MAA FOCUS The Newsmagazine of the Mathematical Association of America December 2008 | Volume 28 Number 9

WHAT’S INSIDE 4 ...... Mathematics and Accounting: A Non-Empty Intersection 7 ...... MAA National 2009 Elections Go Green 10 ...... ICME-11: Mexico, Mathematics, and Mariachis 14 ...... Enhancing Diversity in Graduate Education (EDGE)

FOCUS_Dec_08_FINAL.indd 1 11/10/08 12:29:28 PM MAA FOCUS December 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 9 Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA [email protected] 4 Mathematics and Accounting: A Non-Empty Intersection Senior Writer: Harry Waldman, MAA By Rick Cleary and Jay Thibodeau [email protected] 6 Teaching Time Savers: Working for a Week Please address advertising inquiries to: [email protected] By Bill Fenton President: Joseph Gallian 7 MAA National 2009 Elections Go Green First Vice President: Elizabeth Mayfield, Second Vice President: Daniel J. Teague, 8 What Happens After You Make It to the Tenure Track? Secretary: Martha J. Siegel, Associate By Robert W. Vallin Secretary: James J. Tattersall, Treasurer: John W. Kenelly 10 ICME-11: Mexico, Mathematics, and Mariachis Executive Director: Tina H. Straley By Annie Selden Director of Publications for Journals and Communications: Ivars Peterson 12 Play Review: A Disappearing Number By Barbara A. Jur MAA FOCUS Editorial Board: Donald J. Albers; Robert Bradley; Joseph Gallian; 13 Marcus du Sautoy Hopes to “Turn People On” to Mathematics Jacqueline Giles; Colm Mulcahy; Michael Orrison; Peter Renz; Sharon Cutler Ross; An- 14 Teaching Introductory Data Anaylsis Through nie Selden; Hortensia Soto-Johnson; Peter Stanek; Ravi Vakil. Modeling Workshop By Jean Scott Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of 14 Enhancing Diversity in Graduate Education (EDGE) Mathematics, Waterville, ME 04901, or by email to [email protected]. 15 In Memoriam Subscription and membership questions should be directed to the MAA Customer 16 The MAA Peru Study Tour Service Center, 800-331-1622; email: [email protected]; (301) 617-7800 (outside 19 The Dangers of Dual Enrollment-More Cause for Concern U.S. and Canada); fax: (301) 206-9789. MAA By Theresa A. Laurent Headquarters: (202) 387-5200. 20 What We Learned…by Starting a Seminar Series at a Copyright © 2008 by the Mathematical Association of America (Incorporated). Small School Educational institutions may reproduce By Isaiah Lankham and Jenny Switkes articles for their own use, but not for sale, provided that the following citation is used: 22 What I Learned…by Using an Online Homework System “Reprinted with permission of MAA FOCUS, in Calculus I the newsmagazine of the Mathematical By Sharon Vestal Association of America (Incorporated).” Periodicals postage paid at Washington, DC 24 2007 Individual MAA Donors and additional mailing offices. Postmaster: Send address changes to MAA FOCUS, 29 Employment Opportunities Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. ISSN: 0731-2040; Printed in the United States of America. On the cover: “The Dome,” by Mehrdad Garousi. See the description of this image see page 13. Used by the permission of the artist.

 December 2008 MAA FOCUS

AAAS Meeting in Chicago Features Mathematics and Applications

By Edward Aboufadel, Secretary of Section A of the AAAS

The 2009 Annual Meeting of the Amer- Joys of Recreation to the Frontiers of of AMS and MAA for travel support ican Association for the Advancement of Research and SIAM for support of media aware- Science will be held on February 12–16, (organized by Edward Aboufadel, Grand ness. The AAAS Program Committee is in Chicago, IL. The theme of this year’s Valley State and Patsy Wang-Iverson, genuinely interested in offering symposia meeting is “Our Planet and Its Life: The Gabriella and Paul Rosenbaum on pure and applied mathematical topics Origins and Futures,” which is a nod to Foundation) of current interest, and in previous years the fact that 2009 is the 200th anniversary there have been symposia on subjects of the birth of Charles Darwin and the Other symposia that will be of interest to such as mathematics and the brain, quan- 150th anniversary of the publication of the mathematical community include: tum information theory, the changing On the Origin of Species by Means of nature of mathematical proof, and the Natural Selection. Many of the symposia • New Computing Platforms for Data- mathematical analysis of the performance sponsored by Section A (Mathematics) Intensive Science of baseball players. are interdisciplinary sessions that fit this • A New Kind of Scientist: Profes- theme. sional Master’s Education and U.S. The 2010 meeting will be February 18- Competitiveness 22, 2010 in San Diego. The Steering The Annual Meeting is organized into • Artificial Cells: Models of the Sim- Committee for Section A seeks organizers symposia which have three or more plest Life and speakers who can present substantial speakers, and often a discussant who re- • The Grid, the Cloud, Sensor Nets, new material in an accessible manner to flects on the talks that are given. Section and the Future of Computing a large scientific audience. All are in- A is sponsoring six symposia this year, • Big, Small, and Everything in Be- vited to attend the Section A Committee featuring outstanding expository talks tween: Simulating Our World Using business meeting in Chicago on Friday, by prominent mathematicians. The six Scientific Computing February 13, 2009, at 7:45 PM, where symposia sponsored by Section A this • Providing Science Advice to the we will brainstorm ideas for symposia. year are: U.S. Congress: Is a New Paradigm In addition, I invite you to send me, Needed? and encourage your colleagues to send The Mathematical Twists and Turns of • The Evolution of Knowledge Pro- me, proposals for future AAAS annual Data Sets duction: Exploring Creativity, In- meetings. I can be reached at aboufade@ (organized by Robert Ghrist, University novation, and Networks gvsu.edu. of Illinois, Urbana-Champaign) • Earth’s History and Future Revealed at the Frontier of Scientific Comput- Steering Committee for Section A Games People Play: Challenges of Ap- ing February 2008 to February 2009: plying Mathematics and Computers to • K-12 Engineering Education in the Games United States Chair: William Jaco (organized by Bob Hearn, Dartmouth • Inquiry or Direct? Research-Based (Oklahoma State University) College) Practices in Science Education Chair-Elect: Keith Devlin • Interdisciplinary Approaches to the (Stanford University) Climate and Disease: Quantitative In- Study of Large-Scale Human Net- Retiring Chair: Carl Pomerance sights and Interdisciplinary Challenges works (Dartmouth College) (organized by Mercedes Pasqual, Univer- • The Science of Kissing Secretary: Edward Aboufadel sity of Michigan) (Grand Valley State University) The above symposia are only a few of the Green, Gene, Growing Machines: The nearly 200 AAAS program offerings in Members at Large: Evolutionary Shaping of Plant Form the physical, life, social, and biological (organized by David Baum, University sciences. For further information, includ- Mary Beth Ruskai of Wisconsin) ing the schedule of talks, go to http:// (Tufts University) www.aaas.org/meetings. David Isaacson Mathematical Biology, the New Frontier: (Rensselaer Polytechnic Institute) Educating the Next Generation AAAS annual meetings are the show- Claudia Neuhauser (organized by Bonnie Shulman, Bates cases of American science, and they en- (University of Minnesota) College) courage participation by mathematicians Warren Page and mathematics educators. Section A (City University of New York) Mathematics of Origami: From the acknowledges the generous contributions

 MAA FOCUS December 2008 Mathematics and Accounting: A Non-Empty Intersection

By Rick Cleary and Jay Thibodeau

Most people see mathematics Patterns, Deviations and and accounting as closely related Separating Examples subjects: both are quantitative fields that involve problem solving, and a Mathematicians see themselves as student with an exposure to only entry experts in pattern recognition. When level topics in each area would very a mathematician discovers a new reasonably conclude that they have a object, it is of course compared to great deal in common. A high school known cases, and then deviations algebra course and a first bookkeep- from the known forms are studied ing course, for example, each involve most carefully. Indeed, deviations learning some algorithms that, when lead to new classifications, and a correctly applied, lead to a specific search for generalization leads to result that is the unarguably cor- decision rules about how to classify rect answer; one that can in fact be objects. Separating examples become checked in the back of the book. a stock in trade, one that we expect students to learn even in first year When confronted with evidence of courses in calculus. (“Can you give this perception, for example when a an example of a continuous function new acquaintance says, ‘Oh, you’re that is not differentiable?”) in math? My sister-in-law is great at math, she’s an accountant,’ many Similarly, external auditors looking at mathematicians cringe. They look for the financial statements of a company some way to explain that we work in Cartoon by John Johnson or institution have many details to a field that requires great creativity consider, but at the core, they face and insight, as opposed to just book- innovation led to the creation of associ- what is very simply a binary-choice keeping. In a similar way, professional ated applied mathematical problems in problem: Either the financial statements accountants praised for being ‘good risk management, interest theory, and are free of material misstatement, or with numbers’ are quick to point out that modern actuarial science. they are not. And, if they are not, they there is much more to their work than require that some type of adjustment be just number crunching. They are often In a variety of teaching and research made. At the beginning of every financial proud of their quantitative abilities, but collaborations over the last six years, we statement audit, auditors will rely on their they view their work as much broader, have come to gain significant insight into prior experience and the patterns that are involving settling difficult real-world each other’s fields, with tangible benefits available in the data under consideration, questions, sophisticated decision making, in both our classrooms and our scholarly and seek to identify the deviations that do and communication skills. work. We believe that mathematicians not fit the pattern of a healthy company and accountants should not be so quick to to help make the classification. The end It has not always been the case that the reject the conventional wisdom that they result of these processes may differ (a leading academics in mathematics and actually have a great deal in common. In proof for mathematicians, a decision and accounting were so eager to enforce that this article, we present some of the ways a public statement from the auditor) but distinction. Indeed many great math- in which the work of both groups are there are similarities in process that are ematical discoveries have come about as surprisingly similar and we suggest that well worth considering. the result of attempts to solve problems there may be other topics that could lead in business and commerce. For an excel- to fruitful collaboration among our col- Because of the ‘high stakes’ involved in lent example, see Keith Devlin’s recent leagues. The examples we mention are, auditing publicly traded companies, the column on ‘The Big Mortgage Surprise’ of course, influenced by our specialties cognitive processes of auditors have been at MAA Online. Looking a little bit fur- within our respective fields (i.e., Rick carefully studied by accountants for some ther back into history, Devlin and other is a statistician, and Jay is an auditor). time. In fact, there is a substantial body historians also see the development of However we do believe that the general of research that has studied differences in modern double-entry accounting as a principles apply much more broadly even cognitive processes exhibited by auditors creative quantitative innovation that al- if we can not immediately produce a and then linked those differences to vari- lowed for trade and other types of com- problem that, for example, seems ripe for ous measures of audit judgment perfor- merce to dramatically expand during the joint work between a topologist and an mance. For example, Bedard and Biggs Renaissance. Over time, these types of expert on international taxation. (1991) found that auditors that were able

 December 2008 MAA FOCUS to recognize basic underlying patterns in large and small over a wide range of notation so that external auditors can a set of data were able to perform signifi- dollar amounts. Thus many auditing carefully consider the notions of ‘Type I cantly better in generating and evaluating software packages contain options to test error,’ ‘Type II error,’ and ‘power’ in the a hypothesis about a seeded error in the if the first digits in a particular set follow financial statement audit setting. data. One of the important conclusions of Benford’s law. If they do not, fraud is one this and related audit judgment research of several possible explanations that the As is often the case, when two fields is that pattern recognition is important auditor must explore. Accountant Mark have grown apart there are many ways in for auditors. Nigrini deserves much of the credit for which we can use joint research to edu- bringing this connection to the attention cate each other and provide great value Beyond the importance of pattern rec- of the audit community; see Nigrini and to both fields. We therefore urge our col- ognition, what other similarities exist Mittermaier (1997) for details. leagues to seek each other out and learn between the cognitive processes of expert about other areas of common ground to auditors and expert mathematicians? This auditing example follows the work together, or at the very least to be a Moreover, what are the other opportuni- cognitive framework familiar to both little less dismissive of each other. ties for collaboration that exist for ac- mathematicians and auditors. We have a countants and mathematicians? new object, in this case a firm’s financial References: records. Does this object conform to the Example: Sampling and expected pattern, in this case Benford’s Bedard, Jean and Stan Biggs (1991), Fraud Detection law? And if not, how do we classify the ‘Pattern Recognition, Hypotheses Gen- difference? Is it due to fraud, or is there eration, and Auditor Performance in an The authors of this article have worked an innocent explanation? It is also worth Analytical Task.’ The Accounting Review together at one important intersection noting Benford’s paper proposing this 66 (July): 622-642. of auditing and mathematics, the use of distribution appeared in 1938, and it was Benford’s law as a tool to detect fraud. nearly 60 years later that Nigrini and oth- Cleary, Richard and Jay Thibodeau Benford’s law refers to a probability ers in the field of accounting began to take (2005) ‘Applying Digital Analysis Us- distribution that is startlingly accurate at advantage of the result. It is one of many ing Benford’s Law to Detect Fraud: The representing the first significant digits of wonderful examples of how a ‘pure’ re- Dangers of Type I Errors.’ Auditing: A the entries in many real world data sets. search idea can prove to be an important Journal of Practice & Theory, (May). The Benford distribution is very differ- ‘applied’ idea some time later. ent from the uniform distribution that Nigrini, M.J. and Mittermaier, L.J. many people naively expect first digits While there are some caveats in the ap- (1997), ‘The Use of Benford’s law as an will follow. In fact if we say d is the first plication of Benford’s law to auditing Aid in Analytical Procedures,’ Auditing, significant digit, Benford’s law says that (see for example Cleary and Thibodeau Vol. 16, No. 2, 52-67 the probability that d is equal to i is 2005), the concept is a powerful one that

