Spring 2003 a VIEW from the CHAIR Nicholas Ercolani Department Head and Professor of Mathematics
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Spring 2003 A VIEW FROM THE CHAIR Nicholas Ercolani Department Head and Professor of Mathematics In this Issue The focus of this management as well Spring newsletter as the Department’s page two T concerns our activities Operations and Mathematics for in Collegiate Education and Business managers, Business Decisions our Undergraduate Program. Faye Villalobos and Richard B. Thompson The feature article is about Deborah Gaines. I want the Department’s Business to thank all of them for page four Mathematics course. Richard achieving this much- Adjunct Program Thompson who created this needed expansion in Elias Toubassi course, in collaboration with such a short time. Chris Lamoureux of the Eller page five School of Business, describes I also want to thank News from the this novel curriculum and its the many of you who Southwestern Center recent national impact. This contributed toward the items on our Wish Douglas Ulmer course will be featured in a Congressional presentation in List. Thanks to your page six Washington on June 17. generosity, we will be Awards able to start construction This issue also features on a new state-of-the- page seven our April Math Awareness art computer classroom Costa Minimal Surface Wish List Week (MAW) activities, with for our undergraduate the theme Mathematics and courses. This and Graduate students, many of whom page eight Art. The sculptures on this other developments go on to win prizes and awards Recruiting Workshop page, created by Helaman in our computational such as those described within Lennie Friedlander Ferguson, were inspired by infrastructure will be these pages. constructions in differential discussed in the page eight geometry. These were the next issue of the New Faculty Profiles subject of a special MAW Newsletter. seminar. page nine Special thanks Summer Math Camps In addition we have an article to those of you Daniel Madden describing the diverse roles who continue to our adjunct faculty play in contribute to our page ten Department activities and in scholarship funds. Math Awareness Week courses at the freshman and These funds make Bruce Bayly sophomore levels. it possible for us to offer novel Recently our Undergraduate page twelve opportunities Offices, Mathematics Presentations, in research and Education classrooms, and Symposia, Workshops education to our tutoring rooms moved many talented into a new addition (Math Math Majors and Umbilic Torus East). This new space was realized through the efforts of the Dean of the Contact us at: College of Science and http://www.math.arizona.edu/~mcenter/alum many personnel in facilities or http://[email protected] 2 Mathematics Spring 2003 The University of Arizona The University of Arizona Mathematics Spring 2003 3 Mathematics for Business Decisions by Richard B. Thompson Computers and an interdisciplinary approach make mathematics accessible to business undergraduates. The Program • Robert C. Merton and Myron S. Scholes were awarded the 1997 Until 1998, the University of Nobel Prize in Economics for work Arizona taught all business students containing what is now called the the traditional sequence of finite Black Scholes formula for determining mathematics and brief calculus. the value of a European stock option. Widespread dissatisfaction by all In Project 2 of Mathematics for parties led to the development of Business Decisions Part 1, students a completely new, project-based, compute the present value of a multimedia approach. The Head of European call option. our Finance Department, Christopher The mathematics in these Nobel G. Lamoureux, created four major achievements is challenging, requiring business projects: Loan Work Outs, a background of considerable Pricing a Stock Option, Marketing mathematical sophistication. How Computer Drives, and Bidding on Richard Thompson teaching does Mathematics for Business Decisions an Oil Lease. We identified the make the underlying concepts mathematical and computer tools needed for business accessible to beginning business students? The answer is in decisions in these projects and for the students’ future work two words: Computers and Simulation. and subsequent careers, and I wrote self-contained electronic For example, probability comes alive when actual stock price texts resulting in a sequence of two data is used to approximate the probability density function of courses. These texts, which are now the random variable that gives the normalized ratio of weekly being published and distributed closing prices. Graphs in Microsoft Excel allow students to nationally by the Mathematical relate stock volatility directly to the standard deviation of this Association of America, consist random variable. Project reports use this volatility to explain of Microsoft PowerPoint® course stock option values obtained by boot-strapping from the files supplemented by Microsoft historical data. Excel workbooks, streaming video clips, and internet links. The new In the capstone project, Bidding on an Oil Lease, computation material has now been studied by gives students a direct connection with research level thousands of students and taught mathematics in a practical business setting. (Simulation by dozens of teachers in seven in Mathematics for Business Decisions led me to discover a Christopher Lamoureux different colleges and universities. Nash equilibrium bidding strategy whose existence was At the University of Arizona it is unknown before 2001. Since then, Larry Wright, also of the currently used in Business Mathematics I and II, taken by all Mathematics Department, and I have developed research- undergraduate majors in the Eller College of Business and level mathematical results in auction theory that support Public Administration. the computation. Our freshman Data for a class version of each project is studied and sophomore by all students, while, at the same time, teams of students now present students are also assigned their own analogous applications of this data sets. Immediately after the introduction of a theory in their team project, each student team gives a preliminary report reports.) on its data. After homework assignments have been completed and the necessary mathematical Support and computer tools studied, the teams present final reports in both written and oral forms. To balance And Teaching the teamwork, both midterm and final examinations are taken by students individually. Development of the novel high-tech Student projects are based on significant and material and of new current mathematics. For example, the mathematics teaching methods behind two of our four projects won Nobel Prizes in A Student Project Presentation to support it has Economics for the creators during the last ten years! been a major challenge. Much of our success is the result • John C. Harsanyi, John F. Nash and Reinhard Selten of strong support received from all levels of the university were awarded the 1994 Nobel Prize in Economics for work administration and from national sources. The project has containing what is now called the Nash equilibrium. In been aided by the President, the current and former Provosts, Project 2 of Mathematics for Business Decisions Part 2, the current and former Vice Presidents for Undergraduate students develop a Nash equilibrium bidding strategy in first- Education and the Vice Provost for Educational Technology. price, sealed-bid auctions. 2 Mathematics Spring 2003 The University of Arizona The University of Arizona Mathematics Spring 2003 3 At President Peter Likins’ request, Mathematics for Business Feedback Decisions was showcased in a 1999 presentation before the Arizona Board of Regents. Support and encouragement has These mathematics service courses have elicited positive also come from the current and former Deans of the College responses from students, faculty, administrators and of Science and professional societies. Mathematics for Business Decisions uses of Business sound mathematics, significant business projects, and student and Public teams; all linked together by computers. Administration. The Mathematics I really enjoyed your class…It is such a different feeling Department has coming out of Mathematics for Business Decisions than committed both when I finished other math classes. I am really glad that I financial resources and faculty time to got the chance to take [it]. the program since A student in Mathematics for Business Decisions its inception. The University Mathematics for Business Decisions’ unique blend…of of Arizona’s new quantitative concepts, computer skills, mathematical freshman complex, the Integrated Learning Center (ILC), tools and ideas, and business concepts renders this course provides an excellent venue for most sections of Mathematics sequence a much more interesting educational experience for Business Decisions. We have been able to take full advantage of computer technology available in the ILC. This for both myself and my students than any other course that includes computer I have ever taught. projection equipment, Julie Tarr, Mathematics Department, Pima Community College access to our program files from . stunning success. I’m proud of you and Chris, and I’m the ILC servers, and the ability to have proud of the Math Department for its contribution to the laptop computers success of Eller [Business] College students. delivered to our Dr. Peter Likins, President, University of Arizona classrooms. Using the laptops, I have Mathematics for Business Decisions is a sparkling example developed a program of how interdisciplinary