letter describ- cipline by time of appointment. Preference Science or a Ph.D. in the mathematical ing how your qualifications match posi- will be given to candidates with interest in sciences is required. Preference will be tion requirements, a list of mathematics applied mathematics such as operations given to those with a willingness to teach courses taken in graduate school, a teaching research, numerical analysis, or stochastic at least some courses in both disciplines. A philosophy statement and description of processes. Salary is $45,000 with rank strong commitment to teaching is essential. current research (3-5 pages for each), and commensurate with experience. The Responsibilities center on mathematics and three letters of reference, including at least successful candidate will teach under- computer science teaching ranging from one that addresses teaching effectiveness graduate and graduate courses and direct introductory to advanced undergraduate. to: Ms. Cindy Locke, Human Resources, master’s-level research projects. The Above all we are seeking candidates who University of New England, 11 Hills Beach standard teaching load is 12 credit hours can achieve excellence in teaching and Road, Biddeford, ME 04005. Application per semester. Faculty are also expected to who, in an undergraduate environment, deadline: November 30, 2008. UNE is an continue a program of scholarly activity will find ways to grow professionally. All EEO/AA Employer. commensurate with the teaching load and to faculty in the Department are expected to contribute to the department and university interact with students on a one-on-one basis MARYLAND service missions. and in such activities as summer faculty/ student research, independent studies, or Salisbury University Pittsburg State University is a comprehen- senior capstone projects. The Department is Assistant Professor, Mathematics, sive regional university with an enrollment supportive of all forms of scholarship The Department of Mathematics and of approximately 7,000 students. The Computer Science (http://www.salisbury. Department of Mathematics is one of 14 Applicants should send a cover letter, edu/mathcosc/) at Salisbury University is departments in the College of Arts and resume, transcripts of graduate and un- inviting applications for a tenure-track As- Sciences. The department is comprised of dergraduate work, a statement of personal sistant Professor position in Mathematics a diverse faculty of 12 full-time members teaching philosophy, and three letters of beginning August 12, 2009. who are active in many areas of research recommendation to Professor James and service. Mathematics degrees offered Blackburn-Lynch, Chair, Mathematics For a detailed position description and include a BA, a BS, a BS with an emphasis and Computer Science Department, CPO information about applying please visit our in Actuarial Science, a BS in Education, 2146, Berea College, Berea, KY 40404. web site at http://www.salisbury.edu/HR/ and a MS. Applications must include a vita, Applications will be accepted until search Jobs/default.asp?asearch=faculty transcripts of graduate work, a statement on is concluded but full consideration is guar- teaching philosophy, evidence of effective anteed for those received by November Salisbury University is an EEO employer 29 MAA FOCUS November 2008 and is strongly committed to recruiting NEW JERSEY Mathematics is required, though a PhD in and retaining a diverse faculty, staff and Mathematics is preferred. We are seeking student body Rowan University an enthusiastic individual with excellent Assistant Professor, Tenure-Track, Ph.D. teaching, communication, and administra- MASSACHUSETTS in Statistics (preferred) or related disci- tive skills. The successful candidate will pline, Department of Mathematics, Rowan work with our department to provide our Williams College University, Glassboro, NJ 08028. Visit students with a comfortable transition from The Williams College Department of http://www.rowan.edu/jobs/ for details. high school to college, will encourage them Mathematics and Statistics invites applica- Requirements: a letter of application, cur- to pursue mathematics beyond the elemen- tions for one tenure track position in math- riculum vita, transcripts, and three letters tary level, and will coordinate departmental ematics, beginning fall 2009, at the rank of reference (which as a group must attest organizations and activities. Applicants of assistant professor (in an exceptional to statistical qualifications and to teaching must share our dedication to opening young case, a more advanced appointment may abilities). Completed application deadline women’s minds to mathematics while en- be considered). We are seeking a highly (for guaranteed consideration): January hancing their abilities to think both deeply qualified candidate who has demonstrated 15, 2009. Submit to Dr. Hieu Nguyen, and broadly. See http://www.brynmawr. excellence in teaching and research, and Chairperson, [email protected]. Rowan edu/math for a more detailed description who will have a Ph.D. by the time of ap- University values diversity and is commit- of the department and the position. pointment. ted to equal opportunity in employment. Applicants with excellent teaching and administrative skills should arrange to have Williams College is a private, coeduca- NORTH CAROLINA a cover letter, a curriculum vita, a statement tional, residential, highly selective liberal of teaching interests and philosophy, a list arts college with an undergraduate enroll- Wake Forest University of mathematics courses taken and taught, ment of approximately 2,000 students. The Applications are invited for two tenure official undergraduate and graduate tran- teaching load is two courses per 12-week track positions in mathematics at the as- scripts, and at least three reference letters semester