P(d = i) = log10((i + 1)/i) applies in many fields beyond business. Devlin, Keith (2008), Devlin’s Angle, for values of i in the set {1, 2, 3, … , 9}. A nice example is to sample addresses http://www.maa.org/devlin/devlin_10_ Note that this implies that entries begin- from residents in a local phone book and 08.html ning with 1 are roughly seven times as look at the first digits, which tend to agree likely as entries beginning with 9… you quite well with the Benford distribution. Rick Cleary is Professor and Chair of the can do the calculation to check! Or consider recent allegations of voter Department of Mathematical Sciences at registration fraud. Voters have addresses, Bentley University, visiting the Harvard How can this rather surprising result and one quick check of the validity of University Statistics Department for be of use to auditors? For a collection any list of voters would be to see if the 2008-09. He is a member of the Executive of values to follow Benford’s law, one first digits of the addresses conform to Committee of the Mathematical Associa- basic requirement is that the values span Benford’s law. tion of America, serving as chair of the several orders of magnitude. Think, for Budget and Audit Committees. example, of collecting the resting pulse This application also follows the cogni- rates (measured in beats per minute) tive process of looking for deviations Jay Thibodeau is Associate Professor from a large set of individuals. Would from an expected pattern, just the process in the Department of Accountancy at Benford’s law apply? Certainly not, that we claim that mathematicians and Bentley University. He is a member of resting pulses usually vary from around auditors (and no doubt people in many the Executive Committee of the Auditing 60 to 80, and a first digit of ‘2’ is nearly other fields) share. We believe that there Section of the American Accounting As- impossible! But what if the values are the are many other potential applications sociation, serving as the Secretary and collection of recent accounts payable for that bridge our two fields. In fact, at the the Past Chair of the Auditing Education a business? Then the restriction of many moment we are working on a project Committee. orders of magnitude is almost certainly to recast the model that auditors use to met, as business make purchases both assess risk into more standard statistical

 MAA FOCUS December 2008 Teaching Time Savers: Working for a Week

By Bill Fenton When I started as a teacher, my over- 3b. Create group activities, mostly based do the PERT analysis. Presented in this whelming question was “what am I going on illuminating examples. way, the content of one class relates more to do in class tomorrow?” That question clearly to the content of the previous and showed my mindset, thinking just one The extra thought about how to get succeeding classes. day ahead. What are the upcoming topics; groups involved added about 15 minutes how do they relate to the previous topics; to each class’ preparation time, though For cooperative learning purposes, how can I make all of this clear to the this decreased as I gained experience and planning for an entire week helps me students? There was always a deadline expanded my repertoire of cooperative incorporate a greater variety of in-class looming just ahead of me. This was a learning techniques. In total, a typical 50- activities for the groups, which helps nerve-wracking way to live! minute class was taking about an hour to to keep the students engaged with the prepare — and this happened three times presentations. When I sat down to prepare for a class, I a week for every course. typically used the following steps: A week’s preparation takes me about At some point about a decade ago I de- two hours per course (again with much 1. Read the appropriate section of the cided to plan over a longer period than variation by course). It is necessary to text. just tomorrow’s class. Now I prepare for find a block of time to do this, but the 2. Outline the major concepts from that an entire week’s classes of a course at one designated time is focused and produc- section. sitting. This has some real advantages tive — it is time well spent. I always 3. Create illuminating examples that over the day-by-day approach. First of have a real feeling of accomplishment were different from the examples in all, I have to assemble the necessary when an entire week’s classes are ready. the text. materials (text, references, calculator, Furthermore, the pressure of a deadline 4. Write the presentation, based on the software, etc.) only once a week. is gone for a while! outline and my examples. Secondly, the start-up time of getting my Time Spent: about two hours per course This preparation could take as little as mind focused on the particular subject preparation each week. This varies by 30 minutes for a precalculus class, or as happens only once. I teach lots of dif- course and by topic, but the total time is much as 90 minutes for abstract algebra ferent courses at different levels, from always less than that for several separate or some other upper-level course. The elementary statistics to discrete math to preparation sessions. time varied considerably, of course, de- advanced geometry to… It sometimes pending on the topic of the day. Linear takes me a few minutes to adjust my Time Saved: about an hour per week equations take a lot less prep time than frame of reference. per course. linear transformations! A real plus is that I always have more ma- Bill Fenton is Chair of the Mathematics Since my institution has a teaching terial ready to present in class, so I never Department at Bellarmine University mission, I typically taught three or four lose time at the end of a class period. I in Louisville, KY. He can be reached at courses per semester. It usually has been also believe that preparing for a week at a [email protected]. three courses per semester since I became time leads to greater connectedness from department chair, but often this is three one class period to the next. It has become different courses. Preparation time was very natural for me to design presenta- consuming a large part of my life. tions that introduce a concept in one class Teaching Time Savers are articles and extend it in the next class. designed to share easy-to-implement In the early 1990s, thanks to an intensive activities for streamlining the day-to- calculus reform workshop, I became a In Discrete Math, for instance, we define day tasks of faculty members every- user and proponent of cooperative learn- the concept of combination and develop where. If you would like to share your ing. This has affected every aspect of my the counting formula early in the week, favorite time savers with the readers teaching, especially the class preparation. then do some sample calculations and of FOCUS, then send a separate email I still begin to prepare for class by read- explore basic properties (such as Pascal’s description of each activity to Michael ing the section and outlining the major Identity) later in the week. This gives Orrison at [email protected]. Make concepts, and I still write the presentation students time to digest the basic notion sure to include a comment on “time at the end. However, step 3 has split into before working with its ramifications. spent” and “time saved” for each ac- two parts: In Operations Research, we spend one tivity, and to include pictures and/or class drawing a project network and figures if at all possible. 3a. Decide how best to involve the stu- finding the critical path, then at the next dent groups. class we return to the same project and

 December 2008 MAA FOCUS MAA National Elections 2009 Go Green A Letter to MAA Members

Dear Members,

The MAA National Elections will be held in April and May 2009 This is your opportunity to influence the future of the MAA. It in accordance with Article IV, Sections 1(a) and 2 of the Bylaws is important for these decisions to be made by us, the members. of the Association. You will be asked to vote for candidates for This year we have made some slight adjustments to the voting national officer positions who will assume their respective of- procedures in order to make it easier for our members to vote as fices in January 2010. These positions are President-Elect for a well as to make our elections more environmentally friendly by term of one year (who will become President in 2011 for a term reducing our use of paper ballots. I encourage you to read the of two years), First Vice-President for a term of two years and detailed information below and I invite everyone to vote. Second Vice-President for a term of two years. Martha Siegel, Secretary

Make Sure You Participate! Membership List (CML) does not necessarily mean it is included in the MAA database. Email Only and Paper Ballot By Special Request Requesting a Paper Ballot All members for whom the MAA has an email address on file by February 20, 2009 will receive an email ballot only. This Members who wish to request a paper ballot must do so by email ballot allows for direct voting. It is personalized and no February 20, 2009 through one of the following methods: specific login is necessary. A member for whom the MAA does not have an email address on file by February 20, 2009 will not 1. Email: Send an email with your name and address to receive an email ballot and will receive a paper ballot only if [email protected]. the member has specifically requested it. 2. Mail: Write your request, including your name and address, and send to: Does the MAA Have My Email Address? MAA National Elections 2009 The MAA has your correct email address on file, if you receive 1529 18th Street NW the monthly e-newsletter MathAlert. This e-newsletter is usu- Washington, D.C. 20036 ally sent to members in the middle of each month. If you do not 3. Fax: Fax your request to (202) 387-5948. Be sure to include receive MathAlert, this means that the MAA probably does not your name and address. have your (correct) email address on file. 4. Phone: Call the MAA front desk at (800) 741-9415 to be Checking or Adding Your Email connected to Calluna Euving or Susan Kennedy. Please leave your name and address with either of them. All members can update their personal contact information by following these steps: Questions and Information

1. Go to http://www.maa.org/myaccount. The ballots will be sent out in early April. The elections run through April and May. Should you have any questions or 2. Log in using your User Name and Password. concerns, please contact Calluna Euving or Susan Kennedy at Your User Name is your email address unless you have the MAA headquarters. changed it. If we do not have an email address on file for you, your User Email: [email protected] Name will be your eight-digit Member Number including the Phone: (800) 741-9415 or (202) 387-5200 leading zeros. If you have forgotten your password, please use Fax: (202) 387-5948 the Forgot Password link. Questions? Contact MAA Member- Mail: MAA National Elections 2009 ship Services at (800) 331-1622 (U.S. only) or (301) 617-7800 1529 18th Street NW (outside the U.S.) or via email at [email protected]. Washington, D.C. 20036

3. Once you have logged in, you can add or edit an email ad- Go Green! dress by going to Communications Methods at the bottom of the page and adding or editing as you wish. In order to save time, money, and the environment, we encour- age all members to use their email address for this important Please note that your email address appearing in the Combined process. Thank you!  MAA FOCUS December 2008

What Happens After You Make It to the Tenure Track?

By Robert W. Vallin

Congratulations! You’ve made it to the information, visit their web site at: http:// You will find many classes, workshops, tenure track. Soon you will be settled into archives.math.utk.edu/projnext/. et cetera at the Mathematical Sciences your new office, placed all your books Research Institute (see their web site and journals up on the shelves, and writ- For those who are not involved in the at http://www.msri.org), as well as sev- ten syllabi and lesson plans. You’re also national NExT Program, many sections eral summer workshops to participate preparing your thesis for publication, and run their own Section NExT. Faculty in through the Center for Discrete Math starting on new projects. No worries. members who are within four years of and Theoretical Computer Science (see graduation and in their first four years on http://dimacs.rutgers.edu). The Institute Except… the tenure track may join a Section NExT. for Advanced Studies runs the Park City Section NExTers have workshops and Mathematical Institute, which has an an- What can I do to learn to teach a subject panel discussions along with meeting as nual summer program for mathematicians I’ve never studied? a group during the academic year. Joining of all kinds; (see http://pcmi.ias.org). Section NExT also facilitates meeting How do I balance work and family? others in your geographical area and What if there is no minicourse that you opening up your personal network. wish to take? There are still ways to get What’s the technique for writing a grant career help and advice at meetings like proposal? Women can also find mentoring through the JMM. Welcome to the world of panel the Association for Women in Mathemat- discussions. Panels are great because you How can I get more deeply involved in ics. Information on the AWM Mentoring will hear different points of view from this new research topic not related to my Network can be found through their web people eager to share their experiences. It thesis? site at http://www.awm-math.org/. is also nice to realize that you are not the only person with your questions. Where are the resources I need? Completing your dissertation and finding your new job was a major component of Going back to the program for the 2008 Starting up your career on the tenure track how you spent your last days in gradu- JMM we find “How to Interview for a Job can be a real challenge. Perhaps it’s due ate school. It takes a lot of time, energy, in the Mathematical Sciences,” “Excit- to the increase in the number of classes and focus to finish. Now there’s some ing, Surprising, and Satisfying: Why and you teach, or adjusting to being a faculty mathematical freedom. Perhaps you wish How to Teach Proof,” and “Tenure (and member and not a student, or the juggling you knew more about bringing java into Promotion) – You Know You Want It.” act of teaching, research, and service. the classroom, or maybe you’d like to This last panel was co-sponsored by Proj- In case you run into problems, or better learn some fascinating new ways to look ect NExT and the Young Mathematician’s yet to head them off before they become at combinatorics. Both of these ideas Network. The YMN was founded in 1993 a problem, we will look at some of the you can do on your own. After all, that’s and refers to itself as a “loose organiza- resources available for new faculty. one of the implications of earning your tion of mathematicians in the junior part doctorate: you have the ability to research of their careers.” Their web site is exten- No discussion for newly minted faculty and learn on your own. sive and covers too many topics for us to is complete without mentioning Project delve into here. Their Concerns of Young NExT (New Experiences in Teaching). But you don’t have to. Both the MAA Mathematicians page is http://concerns. This is an MAA program for new or re- and the AMS run courses at the Joint youngmath.net/. cent PhDs in the mathematical sciences. Mathematics Meetings (JMM), which Despite the acronym, it is not exclusively provide intense but enjoyable forays Courses and panels are also available at about teaching, NExT helps in all areas into new topics. For example, this past section meetings. In Spring 2008 the Tex- of a career. January in San Diego the MAA ran 16 as Section Meeting offered a minicourse minicourses on topics such as “Teaching on “Integrating Biological Applications Participants are matched up with men- a Galois Theory Course for Undergradu- in the Mathematics Curriculum,” while tors, and workshops cover very diverse ates,” “Mathematics and the Geometry the Pacific Northwest Section offered topics such as “Alternate Methods of As- of Voting,” “Developing Department two courses, “Women and Minorities sessing Student Achievement,” “Writing Self-Studies,” and “The Fibonacci and in Mathematics” and “Active Learning Grant Proposals,” and “Involving Under- Catalan Numbers.” Also at the meeting Through Classroom Voting and Click- graduates in Mathematical Research.” was a two-day AMS short course entitled ers.” The 2007 Allegheny Mountain Sec- Slots in Project NExT are awarded on a “Applications of Knot Theory.” tion meeting had a panel discussion on competitive basis. About 70 new NExT “Atypical Careers in Mathematics.” Fellows are admitted per year. For more Other organizations have courses, too.

 December 2008 MAA FOCUS

Available outside of the larger meetings Of course, when you find a topic that The first few years of a career on the ten- are the Professional Enhancement Pro- excites you, you wish to share your en- ure track can be an amazing time. While grams (PREP) of the MAA. These are a thusiasm with others who feel that way. getting acclimated to your new location, series of non-interrelated workshops for In school that was easy because there you have the opportunity to look at ev- the professional development of faculty were other students taking those subjects. erything mathematically available and in the mathematical sciences. They are Nowadays you can still become part of decide what you want to become. held in many locations throughout the the community in Math and Biology, or country during the summer. History of Math, or Statistics Educa- Whether you stay with your thesis tion, or more by joining a SIGMAA. topic or branch out into something new, Just a few of the Summer 2008 work- Yes, that’s spelled correctly; it stands for whether you want to focus on courses for shops include “Flash in the Valley: Cre- Special Interest Groups of the MAA. The majors or focus on pre-service teachers, ating Mathlets with Adobe Flash” (Ship- web site for the SIGMAAs is http://www. whether you wish to become a member pensburg University of PA), “Expository maa.org/SIGMAA/. of the nationally known mathematics Writing to Communicate Mathematics” community or help make your section of (MAA Headquarters, Washington, DC), Currently there are 11 different SIG- the world as great as possible, there are and “Inquiry-Based Learning with a MAAs. More than a listserv or web site, programs, workshops, panels, web sites, Focus on Number Theory” (University some SIGMAAs have events during the and more to help you. Take advantage of Texas, Austin). Two PREP workshops JMM or produce a newsletter where of everything out there. You’ll be glad will be taught online this summer (“Cal- research and teaching topics can be dis- you did. culus, Online and Interactive” and “Ge- cussed. Remember, if you do not see a ometry and Art”). For more information SIGMAA that intrigues you, get together Robert Vallin is Professor of Mathematics about these workshops, go to http://www. with like-minded people and begin one at Slippery Rock University and MAA As- maa.org/PREP. of your own. sociate Director for Student Programs.

Technically Speaking Currents on Teaching and Learning links to Public speaking is a common fear. Even Teaching Time Sav- people who are confident about what they are saying (e.g., knowing that they have ers a proof), may be nervous about where they are saying it (at a meeting). Joe Gallian has written two articles for Math Currents in Teaching and Learning is Horizons on giving a good presentation. the new peer-reviewed online publication His tips can be read in one of the MAA of the Center for Teaching and Learning brochures (which can be found on the at Worcester State College. Currents MAA’s student webpage http://www.maa. Volume 1, Number 1 (Fall 2008) has now org/students/). been posted at http://www.worcester.edu/ Currents/. The first issue includes a “Clips Now these tips can been seen in action! and Links” section with pointers to online Lew Ludwig, of the Department of Math- resources on teaching and learning. The ematics and Computer Science at Deni- first one listed is the online archive of our son University, has put together a DVD MAA on a first come, first served basis. Teaching Time Savers series which can, entitled Technically Speaking… A Video Just visit: http://www.maa.org/Surveys/ of course, be found on the MAA web site Guide to Giving Effective Oral Presenta- TakeSurvey.aspx?SurveyID=n2LL879, fill at http://www.maa.org/features/Teaching- tions. Using a series of video vignettes, in the request form, and a copy will be TimeSavers.html. he shows students (and anyone else) the sent to you. That’s all there is to it. Now common pitfalls of an oral presentation is a great time to take advantage of this, and how to avoid them. Best of all, thanks with students preparing to go to the Joint to a generous grant from the NSF, these Mathematics Meetings in January and/or videos are available for free from the spring Section Meetings to give talks.

 MAA FOCUS December 2008

ICME–11: Mexico, Mathematics, and Mariachis

By Annie Selden

The 11th quadrennial Inter- not realized the extent of national Congress on Math- the educational difficulties ematical Education, was held involved in education in a in Monterrey, Mexico, July 6 nation of 300,000 square –13, 2008, on the campus of kilometers, 7107 islands, the Universidad Autónoma 88.6 million people, 12 de Nuevo León (UANL). native languages, 170 There were 2133 participants dialects, and seven ma- from 89 countries. I person- jor ethnic groups. Cath- ally met participants from erine Vistro-Yu of Manila South Africa, New Zealand, University said that most Australia, England, France, math taught is “colonial Norway, Greece, Italy, Israel, math” (whatever that is) Iran, Argentina, Venezuela, and that there is a lack of and Mexico. textbooks, but also that teachers are not prepared The aim of ICME–11 was to Group of mathematics educators receiving NCTM travel grants. to teach from textbooks. “show what is happening in Back row: Bill McCallum, Annie Selden, Jerry Becker, Hortensia That certainly is differ- mathematics and mathemat- Soto-Johnson. Front row: Angie Mentges, Kazuko West, Yvonne Lai, ent from the U.S. where ics education worldwide, in Steve Williams. teachers tend to stick very terms of research as well as close to the textbook. teaching practices” and to was the size and shape of an MAA Notes “inform about the problems of mathemat- volume. In a third plenary, Olimpia Figueras of ics education around the world.” Its logo, CINVESTAV, a research institute for emblazoned on the requisite tote bags Monterrey is a prosperous, industrial, mathematics education in Mexico City, stuffed with assorted Congress materials, Mexican city. One interesting feature noted that 13% of Mexico’s population, was an ingenious Mayan Möbius band. was the Parque Fundidora. Constructed some 12.7 million people, is indigenous. on the site of former industrial plants, A 1992 reform of the constitution defined ICMEs are held every four years under the opening reception, complete with Mexico as a multicultural and plurilingual the auspices of the International Commis- Mariachis, was held here in a brewery country, whereas previously the country sion on Mathematical Instruction (ICMI), turned museum. had aimed for cultural homogenization. which was first established at the Interna- tional Congress of Mathematicians held Four Interesting Plenary Panels While multiculturalism recognizes diver- in Rome in 1908, with Felix Klein as sity and leads to a policy of integration in its first president. In 1952, it became an The Plenary Panel on the “History of the the national society, pluriculturalism rec- official commission of the International Development of Mathematics Educa- ognizes ethnic and linguistic differences Mathematical Union (IMU). tion in Latin American Countries,” had as socio-cultural enrichment factors and speakers from Mexico, Brazil, Chile, and as valuable resources for society as a The 2008 ICME was a smorgasbord of Cuba. Of the many facts the panelists whole. Figueras asserted that multicultra- nine plenary talks and panels; reports mentioned, some of the most surprising lism does not offer equal access to edu- of Survey Teams commissioned in ad- to me concerned Cuba. Luis Campistrous cation because indigenous language and vance to study particular topics such as said that his country’s pupils were in culture have a different status, whereas representations and the role of theory in school eight hours per day every-day, pluriculturalism offers equal access to mathematics education research; 60 regu- that some schools have only one pupil education. In 1990, Mexico set up a study lar hour lectures in 12 parallel sessions; and a computer, and that all teachers have program for indigenous teachers at the 38 topic study groups covering topics technical support. National Pedagogical University. such as new developments and trends in mathematics education at all levels, Just like in the U.S., there is worldwide A fourth Plenary Panel reported the re- gender, task design, and history; and concern with equity and access, and there sults of Survey Team 4 on “Representa- 28 discussion groups on topics such as was another plenary panel, “Equal Access tions of Mathematical Concepts, Objects curriculum reform, promoting creativity, to Quality Mathematics Education,” with and Processes in Mathematical Teaching and rethinking the PhD in mathematics speakers from Mexico, Lebanon, and the and Learning,” and was presented by education. The program booklet itself Philippines. Regarding the latter, I had Gerald Goldin of Rutgers University and

10 December 2008 MAA FOCUS

Katrin Rolka of Germany. Some of the by asking how we should deal with the central questions delineated by the team complexity of learning processes. She were: How do we characterize conceptual interspersed her philosophical remarks understanding in mathematics education? within an example of two four-year- Through multiple representations? As a olds, Roni and Eynat, who were given process of construction of mathematical two identical closed boxes containing objects? According to students’ under- marbles and asked which box had more standings in number and numeration, marbles. Without looking or counting, fractions, data representations, etc.? By they agreed it was Box A. When asked, processes of modeling mathematical “How do you know?” they simply said situations? By considering affect as a Box A was “more huge.” They had to be representation encoding information and urged to count (correctly) the marbles in exchanging information with cognitive each box. systems of representation? By construc- tion of one’s mathematical identity? This prompted Sfard to ask: What is a number and where is the child sup- Many problem-solving studies focus on posed to find it? Her answer: Number is representations. Different countries make The ICME 11 logo. a discursive construct people created to use of different approaches, e.g., the communicate about the world. It is to be Chinese have a concrete view of average found in discourse, not in the world. She whereas the U.S. uses concrete represen- doing various problems that started “Give also asked, if learning is change, what tations of data. There exist opportunities me an example, if possible, of …” One is it that is supposed to change when a and pitfalls in using representations: (1) such problem was “Give me an example, person learns mathematics? Her answer: They can increase cognitive load; (2) if possible, of an injective function on Thinking changes, but what is thinking? They include irrelevant aspects; (3) Flu- [–2, 2] whose limits as x approaches –2 To this she replied: It is communication, ency with representations may indicate and as x approaches 2 are equal.” with the caveat that communication does conceptual understanding; however, not have to be verbal. This led her to researchers Presmeg and Nenduradu Antonini is interested in what strategies introduce the notion of “commognition” have given an example of a teacher with students use to generate examples. After for a blend of communication and cogni- representational fluency who mixes up briefly mentioning trial and error, he tion, which in turn, led her to the view linear and exponential functions; and (4) discussed two additional strategies: a of mathematics as discourse. So what genuine abstraction is not the same as transformational one and an analysis one. does it mean to learn mathematics? Her decontextualized representation. In the transformational strategy, students answer: It means changing the discourse. produce an initial example, and upon This interesting, and perhaps unusual, Technology can add dynamics to repre- realizing it does not satisfy at least one of view is developed further in her book, sentations and students can work with the required properties, modify it. Thinking as Communicating: Human multi-linked representations. There are Development, the Growth of Discourses, questions about how students relate to In the above example, students at first and Mathematics. new technologies, questions about visu- said such a function could not be pro- alization and imagery, questions about duced because they had implicitly as- With the plethora of sessions, there was social and socio-cultural perspectives and sumed continuity, but after being urged enough for all participants to find some- semiotics. Goldin asked: What is needed to look again, they realized continuity thing of interest at ICME–11. The next is a persuasive large-scale study on the was not one of the requested properties. International Congress on Mathematical effectiveness of representations. For ex- Such modification can be done several Education, ICME–12, will be held in ample, what’s most effective? Number times, in a way reminiscent of successive Seoul, Korea, July 8–15, 2012. line models or area models? Also, what approximations. In the analysis strategy, is representational power and how does students assume there is such an example, Annie Selden is Professor Emerita at one measure it? consider what properties it must satisfy, Tennessee Technological University and and then try to produce it. Most students Adjunct Professor at New Mexico State Two Interesting Regular Lectures use a combination of the transformational University. and analysis strategies. Samuel Antonini of University of Pavia in Italy gave the Regular Lecture, “Gen- Anna Sfard, of the University of Haifa erating Examples: An Intriguing Problem and Michigan State University, presented Solving Activity.” He reported on his the Regular Lecture, “Learning Math- research project that involved task-based ematics as Developing a Discourse.” interviews of secondary students, under- With a philosophical turn of mind and graduates, and PhD mathematics students never one to think small, Sfard began

11 MAA FOCUS December 2008 Play Review: A Disappearing Number

By Barbara A. Jur Theater has discovered math- pany policy does not allow it, as ematics as a plot theme. A new “Barbara Jones” explains. She British play, A Disappearing has a pronounced Indian accent Number, by Simon McBurney, despite her English name. They has joined the ranks of Arcadia have several funny conversa- (1993), Proof (2001), and the tions until the end of the play films Good Will Hunting (1997) when she tells him that she has and A Beautiful Mind (2001) as lost her job because the company drama with mathematics playing is recalling the office to England. a significant role. Her name is Lakshmi.