and a winter term course every sistant professor level beginning August sent to: Search Committee, Department of other January. In addition to excellence in 2009. We seek highly qualified candidates Mathematics, Bryn Mawr College, 101 N. teaching, an active and successful research who have a commitment to excellence in Merion Avenue, Bryn Mawr, PA 19010- program is expected. both teaching and research. A Ph.D. in 2899. Applications may also be submitted mathematics or a related area is required. online through http://mathjobs.org. Appli- Applicants are asked to supply a vita and Candidates with research interests in Num- cations should be complete by December have three letters of recommendation on ber Theory, Combinatorics, or Algebra will 15, 2008. teaching and research sent. Teaching and receive first consideration. The depart- research statements are also welcome. Ap- ment has 20 members and offers both a Located in suburban Philadelphia, Bryn plications may be made on-line http://www. B.A. and a B.S. in mathematics, with an Mawr College is a highly selective liberal mathjobs.org/jobs). Alternately, application optional concentration in statistics, and a arts college for women who share an intense materials and letters of recommendations B.S. in each of mathematical business and intellectual commitment, a self-directed may be sent to Olga R. Beaver, Chair of mathematical economics. The department and purposeful vision of their lives, and a the Hiring Committee, Department of has a graduate program offering an M.A. desire to make meaningful contributions Mathematics and Statistics, Williams Col- in mathematics. A complete application to the world. Bryn Mawr comprises an lege, Williamstown, MA 01267. Evalua- will include a letter of application, cur- undergraduate college with 1,200 stu- tion of applications will begin on or after riculum vitae, teaching statement, research dents, as well as coeducational graduate November 15 and will continue until the statement, graduate transcripts and three schools in some humanities, sciences, and position is filled. For more information letters of recommendation. Applicants are social work. The College participates in a on the Department of Mathematics and encouraged to post materials electronically consortium together with Haverford and Statistics, please visit http://www.williams. at http://www.mathjobs.org. Hard copy can Swarthmore Colleges and the University edu/Mathematics. be sent to Stephen Robinson, Wake Forest of Pennsylvania. Bryn Mawr College is University, Department of Mathematics, an Equal Opportunity, Affirmative Action Williams College is committed to build- P.O. Box 7388, Winston-Salem, NC 27109. Employer. Minority candidates and women ing and supporting a diverse population ([email protected], http://www.math.wfu.edu ) are especially encouraged to apply. of faculty, staff and students, to fostering AA/EO employer. a varied and inclusive curriculum, and to Penn State University providing a welcoming intellectual envi- PENNSYLVANIA Penn State York invites applications for a ronment for all. As an EEO/AA employer, tenure track Assistant Professor of Math- Williams encourages applications from all Bryn Mawr College ematics position. Teach undergraduate backgrounds. To learn more about Wil- The Department of Mathematics invites math courses, primarily the first two years liams College, please visit http://www. applications for a continuing non-tenure of college mathematics (pre-calculus, tech- williams.edu. track position of Math Program Coordi- niques of Calculus I, Calculus I, II and III, nator to begin July 1, 2009. The position linear algebra, and differential equations; is a three-year appointment. It can be re- 18 credits per year). Assignments may newed for multiple terms. An MA/MS in include day, evening and Saturday classes.
30 November 2008 MAA FOCUS
Research and service expected. Ph.D. in pure or applied mathematics is required by time of appointment. Evidence of potential for excellent teaching, research and publication in high-quality journals, and professional growth is expected. To learn more about the campus and Penn State, visit http://www.psu.edu/ur/cmp- coll.html. To learn more about the posi- tion and how to apply, visit http://www. psu.jobs/Search/Opportunities.html and follow the Faculty‰ link. AA/EOE.
WASHINGTON
Pacific Lutheran University Tacoma, WA Department of Mathematics We seek to fill two tenure-track assistant professorships, one in mathematics and one in statistics, beginning September 2009. PLU is a comprehensive university offering a curriculum integrating the liberal arts and professional programs. A Ph.D. or doctoral degree in mathematics, statistics or a related field is required, as is evidence of exemplary teaching. For further information visit our website at www.plu.edu/employment. AA/EOE.
WISCONSIN
University of Wisconsin Oshkosh University of Wisconsin Oshkosh invites applications for two tenure-track Assis- tant Professor positions in Mathematics Education. Ph.D. in Mathematics with experience in and commitment to mathe- matics education or Ph.D. in Mathematics Education (or related field with equiva- lent of Masters degree in Mathematics), at least two years experience teaching undergraduate mathematics (including graduate TA experience), ability to ap- ply technology in classroom, potential to continue scholarly development, and student advisement required. Submit application letter, CV, statement of teach- ing philosophy and research interests, three current letters of recommendation and transcripts (official or photocopy) to: Chair, Mathematics Department, University of Wisconsin Oshkosh, Os- hkosh, WI 54901-8631 by January 16, 2009. Employment requires criminal background check. AA/EO employer. For additional information: www.uwosh. edu/mathematics.
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