The source of much of the play’s The play is often funny, but ulti- action is the interaction between A scene from A Disappearing Number. Used by permission mately it is about loss. Ramanu- Ruth, a university mathematician, of Complicite. jan dies. Ruth dies. Lakshmi and Al, an American/East Indian loses her job. How we choose futures trader, who pursues and stage and off the stage. This provided to deal with such losses may marries Ruth despite an almost total an amazing and continuous flow to the give them meaning. Hardy worked on incomprehension of what she does. In story line. explaining his protégé’s mathematics. Al parallel, we see the story of the col- reconnects with his roots by journeying to laboration of Srinivasa Ramanujan and Cultural divides permeate the tension India where Ruth died. He also discovers G. H. Hardy. among the characters — like invisible the significance of 1729. walls. Hardy and Ramanujan were sepa- In A Disappearing Number, the audience rated by their approaches to mathemat- The play is staged by Complicite, a Brit- has the opportunity to see real mathemat- ics. Ramanujan was self-taught and did ish Company. It is an amazing production ics — specifically number theory. In fact, not see the need for proofs. Hardy was a which combines action, dialog, staging, the actors admit that nothing is real about formalist who struggled to understand the Indian music, and video in a thoroughly the play except for the mathematics, insights of his Indian colleague. Al and engrossing performance. If you have which is present in the play to a much Ruth struggle to understand each other’s an opportunity to see A Disappearing larger extent than in Good Will Hunting, work. Al happens to be of East Indian Number, do not miss it. with its brief glimpses, or Arcadia, in descent and has interactions with others which the equations described in poetic who have a similar heritage. He has a Barbara A. Jur is Associate Dean of terms but never seen, or Proof, in which recurring encounter with the customer Mathematics and Science at Macomb we only hear of the process of working service representative of his cell phone Community College in Warren, MI. This out “lumpy,” or “elegant” solutions to company, who is heard as a voice over. review is based on a showing of the play problems. Ruth is seen lecturing on one He wants to change his phone number to at the University of Michigan. of Ramanujan’s results, which she pres- his deceased wife’s number, 1729. Com- ents in its entirety on a white board. When she encounters Al, she tries to explain A Disappearing Number what she does by talking about sums of sequences, which gives the audience Directed by Simon McBurney with music by Nitin Sawhney a hint, if not full understanding, of the direction the mathematics is taking. Prizes: Laurence Olivier Award 2008 for Best New Play The staging was a strong element of Evening Standard Award 2007 for Best Play the production. Although the stage was Critics’ Circle Theatre Award 2007 for Best New Play almost bare, there was a wall and a flip board dividing the stage front to back. Currently on tour in Australia; there are plans to bring the play to New York in the The wall functioned variously: as a Fall of 2009. projection screen for action clips of city scenes in India, as white board, and as a An adaptation for radio was presented by the BBC on September 21, 2008. scrim that allowed action to be observed in the front and rear of the stage simul- Presented by Complicite; see http://www.complicite.org for more information about taneously. The flip board allowed actors this and other productions. to pass from the front to back of the

12 December 2008 MAA FOCUS On the Cover: Marcus du Sautoy Hopes to “Turn People On” The Dome to Mathematics By Mehrdad Garousi Oxford Mathematician Marcus du The aim of the Sautoy has been named the new Simonyi Simonyi Pro- At first glance, this work reminds us Professor for the Public Understanding of fessorship at of the interior tiling of Islamic mosque Science, a post held by biologist Richard Oxford is “to domes. In these mosques, tiles and forms Dawkins until his recent retirement. The communicate on the sides of the dome view seem new position, which took effect on De- science to the smaller due to spherical shape and much cember 1, 2008, recognizes and supports public without, smaller as we approach the center, which du Sautoy’s work as a popularizer and in doing so, los- is more distant. But this image, on a flat expositor of mathematics ing those ele- surface, goes beyond and continues this ments of schol- tiling not to the dome center but to infin- As a number theorist, du Sautoy has arship which ity. As we move toward the inside of the done significant research on such things constitute the Marcus du Sautoy. picture, the tiles get smaller in a fixed as zeta functions, elliptic curves, and essence of true Photograph by Niall p-adic Lie groups. He is the author of ratio to the previous tiles and keep their understanding.” McDiarmid. coherence and continuity in a certain ratio two books for the general public: The It was estab- as well, making the image fractal. Music of the Primes, which is a tour of lished in 1995 number theory centered on the Riemann by a donation from Dr. Charles Simonyi, As in Islamic tiling, color plays a key Hypothesis, and Symmetry: A Journey and was first held by Richard Dawkins. role in this work, increasing the clarity into the Patterns of Nature, whose UK The new appointment was announced on of forms like flowers or stars in the tiles. title, Finding Moonshine, reveals it to October 28; see http://www.ox.ac.uk/me- Here the very small basic rectangular be about the mysterious connections dia/news_stories/2008/081028.html. and triangular mosaics make hexago- between distinct mathematical embodi- nal and six pointed star flowers, all of ments of the notion of symmetry: groups In an interview with the Guardian, du which match side by side and create an and modular forms. A third book, entitled Sautoy said that he feels “a bit of geek infinite seamless texture with a nice self The Num8er My5teries: A Mathematical chic is coming in” and hopes to be able similarity at the center. Notice that the Odyssey Through Everyday Life, is forth- to get people excited about mathematics: colors of the mosaics in the image are coming in 2009. In addition to books, “I don’t want to preach to the converted, I like the colors used in real dome mosaics: du Sautoy has written many newspaper want to capture the people who say they orange, lemon, amethyst, blue, pink, and articles and columns, participated in tele- hate maths. I see people like that as a grass green. vision programs, and undertaken many challenge. Once you show them it’s not other activities in the world of culture. a load of boring multiplication and long (Used by permission of the artist. See He was the mathematics advisor for the division, you can say it has beauty and http://mehrdadart.deviantart.com/ for play A Disappearing Number (see page aesthetics and excitement and drama and more of Garousi’s work.) 12). His web site, at http://people.maths. emotion. Those are things I think might ox.ac.uk/~dusautoy/, has separate sections turn people on.” on “left brain” activities (communication of all sorts) and “right brain” activities (research in mathematics).

Archimedes Palimpsest Data Released

On October 29, exactly ten years after it is possible to read the older text, which and the associated project can be found a private American collector purchased in this case contains work by Archimedes at the project’s web site at http://www. a Greek manuscript containing several and others. The history of the manuscript archimedespalimpsest.org. The dataset works by Archimedes, the Archimedes and the story of the efforts to restore it itself is available at http://www.archi- Palimpsest Project announced that their and read the underlying text are told in a medespalimpsest.net. The dataset was data would be released online for the use wonderful book for “the general public,” published under a Creative Commons of scholars. The manuscript is a palimp- The Archimedes Codex, by Reviel Netz 3.0 attribution license, which assures it sest, which means that the parchment and William Noel (Da Capo Press, 2007; can be easily accessed and used. In fact, pages have been washed and new text see MAA Reviews for more). a complete facsimile of the revealed texts written over the older material. With spe- is available on Googlebooks as “The cial imaging techniques and a lot of work, More information on the palimpsest Archimedes Palimpsest.”

13 MAA FOCUS December 2008 Teaching Introductory Data Analysis Through Modeling Workshop By Jean Scott Going to JMM? The Consortium for models can be used for description, the Logistics: Sunday, January 4, 2009, the Advancement of Undergraduate interpretation of models in terms of asso- 8:30am–5:00pm at the Marriott Ward- Statistics Education (CAUSE), in con- ciation, change, and partial change (that man Park Hotel located at 2660 Wood- junction with SIGMAA Statistics Edu- is, change in one variable while holding ley Road, NW Washington, District Of cation, is very pleased to offer an MAA others constant). In place of the usual Columbia. There is no registration fee Auxiliary Workshop on Sunday, January matrix-based theory of linear models, for this workshop. Workshop materials 4, 2009 — the day preceding the Joint the workshop will present a geometrical and lunch during the workshop will be Mathematics Meetings in Washington, approach to theory that is accessible to in- provided. Workshop participants are D.C. The presenter for the workshop is troductory students and fully illuminates encouraged to bring their own laptops. Danny Kaplan of Macalester College. important ideas in data analysis: fitting, Workshop participants are responsible for The intended audience is teachers of confounding and Simpson’s paradox, their own transportation and lodging. Be introductory statistics in colleges and correlation and collinearity. Inference is sure to register for JMM and book your universities. introduced using resampling and simu- rooms early through their lodging service lation, from which it is straightforward to obtain conference rates for your JMM This hands-on workshop will present a to transition to a general framework stay. Enrollment is limited to 40. For new way of teaching introductory data for inference, analysis of covariance. registration and additional details go to analysis that gives a central role to mod- Computation (using the free package R) http://www.causeweb.org/workshop/mod- eling techniques. Modeling provides a will feature prominently in hands-on ac- eling_jmm09/ strong unifying framework for statistics tivities; participants should bring laptop and at the same time ties statistics closely computers if possible. Participants do not Jean Scott is Program Coordinator for to the scientific method and the demands need to have previous experience with R CAUSE. She can be reached at jscott@ of realistic multi-variable data. The work- or with statistical modeling. Our students stat.osu.edu. shop will introduce the ways in which can learn it and so can you!

Enhancing Diversity in Graduate Education (EDGE)

The EDGE Program was launched in 1998 by Bryn Mawr College and Spelman College with the goal of strengthening the ability of women students to successfully complete graduate programs in the math- ematical sciences, with particular inclu- sion of women from minority groups. The 2009 EDGE Summer Program will be held June 8 to July 3 on the campus of Spelman College with local coordinator Fred Bowers and national co-directors Sylvia Bozeman and Rhonda Hughes. EDGE 2006 Participants, Staff, and Faculty, New College, Sarasota, Florida. The EDGE Program provides courses in analysis and algebra, a topical mini completed standard junior/senior-level dation from mathematics faculty; (4) a course, guest lectures, and advanced undergraduate courses in analysis and transcript; (5) a current resume; and (6) graduate student mentors. The Program abstract algebra and expect to earn a a ranked list of graduate programs to also provides follow-up mentoring and PhD in the mathematical sciences. Par- which the applicant has applied. For ap- networking opportunities throughout the ticipants are provided travel, room and plication materials and more details, visit academic year. board, a stipend of $2,000, and a small the website at http://www.edgeforwomen. research fund. org/. The deadline for applications is Applicants to the EDGE Program must March 6, 2009. be women who have applied to graduate Applications should include: (1) a com- programs in the mathematical sciences pleted application form; (2) a personal for Fall 2009. All applicants should have statement; (3) two letters of recommen-

14 December 2008 MAA FOCUS In Memoriam

Andrew Gleason died on October ful course notes. He was generous with 17, 2008, at the age of 86. Born in 1921, ideas and wore his immense knowledge Gleason showed a talent for mathemat- very lightly. Everyone who interacted ics early on. He graduated from Yale in with him came to respect him. 1942, and then enlisted in the Navy to do cryptographic work. In 1946, he was ap- Gleason was always interested in teach- pointed to Harvard’s Society of Fellows. ing. Beginning in the mid-1980s, Gleason He was still a Junior Fellow when he became involved in “calculus reform.” did his work on Hilbert’s Fifth Problem, This eventually led to the “Harvard which established him as an important Calculus Consortium” and the calculus mathematician. textbook that he co-authored with Debo- rah Hughes Hallett and others. People Gleason reenlisted in 1950 to do crypto- who interacted with Gleason during that graphic work during the Korean War. The period remember his deep interest renew- details of his activities are (of course) not ing calculus teaching, his sharp analyses known, but rumor has it that he was not of what was essential (and what wasn’t) students, including several well-known surprised by the revelations to be found in a calculus course, and his willingness names. (The list may well be incomplete.) in the famous “Venona” transcriptions of to put his prestige behind what was still Gleason retired in 1992. Soviet communications. a controversial project. As a mathematician, Gleason is best After the war, he returned to Harvard, Gleason was a longtime member and known for his work on Hilbert’s Fifth was promoted, and eventually was named supporter of MAA. In 1996 he received Problem, which he solved together with Hollis professor of Mathematics and the MAA’s highest honor, the Yueh-Gin Deane Montgomery, Leo Zippin, and Natural Philosophy. The Mathematical Gung and Dr. Charles Y. Hu Award for Hidehiko Yamada. He was a remarkable Genealogy web site lists eighteen PhD Distinguished Service to Mathematics. and inspiring teacher, known for his care-

Saint Louis University offers master’s and doctoral programs of study in mathematics. The M.A. program provides a strong foundation in algebra, analysis, and topology preparing graduates for continued study and careers in teaching and industry. The Ph.D. program brings students to the forefront of mathematical research and pre- pares graduates for research and teaching ca- reers. The Department of Mathematics and Computer Science continues a long- standing tradition as a national leader in the number of masters and doctoral degrees granted to African-Americans and women. Small class size, personal attention and a learning environment that promotes stu- dent engagement provides collaboration between students and faculty. Assistantships and fellowships are available to students who qualify.

For more information visit http://math.slu.edu/ or email [email protected]

15 MAA FOCUS December 2008

The MAA Peru Study Tour

The MAA’s study tour and explora- these figures were carved into tion of Peru began on July 7, 2008. the soil centuries ago. Machu Twenty five study tour enthusiasts were Picchu, high in the Andes, and led by Doug Sharon, former director of higher yet, the city of Cusco, the Hearst Museum of Anthropology at at 12,000 feet, was base camp UC-Berkeley, and Carrie Brezine, khipu while the group enjoyed the database administrator at Harvard Uni- archeoastronomical aspects of versity. The group examined khipu at the this area. Anthropology and Archaeology Museum in Lima, visited the Gold Museum for A visit to Quito, Ecuador and a look at an extraordinary private col- its surroundings plus a five day lection of cultural artifacts, and viewed sail in the Galapagos Islands mathematical texts at the Biblioteca was enjoyed by 13 adventur- Nacional de Peru. ers, all of whom received their The group at Machu Picchu. “Equatorial Line Diploma” A flight over the famous Nasca Lines in while on board the Galapagos four and six seater airplanes was a high- Legend. light for many. Seeing the hummingbird, 1, 2009. Contact Lisa Kolbe at lkolbe@ lizard, monkey, and condor brought to The seventh annual MAA Study Tour will maa.org or by phone at 202-293-1170 for life the strange and unusual way in which be a visit to Egypt from May 20 to June more information.

An Amazing Trip

By Gordon Swain

This trip was amazing! I had been to their knowledge, advice, Peru before, and am planning to lead a and coaxing, and remark- student tour there next year, so this should ably adept at herding fac- have been just a professional experience. ulty. Traveling with a group But after two meals and a few half-hour let me see through other trips on the bus in Lima, I was smitten eyes what I took for granted with this gang of not-so-nerdy mathema- in Latin America. I highly ticians (and other sorts). recommend joining one of these MAA tours. Peru did not let us down: the highlights for me were flying over the Nazca Lines, Free tour advice: tromping around the Inca ruins at Pisac, and the austere beauty of the Ballestas • Look deeper — there Islands. And my favorite mountains, the were so many layers Andes, were themselves worth the trip. beneath what we’d read Gordon Swain and Pat Trafton aboard for a flight about Incas and Span- over the Nazca Lines. We’d read that the pre-Columbian peo- iards, and we could ples of Peru had no written language but, only really appreciate • The people make the trip — I believe along with the khipu, which held their nu- it through the eyes and voice of their these folks could have spent a week merical stories, their pottery and textiles people. anywhere, had way too much fun, and spoke volumes. Their artistic expression • Listen to the leaders — I ignored the found something to buy! through everyday objects portrayed in bug spray advice and at Machu Picchu extreme detail the flora and fauna, the enough bugs (re)discovered me that I Gordon Swain is Professor of Mathemat- emotion, worship, pride, along with their brought back a Southern star map on ics at Ashland University in Ashland, daily toil. You just had to see it all. my legs. OH. • bring lots of good batteries — I’m The tour was incredibly well organized crying over the gaps in my photo and the leaders were great, generous with album.

16 December 2008 MAA FOCUS

Going to Peru with the MAA

By Jonathan Kane and Janet Mertz

Janet and I had always thought of Peru us were rewarded with our as one of the more interesting locations own fresh sample. I shot in South America. On the other hand, it 100 pictures in an hour. is a place we would not go on our own, so we decided to give the MAA Study Our trip into the Andes to Tour a try. see Incan ruins and learn about native weaving tech- In Lima, we enjoyed learning about niques gave an appreciated the long history and culture of the lo- change of pace and scen- cal Indian civilizations and the Spanish ery. The Incan structures invasion. We saw about as much ancient at Pisca and Machu Picchu pottery and as many quipu as we could were every bit as spec- stand, but the combined effect contrib- tacular as advertised, and uted substantially to our understanding we enjoyed the increased Jonathan Kane and Janet Mertz with the pilot prior to of Peruvian history and culture. hiking opportunities they their flight over the Nazca Lines. offered. Having never been in a four-seater air- plane before, our flight over the famous Cuzco is a beautiful city full of Incan Nazca Lines was a combination of and Spanish history and culture. It was made bonding easy. The tour managers impressive scenery, surprising pictures great to wander through the indigenous took very good care of us, and in spite in the dessert, and thrilling amusement market seeking sweaters, foods, and of some very long days, too much good park ride. We were thankful our flight Andean flutes. We spent five minutes at food, and a couple of bouts with travelers’ was before lunch. a street corner discussing which direction ailment, it was a great experience. was east after one of us forgot that the A definite highlight of the tour was the sun was, for the first time in our lives, Jonathan Kane is Professor of Math- two hour boat trip to the Ballestas Islands, to the north. ematics at the University of Wisconsin heavily populated by pelicans, cormo- Whitewater. Janet Mertz is Professor of rants, boobies, sea lions, and penguins. Traveling with academics, and with Oncology at the University of Wisconsin The sheer number and density of birds mathematicians in particular, was com- Madison. was breathtaking. We learned about the fortable from the very beginning because harvesting of the guano, and several of our shared backgrounds and language

Peru Study Tour

By Ralph Czerwinski

Although I didn’t know it at the thropology/UC Berkeley), had lived time, my Peruvian journey actually and worked in Peru for ten years, began at MathFest in San Jose when he was able to provide us with en- my graduate school friend, Ralph thusiastic and detailed insights into Neuhaus, declared he was looking the cultural heritage and history of for a post-retirement adventure. Peru. From the moment we visited When the MAA announced its Peru the Anthropology and Archaeol- Study Tour, I knew a Machu Picchu ogy Museum in Lima, I became adventure awaited us. enamored with the ceramic pottery of ancient Peru which was amaz- Also awaiting us were museums, ingly varied and rich in symbolic historical sites, and archaeological depictions. sites along the coast of Peru and peaks of the Andes. Because our Ralph Czerwinski with Peruvian dancers. Carrie Brezine (PhD candidate, main guide, Doug Sharon (retired Harvard University) is an expert Director, Hearst Museum of An- on khipus and the traditional weaving

17 MAA FOCUS December 2008 techniques of the Andean cultures. response that was renewed throughout I was intrigued by the connections the day as I encountered the children between math and art seen in the na- on the streets after school. tives’ traditional weaving techniques and in the symmetry patterns of their And, of course, Machu Picchu! The finished weavings. site of the city ruins and the impres- sive workmanship of the stone work One of our local guides, Tino, was at the site made for a breath-taking, very informative and charismatic. awe-inspiring experience. The site was He provided us with some wonderful much larger than I had envisioned and and entertaining insights into Peru- the quality of the restoration of the site vian culture through his rituals at the was truly remarkable. archaeological sites and stories attrib- Lonesome George – The Last of a Species at the uted to his native Indian grandmother. Darwin Research Centre, Santa Cruz. Photo- The well-organized trip was an ad- He spoke from experience about the graph by John Wilkins. venture filled with information, cul- present-day cultural mix in Peru (his tural interaction, scenery, and food other grandparents are of Spanish, the day was redeemed by a stroll around for thought and stomach — topped off Chinese, and Italian descent). Urubamba where I interacted with the with the Peruvian cure-all, cocoa tea. teachers and students at an elementary Although a 24-hour flu prevented me school. They were appreciative of the Ralph Czerwinski is Professor and Dean from visiting Chincheros, a small Andean ballpoint pens I had brought along as gifts Emeritus at Millikin University and a town known for its pottery and weavings, and they gave me an energetic, friendly former Governor of the Illinois Section of the MAA.

South of the Equator and Back Again By Mike Bankhead An MAA program guide arrived, and again each afternoon. On days when we on the back page I noticed an ad for a were going to snorkel, we battled our study tour to Peru with a pre-trip to the way into a wet suit, before donning the Galapagos Islands. The Galapagos, trav- life jacket, and then the routine was the eling south of the equator, and going on a same. While iguanas and blue-footed tour were all on my list of things I want to boobies were everywhere, we also saw do before popping upstairs for eternity, so some less common forms of wildlife, I applied. I took an exercise book with me and even Lonely George was obligingly to keep a log of everything I did each day sitting in the middle of his pond easily throughout the trip because the itinerary visible to us all. looked packed. I would urge everyone going on a tour to do the same, just don’t Then on to Lima; we arrived at the stop writing in it after the third day. hotel and met up with another thirteen mathematicians the following morning. The trip to Quito, Ecuador, was delayed Then the mathematical part of the tour and long but otherwise uneventful. I began. We studied khipus: strings joined met up with 11 other mathematicians at together with knots in them — the Inca breakfast the following morning. The information recording system. But there first day in and around Quito was long was also plenty of time to visit a large and hectic, but enjoyable, then on to the number of famous places all over Peru. Mike Bankhead in the Galapagos Galapagos Islands. The cruise ship was Islands. small, only 100 passengers, but the crew In spite of the fact that it was a math- went to extraordinary lengths to meet our ematics study tour, for me the best part memories of this hectic trip, not only needs. Each morning we were fed, fitted of the entire trip was being on a boat near because of the places I saw, but because with life jackets, popped into pangas, Ballestas Islands surrounded by tens of of the fact that the folk I was with were the dinghies that took us from the ship to thousands of cormorants sploshing about also mathematicians. the shore, and dropped off on an island in the sea and flying low all around us. with a guide. After snorkeling or trek- Machu Picchu came in a very close sec- Mike Bankhead teaches at Bellarmine king across an island, we then returned ond — a photo cannot do it justice. Over- University in Louisville, KY. to the ship and the same thing happened all I have been left with some wonderful

18 December 2008 MAA FOCUS The Dangers of Dual Enrollment – More Cause for Concern

By Theresa A. Laurent

After reading David Bressoud’s article earned credit status using the following Credit students were reviewed to see if on “The Dangers of Dual Enrollment” definitions: there was an unusually large number of in the December 2007 issue of MAA Cs in the group. No: 20 students earned FOCUS, and given that my institution, No Credit: Took a calculus course in an A, eight students earned a B and only the St. Louis College of Pharmacy, high school but did not earn college credit one earned a C. grants credit for students who complete for Calculus I; a dual enrollment calculus course in high AP Calculus AB ≥ 4: Earned credit for Since so many students at the St. Louis school, I felt compelled to investigate the Calculus I with an AP Calculus AB score College of Pharmacy come from the calculus achievement for our entering of 4 or higher; and surrounding area, I was concerned that freshmen. Dual Credit: Earned credit by success- maybe just one higher education institu- fully completing a dual credit course with tion was awarding dual credit to several Although my institution is small and a grade of C or higher. of the students without appropriate stan- specialized, of the 238 freshmen admit- dards and thus skewing the results. How- ted this fall, 145 had just taken a calculus Scores ranged from 0 to 21 out of a pos- ever, dual credit transcripts represented course in high school. Of those students, sible 29 with a mean of 5.48 and standard 16 different higher education institutions 50 earned credit for Calculus I by dual deviation of 5.00. The low mean should in the Midwest. In fact, 17 of the 28 dual enrollment grades of C or better or AP not be surprising, since students did not credit students had earned their credit Calculus AB scores of 4 or better. This prepare for this exam and most of them from institutions with accreditation or seemed to be a nice population to inves- had no exposure or practice with calculus provisional accreditation from the Na- tigate differences between students who over the summer. Additionally, the major- tional Alliance of Concurrent Enrollment earn credit by AP Calculus Exam versus ity of these students registered to re-take Partnership (NACEP). students who earn credit by dual enroll- Calculus I in their first semester of col- ment versus student who take calculus lege. For those students who earned credit The results of this investigation were in high school but do not earn college for Calculus I, however, these scores are strong enough for our institution to credit. disturbing. change its credit granting policies for Calculus I. In Bressoud’s article, he Two days prior to the start of the fall Results by earned credit status are shown pointed out that mathematics depart- semester, 143 freshmen with high school in the table on this page. The differences ments’ involvement in many dual credit calculus experience completed a vali- in means are striking with the AP Calcu- programs lack oversight. If dual credit is dated calculus-based placement test. The lus group having the highest mean by far. to be taken seriously by higher education test was a modified version of the Cal- Additionally, comparing means of the No institutions, it is imperative that college culus Validation Exam developed at the Credit group and the Dual Credit group mathematics departments take more U.S. Military Academy — West Point; show no statistical difference. responsibility in the administration and this exam was described in “Calculus oversight of these courses. Placement that Really Works!” (MAA Several explanations of the poor perfor- FOCUS, January 2008). The modified mance of the Dual Credit group were Theresa Laurent is an assistant professor test consisted of 16 questions worth a considered. For example, the groups of mathematics at the St. Louis College total of 29 points. were compared controlling for Math of Pharmacy. This research was done as ACT scores; no major differences were part of her dissertation at the University Students were categorized based on their found in the results. Grades of the Dual of Missouri – St Louis.

Means and Standard Deviations of the Modified Calculus Validation Exam by Earned Credit Status (No Credit, AP Calculus AB ≥ 4, Dual Credit)

Earned Credit Status Number Mean Standard Deviation

No Credit 93 4.17 3.70

AP Calculus AB ≥ 4 22 12.14* 5.57

Dual Credit 28 4.61 4.28

* Mean was statistically different from other groups, p ≤ .01. 19 MAA FOCUS December 2008 What We Learned… by Starting a Seminar Series at a Small School

By Isaiah Lankham and Jenny Switkes

Imagine that you recently We also brought in Simp- started teaching at a small son faculty colleagues college or university in from other disciplines: a rural area. Armed with Michael Lyons, a profes- memories of mathematics sor of Old Testament, seminars and colloquia spoke on “Numbers and from past schools, your Number Usage in An- enthusiasm is high for cient Israel”; and Wally starting something similar Quirk, a professor of at your new school. You business administration, soon realize, however, spoke on “Expansion of that this seminar will not the Money Supply.” look quite the same as it did at any of the large We invited students to universities where you give talks: Senior psy- have previously been. In chology major Jillian this article, we describe Ducker spoke on “An the unexpectedly great Investigation of the In- things that happened as we fluence of the Simpson grappled with this prob- One of the slides from Michael Huster’s seminar. University Culture on lem and found unique Selected Characteristics opportunities at Simpson of Emerging Adults,” and University in Redding, California. senior mathematics education majors Kaela Corbet, Michelle Long, and Ashley Mathis jointly gave a talk entitled “Factors The Setting Influencing Post Graduate Aspirations.” Both talks were based upon year-long research projects directed by our mathematics Simpson University is a small Christian liberal arts university in colleague Mel Shuster. Northern California. We offer majors in mathematics and mathe- matics education, and our mathematics students are enthusiastic We did invite speakers from “nearby” UC Davis, which is about and a joy to teach. However, until this past year, our mathematics two and a half hours away from Simpson University. UC Davis majors had not been exposed to such almost-legendary staples of senior mathematics major Paul Prue drew from his most recent study as the Putnam Mathematical Competition, summer REU REU project when he spoke on “Geometric Approaches to Hy- programs, seminar series in mathematics, etc. This past year, perspectral Imaging,” and mathematical physicist Craig Tracy, with a number of our students interested in graduate study in who was Isaiah’s dissertation advisor, spoke on “Universality mathematics, with both co-authors newly arrived at Simpson, in Mathematics and Physics.” and with the expressed support of our Simpson colleagues, it was a good time to start new things. Among other projects, a Our Audience mathematics seminar series was begun. Our next challenge was to build an audience for our seminar Our Speakers series. In order to have a consistent core audience, we offered a newly created one-unit course that students could take for Simpson University is located in a fairly rural area, with neigh- pass/fail credit. Five students enrolled in this course and were boring four-year colleges and universities located more than required to attend at least nine of the twelve seminar talks. We an hour away. As a result, it was simply impossible to invite also required students to take notes at each talk and to turn in a full schedule of mathematicians from other schools, as both their notes at the end of the semester. In addition, we required co-authors had been used to doing. So we gave talks: Isaiah them to write one-page response essays for the three talks that spoke on “A User’s Guide for Fixing Elections with Discrete they found most interesting. Mathematics”; Jenny spoke both on “Summer Math Research Adventures” and on “Perceived Highway Speed;” mathematics A sign-in sheet was also prepared for each talk, which enabled colleague Harold Lund opened our seminar series with “A Fun us to keep a record of both enrolled students and non-enrolled Introduction to Topology”; and physics/mathematics colleague guests. We actively invited and often had non-mathematician Michael Huster drew from his sonar design experience when he faculty, administrators, and staff attend. Guests included the spoke on “Noise, Noise Everywhere and Not a Sub to Sink.” President of the University, recent Simpson alumni, students

20 December 2008 MAA FOCUS from a wide variety of non-majors courses (including one Inter- How I wish I could recollect of circle round mediate Algebra student), and a friend of Jenny’s who, among The exact relation Archimede unwound other things, works as a gardener at Simpson. And, of course, our mathematics and science colleagues were also strong sup- (source: http://paginas.fe.up.pt/~fsilva/port/pi2.html) porters and attendees of the seminar. and “pi-kus” like The newly created Math Club played an important role in building this audience. Math Club President Rebekah Hoffman Pi — ratio of designed professional-looking flyers for us, which allowed us Around : across a circle — to advertise to the entire Simpson campus community. She An endless number? also coordinated thank you cards for each speaker and had the audience at each talk sign them. (source: http://www.exploratorium.edu/pi/Pi-Ku/)

We held the seminar on Monday evenings in a conference We were also delighted to have a colleague illustrate the concept room located within the campus dining center. Attendees were of circumference in non-Euclidean geometry, and a student welcome to bring their dinner to each talk. This created a fun, was kind enough to entertain us with such song parodies as informal atmosphere for the seminar. “American Pi,” the refrain of which includes the first 30 digits of π. It was a fun end to a fun semester of talks, and we will Results of Our Seminar certainly continue the tradition.

Our audience included more than just those who could attend in For Next Time person. We posted speakers’ slides online, and we found that a number of faculty and administrators from across the university Overall, we are extremely happy with how this first mathemat- accessed these slides. In addition, several other departments ics seminar series went. There were some minor issues, though. either have created or are in the process of creating a seminar No formal prerequisites were placed on the accompanying series in their own disciplines. one-unit course, and one student did enroll who was not at all suited to the course. Next year, we will most likely deal with We found that students also genuinely enjoyed the seminar and this by adding a suggested prerequisite of calculus. Although felt that they learned a lot from it. Based upon their response the dinner-time meetings created a nice atmosphere for talks, it papers, they especially enjoyed seeing ties between mathematics prevented student-athletes and faculty from a nearby community and other fields of study through presentations by faculty whom college from attending. It may be necessary to experiment with they already knew in other contexts. Students were additionally a different time of day. As far as speakers go, several additional inspired both by presentations from fellow students and by our Simpson faculty colleagues have already volunteered to speak off-campus faculty guests, the latter in particular pointing them about interesting things in their discipline that in some way towards graduate-level mathematics. connect to mathematics. We are sure that the mathematics and science faculty will also continue to contribute to the seminar Our last meeting was a Math Club co-sponsored “Pizza, Puzzle, series, and we like how it went with undergraduate student and Pi(e) Party” during final exam week. The Mathematics speakers as well. Department provided funding for pizzas and pies, and we encouraged attendees to bring a “silly pi trick to share.” Jenny Our new seminar series was a success. We believe it is important shared MATLAB code for approximating π using the Taylor that we were willing to relax our ideas of what a seminar series in expansions mathematics “should look like” and to tailor the seminar series to the culture of the university, while realizing that this seminar represented something new and unusual at our university. As a result, things that initially seemed to be difficulties led to some of the most special aspects of the seminar!

Isaiah Lankham ([email protected]) recently completed his first year as an Assistant Professor of Math- the latter providing astonishingly better approximations for π ematics at Simpson University in Redding, California, where upon truncation, and using a Monte Carlo method based upon he started Simpson’s new Mathematics Seminar and brought the integral other exciting new things to Simpson’s enthusiastic mathematics

1 majors. Jenny Switkes ([email protected]) is an Asso- π =4 1 − x2 dx. ciate Professor of Mathematics at California State Polytechnic ∫0 University, Pomona; during an academic year off in Northern Isaiah brought some lighter pi fare, including such standard California, she taught part-time at Simpson University and piphilogical “pi-ems” as helped Isaiah start the seminar.

21 MAA FOCUS December 2008 What I Learned… by Using an Online Homework System in Calculus I

By Sharon Vestal

D uring the 2006–2007 The problem with academic year, I taught one this approach is two- Calculus I course each se- fold: students don’t mester. While I believe that always read direc- students do better when they tions; and how would have graded homework, it these problems get seemed to be the practice of graded? I decided many faculty members to that I was going to give quizzes but not collect rely on the students to homework. Since I had just be adults and do these moved, started a new job, problems and I would and had a baby, I decided that not grade them. I test- I didn’t really have time to ed their understand- grade homework so I would WebAssign assignment settings. ing of graphing using succumb to peer pressure and calculus by assigning give quizzes. I also assigned a graphing project that I graded prior to the exam. I am happy to ‘projects,’ which essentially are more difficult homework report that WebAssign is currently working on adding graphing problems. capabilities to their software!

What I observed was not too surprising: my students were not As with most online homework systems, WebAssign uses ran- doing much homework; and as a result, they were not doing domly generated numbers in their problems. As most of us know, well in the course. In Spring 2007, we decided to adopt the new sometimes simply changing a number in a problem can make the edition of Stewart’s Single Variable Calculus Early Transcen- problem more difficult or it can change the answer completely. dentals and I found out that we could use an online homework In the homework after the section in which the students learned system with this textbook. I volunteered to be the ‘guinea pig’ to differentiate ex they decided to ask the students to find the for the department and use Enhanced WebAssign to assign and derivative of eax , where a was an integer. This problem is not grade homework for this course. One of my colleagues also used difficult, but the textbook had not yet introduced the chain rule, it for some of the homework in his class. In Fall 2007, I had two and most students wouldn’t recognize ea as a constant factor. sections of Calculus I and I used WebAssign for both sections. So while randomizing the problems is good, they need to be careful to not create a question containing a concept that has I spent time in the summer of 2007 putting together all the not yet been covered in the textbook. homework assignments for the course. Luckily the problems in the new edition of Stewart are similar to those in the old Another situation arose when one of my students was given edition, so I already knew what type of problems I wanted to a rational function with quadratics in both the numerator and denominator, and asked to find all asymptotes. The students were given one box to fill in for the horizontal asymptote and two boxes for the vertical asymptote(s). One student’s particular randomiza- tion resulted in one vertical asymptote and one removable discontinuity. Yet WebAssign had two boxes for vertical asymptotes so the student kept assign. However, I was a bit disappointed when I went to select getting the problem counted wrong. The student had graphed the problems that involved graphing, such as ‘sketch a graph that function on his calculator so he knew that there was only one has the following characteristics,’ because those problems were vertical asymptote. I told the student if he could explain to me not available in the WebAssign database. They have problems why the function had only one vertical asymptote, I would give such as the following. him the points back on his online assignment. I am unhappy to If these were assigned for points, they would have to be graded report that he did not earn those points for that problem. by hand. The support people at WebAssign suggested that I supplement problems that were missing from their database Another issue that came up was that sometimes WebAssign by adding directions to each appropriate WebAssign assign- wanted exact answers and other times, they wanted decimal ment, such as ‘In addition, do the following problems from answers. They have programmed an error tolerance of ±1%, the textbook.’ but there were times when students would need to put in the

22 December 2008 MAA FOCUS exact answer and it would count complaints. For example, some stu- a decimal answer out to 4 places dents found it ‘a real pain’ to enter incorrectly. They are aware of this their answers online. One student issue — I mentioned to them that commented that WebAssign ‘did not they need to be very explicit in care how we got the answer,’ and their directions for a problem so a complained that his methods ‘were student knows whether to give an not accepted on tests.’ I suspect that exact answer or a decimal answer. this means he was using a calcula- Personally, I always want exact an- tor to do his homework. Others swers as I don’t like having to grab remarked that the program online a calculator while I am grading. marked their answers right or wrong, without giving explanations or com- Some issues were not related to ments. That is my job as teacher, of mathematics. For example, some course, and I encouraged students students had trouble with certain A multiple choice problem in WebAssign. to use email when they needed my browsers interacting with WebAs- help. In fact, I think that there was sign. The support people suggested more student/teacher interaction that semester than in previous that we use Mozilla Firefox as it seems to be the most stable semesters when I didn’t collect or grade homework. browser to use with their system. On questions that required the students to enter an algebraic expression, WebAssign was I feel strongly that online homework can be a good tool for Cal- using Math Palette. Math Palette is a third-party product culus I. I felt it created a different atmosphere in my classroom: and sometimes seemed to cause problems for some students. students were talking to each other about calculus problems WebAssign is developing their own tool for entering algebraic and helping each other figure them out. I will definitely use expressions. this program again when I teach Calculus I. In fact, all of my colleagues are currently using the program for Calculus I and At this point, you might think that I don’t like WebAssign, but it some are using it for Calculus II. does have many advantages. This online homework system can be used by both Mac and PC users — I have previously used a Sharon Vestal is an Assistant Professor at South Dakota State system that only worked on PCs. The gradebook is wonderful University. She is an Enhanced WebAssign Instructor Trainer and very flexible. You can use a point system or a weighted for Cengage Learning. average to calculate grades. You can put in paper assignments or exams by hand or import a spreadsheet. There a lot of settings that can be changed, such as the number of attempts a student has for each problem. (The default setting is five attempts and I think that seemed to be a good number.) You can set the due date and the time when each assignment is due.

I learned a very valuable lesson regarding this last point. I had each assignment due at midnight on the due date. The result was that I had several students sending me questions via email in the evenings. I did answer these emails because I had set the due date at midnight and am aware that students generally pro- crastinate, but next time I will have the assignments due during the day. On derivative problems, WebAssign accepts both the unsimplified answer and the simplified answer. At first, students were very excited that they didn’t have to simplify their deriva- tives, but then they realized that they had to type their answers in very carefully so as to not have misplaced parentheses. This was actually a good exercise for them in orders of operations.

The biggest benefit was that most of my students actually did their homework. I truly felt that the students completing Calcu- lus I were much stronger calculus students because they were forced to do homework (despite the fact that it was only 5% of their grade). I have increased the value of the homework to 7% of their grade for Fall 2008.

When the students completed evaluations for the course, I asked them to comment on the use of WebAssign. There were some 23 MAA FOCUS December 2008 2007 Individual MAA Donors President’s Circle Edmund A.C. Crouch Anonymous (Gifts of $5,000 and above) Jean E. De Valpine Howard Anton Gerald L. Alexanderson Gregory M. Dotseth in memory of George Bachman Richard D. Anderson William L. Duren Kenneth I. Appel Anonymous Jerrold W. Grossman Ronald L. Arms in memory of Leon Cohen, Larry Corwin, Joel and Linda Haack in memory of Glen Eugene Bredon Leon Henkin, Paul Halmos Joseph E. Kist Clayton V. Aucoin Tom & Jane Apostol Peter Klein in honor of William Lucas Robert P. Balles Peter Marineau Joseph Auslander Roger and Susan Horn Arnold M. Ostebee in honor of William Lucas Joan R. Leitzel Robert A. Rosenbaum Theodore J. Barth in memory of James R.C Leitzel in memory of Louise J. Rosenbaum Jerry P. Becker Harry Lucas, Jr. Ronald C. Rosier in honor of Izaak Winszup Carl B. Pomerance Paul J. Sally, Jr. Julie A. Belock Gerald and Judith Porter Richard M. Schori Manuel P. Berriozabal Marvin and Mary Alice Schaefer Norman E. Sexauer in memory of Arnold Ross Martha J. Siegel Andrew Sterrett, Jr. Delmar L. Boyer Robert Steinberg T. Christine Stevens in memory of Frederick Bodo Strauss Tina H. Straley in memory of Donald Kreider David M. Bressoud Patricia Witte and Deborah Tepper Haimo Robert E. Brown Richard E. Stone Robert L. Bryant Grand Benefactor in memory of Deborah Tepper Haimo Raymond J. Cannon, Jr. (Gifts of $3,000 and above) Richard M. Van Slyke John E. Carson Alfred & Dorothee Aeppli William F. White Onn Chan Arthur T. Benjamin in memory of Donald Kreider Ronald J. Chase in honor of William Lucas Concordia C. Chen Lida K. Barrett Associate Lily E. Christ Joseph A. Gallian (Gifts of $300 and above) Pi-Chun Chuang John W. Kenelly Louis J. Billera Alfred Clark, Jr. in memory of Donald Kreider and John in honor of William Lucas Robert A. Clark Harvey Peter B. Bjorklund L. Clifford in honor of Joe Gallian and William Lucas Stewart E. Boden Daniel I.A. Cohen Carolyn D. Lucas Ezra A. Brown A.J. Coleman in honor of William Lucas Wade Ellis, Jr. James W. Daniel Walter M Patterson, III and Frederick S. Gass Ingrid Daubechies Susan R. Patterson in memory of Donald Kreider M. Hilary Davies David R. Stone Stephen P. Gill Guy M. De Primo John E. Wetzel in memory of Hilda Geiringer Von Mises Irene DeVivo J.H. Graham Benefactor Nicholas Duchon Mark D. Hamlen (Gifts of $1,000 and above) Bill and Penny Dunham Thomas C. Hull Nathaniel Chafee in memory of Jim Leitzel Yadong Jiang in memory of John D. Neff John W. Duskin in honor of MAA members Douglas J. Dunham Susanna S. Epp Rudolf B. Lim John D. Fulton Grant W. Erwin, Jr. in memory of Foon Lim in memory of Maria A. Fulton John H. Ewing Richard A. Little Deanna B. Haunsperger & in honor of Al Willcox Patti Frazier Lock Stephen Kennedy Robert E. Fennell Warren S. Loud Ellen E. Kirkman in honor of William Lucas in memory of William Ted Martin Paul A. Kreider James T. Fey Michael E. Moody in memory of Donald Kreider Karen B. Gaines Nicholas Pippenger Sharon Cutler Ross in honor of Project NExT Alan G. Poorman Harvey M. Weitkamp Joseph M. Gani Jon W. Scott Susan S. Wildstrom in memory of Ruth Gani James G. Timourian in honor of Jake Wildstrom Richard L. Gantos Joe F. Wampler in memory of Deborah Tepper Haimo Murray Gechtman Allyn J. Washington Richard A. Gibbs Patron Christopher C. White in memory of J.S. Frame (Gifts of $500 and above) Anthony A. Gioia Raymond A. Barnett Sponsors Anthony J. Giovannitti Felice D. Bateman (Gifts of $100 and above) Milton A. Glass, Jr. Karl E. Byleen William W. Adams Samuel Goldberg Antony Chang Michael I. Aissen William C. Allen, III Basil Gordon 24 December 2008 MAA FOCUS

Jack E. Graver William G. Pertusi Jean-Christophe Aubert Nancy L. Hagelgans John W. Petro Robert J. Austin M.E. Hamstrom Marjorie E. Poorman in honor of Georgia Southern University John L. Hank Vaughan R. Pratt Math Department William J. Hardell Corrado D. Quintiliani David R. Bainbridge Joe T. Harris, Jr. Janet P. Ray Gerald E. Bergum Adam O. Hausknecht Robert R. Reitano Colin R. Blyth Gloria C. Hewitt Kyle L. Riley Allan D. Bobko Joseph A. Hughes Charles D. Robinson William M. Boothby George W. Hukle David Royster in memory of Alex Rosenberg Craig L. Huneke Martin Salter Donald J. Boyce Franklin T. Iha David H. Sanders Richard S. Bremiller Herbert E. Kasube Donald E. Sanderson Edgar H. Bristol Daniel Kennedy Katherine W. Sandek Pierre Victor Bulens Thomas C. Kipps in memory of Deborah Tepper Haimo Richard T. Bumby Benjamin G. Klein Ignatius P. Scalisi Marjorie V. Butcher Ralph M. Krause Doris J. Schattschneider in memory of Cecil J. Nesbitt, Harold L. David E. Kullman in memory of Victor Klee Dorwart, Robert W. Butcher in memory of James Leitzel David I. Schneider Thomas R. Butts Kenneth Kunen Henry A. Seebald Martin F. Carr, Jr. Jeanne LaDuke George Seifert in memory of Martin F. Carr, Sr. Judith Landwehr in memory of Bertha Seifert Hillel J. Chiel in memory of Deborah Tepper Haimo Stuart J. Seligson Sharon Cloninger Katherine P. Layton Melvin A. Shader in memory of John Grover Harvey, II Robert N. Leggett, Jr. Richard J. Shaker Carolyn Connell Brian Lessing Greg Shaw Thomas A. Cootz Norman W. Lord Frank C. Sherburne Henri Cornet in memory of Estella Cahan Lord Angela B. Shiflet Ronald W. DeGray Thomas A. Mackey Louise A. Simon Clayton W. Dodge in memory of James Burling Louis Solomon Joanne M. Dombrowski Moray S. Macphail Norton Starr Roy J. Dowling Thomas J. Marlowe Henry E. Stern Sylvan H. Eisman David K. Masunaga Richard E. Stone David L. Finn Andrew J. Matchett in memory of Deborah Tepper Haimo James H. Freeman Jacob R. Matijevic Joe W. Sullivan Susan L. Friedman Stephen B. Maurer Marcia P. Sward in memory of Tilla Weinstein M. Hope McIlwain in memory of Deborah Tepper Haimo and John D. Glaus Mercer University Faculty and Staff Alfred B. Willcox Robert A. Glover in memory of Matthew Reddy Maja-Lisa W. Thomson Richard P. Goblirsch Ernest A. Michael in memory of Stu Lloyd and David Slepian Park Wi Gom J. Lyn Miller John A. Thorpe Joaquin Hernandez Gomez Patrice L. Miner Eugene Toll Charles B. Grosch in memory of Donald Kreider Thomas W. Tucker Robert G. Hathway Richard A. Moore United Way of Central New Mexico Francis M. Henderson Cathleen S. Morawetz Justin C. Walker Hans-Heinrich W. Herda Albert A. Mullin David S. Watkins V. Dwight House in honor of Claude E. Shannon James D. Watson John Houstoun Michael L. Mumford Thomas Wellington in memory of Morris Kline Teri J. Murphy Alexander Weintraub Thomas E. Ikard Larry D. Nelson Rer Nat Heinz-Wolfgang Wisse in memory of Jeanne Agnew George M. Nielsen Esther Woolf Godfrey L. Isaacs Victor T. Norton, Jr. in memory of Deborah Tepper Haimo I. Martin Isaacs Paul E. Olsen Arthur H. Jerbert Contributor Grace G. Orzech David L. Johnson (Gifts of $50 and above) Calvin I. Owens Gerald W. Johnson Irving Adler Kenneth Pacholke Norman W. Johnson Joe Albree Charles E. Pagano, Jr. Diana Kalish Beverly J. Anderson Hiram Paley Paul A. Kaschube David F. Appleyard Philip E. Parker Wayne G. Kellner Myra M. Archer Brad Parsons David I. Knee Shoshana Asher Franklin and Katherine Pederson in memory of Donald Kreider in honor of Jerrold E. Marsden in memory of Deborah Tepper Haimo B. Melvin Kiernan George L. Ashline and John Harvey 25 MAA FOCUS December 2008

Robert E. Lehman 2007 Donors to the Paul R. Halmos Commemorative Walk in honor of Robert F. Lehman and in memory of Carol A. Lehman Edward Aboufadel David V. Finch Nancy L. Laing Christoforos Achtsalotidis William G. Frederick Edward M. Landesman Gerald Alexanderson J. William Friel Bernard W. Levinger Allegheny Section Nathaniel A. Friedman George M. Lewis Laurence R. Alvarez Joseph A. Gallian in memory of Earl J. Hoppes Alfred Aeppli James W. Galvin Xiaoyan Liu Tom and Jane Apostol Razvan Gelca John M. Long Association of State Supervisors of Mathematics Georgia Southern University Department of in memory of William Wunch Christina A. Bahl Mathematical Sciences W.K. Moore Robert P. Balles Joel and Linda Haack Philip Oppenheimer J. Michael Pearson Carol A. Baxter Nancy J. Hagelgans Richard J. Pirchner Donna L. Beers Deanna B. Haunsperger J.W.Poole Lowell W. Beineke Siegfried Haenisch Alvin Portnoy Arthur T. Benjamin Johnny and Darlene Henderson Andrew P. Porter James E. Bennett James B. Herder Jack Price Manuel P. Berriozábal Gerald A. Heuer in memory of Donald Kreider Betsy Berry Chris and Cheryl Hough Donald M. Redmond Satish C. Bhatnagar Thomas W. Hungerford Ann M. Reisel Kenneth G. Boback Illinois Section in memory of Robert B. Reisel Guy Boillat Hadrian Katz Glenn Rennels Monte Boisen Victor and Phyllis Katz William D. Romaine Robert L. Brabenec Stanley Kelly-Bootle Jean-Louis Roque David M. Bressoud John W. Kenelly Daniel M. Rosenblum John F. Bukowski Daniel Kennedy David Sachs Mehmet I. Celebiler Stephen F. Kennedy Hatem Abdul Mohsin Samman Karen Saxe Jean Bee Chan Henry S. Kepner John Schue Robert T.P. Chan Stan Kerr in memory of Joe Konhauser Peter Chu Leonid Khazanov Seymour Schuster Richard Cleary Clark Kimberling Derek Schulte Adam Coffman Allan M. Kirch in memory of Owen Garrick Joel S. Cohen Maria M. Klawe Chantal M. Shafroth Marshall M. Cohen Laura S.K. Kodama Amy E. Shell-Gellasch Conference Board of the Mathematical Sciences Lisa R. Kolbe Robert T. Seeley William R. Cordwell Fat Cheung Lam John K. Seymour John B. Cosgrave Carl L. Lambert Michelle R. Sisto Carl C. Cowen Violet H. Larney Louise M. Smith Margaret B. Cozzens David C. Lay Ronald Smith Annalisa Crannell Steven R. Lay Jimmy L. Solomon John D. Culverhouse Katherine P. Layton Stephen E. Spielberg Theresa Early Curd Joan Leipnik Olaf P. Stackelberg Richard S. Stevens James W. Daniel Joan R. Leitzel Philip D. Straffin Vivian Ann Dennis William James Lewis Ross H. Swanson Ronald G. Douglas Stuart P. Lloyd Robert E. Thomas Peter Dragnev Madeleine J. Long Roseanna F. Torretto Penelope H. Dunham Ronald E. Loser Elias Toubassi William W. Dunham Louisiana-Mississippi Section Calvin R. Van Niewaal William L. Duren, Jr. William F. Lucas Wolmer V.Vasconcelos Irene DeVivo Riikonen Matti Shardul Vikram Abe Elfadel Betty Mayfield Evelyn K. Wantland EPADEL Section Brian J. McCartin Bette L. Warren Jessie Ann Engel Michael M. McCrea Robert B. Wenger Douglas E. Ensley Guillermo Romero-Melendez Sylvia M. Wiegand James T. Fagan Russell L. Merris N. Convers Wyeth Graeme Fairweather Metropolitan New York Section Cheng Xiang Zhai Joseph R. Fiedler Ernest A. Michael in honor of Alex Zhai Charles Fleenor Yozo Mikata Tien Yu Zhao Richard J. Fleming Michael G. Miller

26 December 2008 MAA FOCUS

Richard E. Mitchell C. Bradley Tashenberg American Mathematics Montie G. Monzingo John F. Thorne, III Competitions 2008 Nitsa Movshovitz-Hadar Mary P. Tong Albert A. Mullin John Travis Sponsors Kazumi Nakano Ravi D. Vakil Akamai Foundation National Council of Teachers of Mathematics Calvin R. Van Niewaal Mathematical Association of America Dale A. Nelson Linda D. Van Niewaal Robert W. Newcomb Teisha Vest Contributors North Central Section Pelegri Viader Academy of Applied Science Northern California Section Linda J. Wagner American Mathematical Association of Ohio Section Evelyn K. Wantland Two-Year Colleges Oklahoma/Arkansas Section Bette Warren American Mathematical Society Mary M. O’Keeffe William and Cecilia Weakley American Statistical Association Gerardo S. Parades Maurice D. Weir Art of Problem Solving, Inc. J. Michael Pearson Randy F. Westhoff Awesome Math P.N. Phutane John E. Wetzel Canada/USA MathCamp and MathPath Robert Piziak Stephen and Susan Wildstrom Casualty Actuarial Society Gerald J. Porter Ronald O. Williams Clay Mathematics Institute W. M. Priestley Stephen J. Willson Institute for Operations Research and the Jennifer J. Quinn Rer Nat Heinz-Wolfgang Wissner Management Sciences Maxwell O. Reade Robert T. Xeras Mu Alpha Theta Robert Redfield Genji Yoshino National Assessment and Testing Glenn Rennels National Council of Teachers of Mathematics Diane Resek Pedagoguery Software, Inc. Robert J. Reynolds Pi Mu Epsilon Kyle L. Riley Society of Actuaries Charles D. Robinson U.S.A. Math Talent Search Stephen B. Rodi Table Sponsors at the 37th USA Mathematical Beatrice G. Rosenberg Project NExT 2008 Ronald C. Rosier Olympiad Awards Ceremonies Kenneth and Ruth Ross Sponsored fellows number 1090 since its Akamai Foundation Carol B. Roush inaugural year in 1994 thanks to individuals, American Mathematical Association of William W. Rowell sections, and organizational supporters of Two-Year Colleges Beverly Ruedi Project NExT. American Mathematical Society Daniel Saltz American Statistical Association Donald E. Sarason American Institute of Mathematics Casualty Actuarial Society Doris J. Schattschneider American Mathematical Society Clay Mathematics Institute Douglas R. Shanklin American Statistical Association Conference Board of the Mathematical Sciences Martha J. Siegel Association for Symbolic Logic Institute for Operations Research and the Michael S. Skaff Association of Mathematics Management Sciences Skidmore College Teacher Educators IMO 2001 USA Don Slater Mary P. Dolciani Halloran Foundation Mu Alpha Theta Alvy R. Smith Mary P. Dolciani Halloran Foundation National Council of Teachers of Mathematics Kay B. Somers Endowed Fellow Society for Industrial and Applied Mathematics Richard E. Sours Education Advancement Foundation Society of Actuaries Southeastern Section ExxonMobil Foundation Peter Stanek Illinois Section Lynn A. Steen John Wiley & Sons Stetson University MAA Fall Appeal Donations Tina H. Straley Maplesoft Lonette Stoddard MD/DC/VA Section Paul J. Sugarman National Council of Teachers of Mathematics Elaine P. Sullivan Metro New York Section V.S. Sundar Robert F. Witte Endowed Fellow Thomas F. Sweeney Southeastern Section Choy-Tak Taam Texas Instruments, Inc. Lajos F. Takács W.H. Freeman Richard G. Taranto

27 WebAssign ad AJP 8/16/07 1:30 PM Page 1

MAA FOCUS December 2008

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28 December 2008 MAA FOCUS

Employment Opportunities mathematics for all undergraduates. gins August 2009. For more details and to apply online, please visit: https://jobs. ALABAMA Fairfield University, the Jesuit Univer- montgomerycollege.edu sity of Southern New England, is a com- Spring Hill College prehensive university with about 3,200 Online applications must be received by Spring Hill College seeks applications undergraduates and a strong emphasis 12 noon, Monday, December 8, 2008. for a tenure track position in Math- on liberal arts education. The depart- ematics beginning Fall 2009. Position ment has an active faculty of 14 full- Mathematics Faculty – Position #2224– rank: Assistant or Associate Professor, time tenured or tenure track members. Rockville Campus depending on qualifications. Ph.D. in We offer a BS and an MS in mathemat- the mathematical sciences is required. ics, as well as a BS in computer science. Required Qualifications: Demonstrated excellence in teaching The MS program is an evening program • Master’s or Ph.D. in Mathematics, and potential departmental leadership and attracts students from various walks Mathematics Education, or a qualities highly desirable. A strong of life secondary school teachers, even- strongly related field. Degree must commitment to teaching is required; tual Ph.D. candidates, and people work- be earned by July 1, 2009. candidates will be expected to teach a ing in industry, among others. • At least 18 semester hours of gradu- full range of courses from Basic Algebra ate level courses in mathematics to upper division courses required for a Fairfield offers competitive salaries and For more details and to apply online, bachelor’s degree in mathematics. Inter- compensation benefits. The picturesque please visit our website at: https://jobs. est in pursuing undergraduate research campus is located on Long Island Sound montgomerycollege.edu experiences is also strongly encouraged. in southwestern Connecticut, about 50 Position is open until filled. miles from New York City. Fairfield is Office of Human Resources – 240 567- an Affirmative Action/Equal Opportuni- 5353. Send letter of application, vita, state- ty Employer. For more information see Montgomery College is an academic in- ments on teaching and research, unof- the department web page at http://www. stitution that is committed to equal op- ficial academic transcripts and three let- fairfield.edu/macs_index.html portunity and fostering diversity among ters of reference to Dr. Charles Cheney, its student body, faculty, and staff. To- Dept. of Mathematics, Spring Hill Col- Applicants should send a letter of appli- bacco Free Workplace lege, 4000 Dauphin St., Mobile AL cation, a curriculum vitae, teaching and 36608, or [email protected] Spring research statements, and three letters of United States Naval Academy Hill College is a Jesuit, Catholic liberal recommendation commenting on the The USNA Mathematics Department arts college dedicated to quality teach- applicant’s experience and promise as anticipates at least one tenure-track po- ing. Equal Opportunity Employer. a teacher and scholar, to Matt Coleman, sition (subject to approval and funding) Chair of the Department of Mathematics at the Assistant Professor level to start CONNECTICUT and Computer Science, Fairfield Uni- in August 2009. See web site http:// versity, 1073 N. Benson Rd., Fairfield www.usna.edu/MathDept/website/em- Fairfield University CT 06824-5195. Full consideration will ployment.html for full information. Assistant Professor be given to complete interviewing at the Tel: 410-293-6701; Fax: 410-293-4883; Department of Mathematics and Com- Joint Mathematics Meetings in Wash- Email: [email protected]. The United puter Science ington DC, January 5-8, 2009. Please let States Naval Academy is an Affirmative The Department of Mathematics and us know if you will be attending. Action/Equal Employment Opportunity Computer Science at Fairfield Univer- Employer and provides reasonable ac- sity invites applications for one tenure MARYLAND commodations to applicants with dis- track position in mathematics, at the abilities. rank of assistant professor, to begin in MONTGOMERY COLLEGE September 2009. We seek a highly qual- A Learning College MASSACHUSETTS ified candidate with a commitment to OFFICE OF HUMAN RESOURCES and demonstrated excellence in teach- Your Resource to Excellence Williams College ing, and strong evidence of research po- Consider Montgomery College for your The Williams College Department of tential. A doctorate in mathematics is re- next career move! Mathematics and Statistics invites ap- quired. The teaching load is 3 courses/9 plications for one tenure track position credit hours per semester and consists Montgomery College, one of Mary- in mathematics, beginning fall 2009, primarily of courses at the undergradu- land’s oldest community colleges, is at the rank of assistant professor (in an ate level. The successful candidate will a multi-campus institution located in exceptional case, a more advanced ap- be expected to teach a wide variety of Montgomery County, Maryland. pointment may be considered). We are courses from elementary calculus and seeking a highly qualified candidate who statistics to graduate level courses; in Montgomery College is seeking a full- has demonstrated excellence in teaching particular, Fairfield University’s core time Mathematics faculty member for and research, and who will have a Ph.D. curriculum includes two semesters of the Rockville Campus. Assignment be- by the time of appointment. 29 MAA FOCUS December 2008

Williams College is a private, coeduca- job classification, including improved in Mathematics at the Assistant Profes- tional, residential, highly selective lib- job security and a clear promotion path, sor level, to begin September 1, 2009. eral arts college with an undergraduate have made it possible to have a highly Details, including application instruc- enrollment of approximately 2,000 stu- satisfying and rewarding career as a lec- tions, can be found at www.mathjobs. dents. The teaching load is two courses turer at Michigan Tech. org and the College website www.car- per 12-week semester and a winter term leton.edu/campus/doc. Carleton is an af- course every other January. In addition The Department of Mathematical Sci- firmative action/equal opportunity- em to excellence in teaching, an active and ences offers BS, MS, and PhD programs. ployer. We are committed to developing successful research program is expect- It also supports many other degree pro- our faculty to better reflect the diversity ed. grams at Michigan Tech, which boasts of our student body and American soci- a motivated and mathematically-savvy ety. Women and members of minority Applicants are asked to supply a vita and student body largely pursuing degrees groups are strongly encouraged to ap- have three letters of recommendation in the sciences, engineering, and tech- ply. Review of applications will begin on teaching and research sent. Teach- nology. December 1, 2008, and continue until ing and research statements are also the position is filled. welcome. Applications may be made Required qualifications for the position on-line http://www.mathjobs.org/jobs). are an MS in mathematics or a related NORTH CAROLINA Alternately, application materials and field and a record of outstanding teach- letters of recommendations may be sent ing at the university level. Desirable Wake Forest University to Olga R. Beaver, Chair of the Hiring qualifications include a PhD in math- Applications are invited for two tenure Committee, Department of Mathemat- ematics or a related field, experience track positions in mathematics at the as- ics and Statistics, Williams College, in recruiting students into the math sistant professor level beginning August Williamstown, MA 01267. Evaluation major, experience in teaching enrich- 2009. We seek highly qualified candi- of applications will begin on or after ment courses designed to attract middle dates who have a commitment to excel- November 15 and will continue until the and high school students to the study of lence in both teaching and research. A position is filled. For more information mathematics, and the ability to teach dif- Ph.D. in mathematics or a related area on the Department of Mathematics and ferential equations, linear algebra, and/ is required. Candidates with research Statistics, please visit http://www.wil- or discrete mathematics at the interme- interests in Number Theory, Combi- liams.edu/Mathematics. diate (i.e. sophomore or junior) level. natorics, or Algebra will receive first consideration. The department has 20 Williams College is committed to build- The position starts 17 August 2009. members and offers both a B.A. and a ing and supporting a diverse population Review of applications will begin 15 B.S. in mathematics, with an optional of faculty, staff and students, to foster- January 2009; candidates applying by concentration in statistics, and a B.S. ing a varied and inclusive curriculum, that date are assured full consideration. in each of mathematical business and and to providing a welcoming intellec- Interested candidates should send a vita, mathematical economics. The depart- tual environment for all. As an EEO/AA teaching statement, and three letters of ment has a graduate program offering employer, Williams encourages applica- recommendation to: an M.A. in mathematics. A complete tions from all backgrounds. To learn application will include a letter of ap- more about Williams College, please Search Committee plication, curriculum vitae, teaching visit http://www.williams.edu. Lecturer Position statement, research statement, graduate Department of Mathematical Sciences transcripts and three letters of recom- MICHIGAN Michigan Technological University mendation. Applicants are encouraged 1400 Townsend Drive to post materials electronically at http:// Michigan Technological University Houghton, MI 49931-1295 www.mathjobs.org. Hard copy can be Department of Mathematical Sciences sent to Stephen Robinson, Wake Forest Lecturer in Mathematical Sciences The teaching statement should specifi- University, Department of Mathemat- Applications are invited for an ongoing cally address the required and desirable ics, P.O. Box 7388, Winston-Salem, teaching position in Mathematical Sci- qualifications listed above. NC 27109. ([email protected], http://www. ences. The successful candidate will math.wfu.edu ) AA/EO employer. teach a variety of courses at the intro- Michigan Technological University is ductory and intermediate levels, and an equal opportunity educational insti- VIRGINIA will support the larger mission of the de- tution/equal opportunity employer/affir- partment by spearheading recruiting and mative action employer. National Council of Teachers outreach efforts. Initial appointment is of Mathematics anticipated at the Lecturer level, but ex- MINNESOTA Executive Director ceptional candidates will be considered The National Council of Teachers of for appointment as Senior or Principal Carleton College Mathematics (NCTM), a nonprofit Lecturer. Tenure may not be earned in The Carleton College Department of membership association in Reston, Vir- this position, but recent changes in the Mathematics has a tenure-track position ginia, is dedicated to improving math- 30 December 2008 MAA FOCUS ematics teaching and learning from pre- kindergarten through grade 12. Advertising Specifications Guaranteed Special Positions NCTM is conducting a search for an Ex- 10% additional charge; first-come, first-served basis. Classified rates: $2.50 per ecutive Director who is a proven vision- word. ary leader in mathematics education and who will provide strategic direction for Mechanical Specifications its members, staff and mathematics edu- Trim Size: 8 1/4" wide x 10 5/8" high cation. The Executive Director serves Screen: 150-line halftone as the chief staff officer and reports to Full page bleed: 8 1/4" x 10 5/8" the President and Board of Directors. (10% extra charge) He or she is responsible for executing Color: FOCUS standard second the policies and strategic plans of the color available (15% extra charge) association with a $16 million budget, Column Width: 2 5/16, 100,000 members, and 100 employees. 4 13/16", 7 3/8" Printing: Offset, saddle-stitched

A candidate should be a strong, inspir- How to send your materials: ing leader, with demonstrated manage- PDF files are preferred (please embed your fonts). ment skills, business acumen, and ex- perience working with volunteers in a To place an ad - send files [email protected] or call 1-877-622-2373. professional organization. A masters or doctorate degree in mathematics educa- tion or a related field is required.

If you have a passion for mathemat- ics education and can offer vision, Egypt Awaits You leadership, and strategic direction for NCTM’s members and for mathemat- Tour is filling up! ics education, please see the position announcement on our Web site (www. Call today to reserve Your space nctm.org) http://and e-mail your résumé to HR Advantage at tina@hradvantage- inc.com. NCTM is an equal opportunity employer.

WEST VIRGINIA

Shepherd University Assistant Professor of Applied Math- ematics, Shepherd University. Tenure- track, 9-month faculty position, to begin August 2009. Teach courses in mathe- matics, engineering and/or related fields in computer engineering. Requirements: Ph.D. in applied mathematics or closely related field in electrical engineering or computer engineering required by the date of appointment. Looking for an 7th Annual Mathematical Study Tour energetic individual who can interact closely with students, engage in under- May 20 - June 1, 2009 graduate research, participate in com- Full details, itinerary, and application are available on the MAA munity activities such as mathematics website (www.maa.org). contests, and inspire students. Teaching experience at the university level is de- Contact information: sirable. To apply for full consideration Lisa R. Kolbe and other details regarding this position; [email protected] 202-293-1170 please refer to https://jobs.shepherd.edu. Applications are accepted until the posi- tion is filled. EOE. 31 MAA FOCUS December 2008

The Mathematical Association of America Periodicals Postage paid at 1529 Eighteenth St., NW Washington, DC and Washington, DC 20036 additional mailing offices To order visit us online at: www.maa.org or call us at: 1-800-331-1622

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