Armed with a healthy fear of all things mathematical, I strode purposefully into the Mathematics Department and spent a few moments eyeing some of the academic papers on display. I reached a new high in anxiety as my eyes scanned the following titles: “Swirl Ratio and Mathematical Modeling of Vortex,” “Analysis of a Brownian Particle Moving in a Time-Dependent Drift Field,” and “Generalized Koch Snowflakes.” Finally, a subject I could get my hands around – snowflakes.
Fortunately, these heady-sounding research papers belie a department filled with dedicated, engaging and engaged professors who are only too happy to discuss their field and their department. My initial interview with Dr. John Kemper, who has a Ph.D. from Rice University and was former chair of the department, provided some context in which to place the department and its focus.
Kemper, named 2001 Professor of the Year, believes the department has undergone a clear evolution from “pure math” (math for its own sake) to “applied math” (mathematics that finds immediate application). Kemper has done his own form of application. Although much of his research is in differential equations, he has pursued post-doctoral work in mathematical epidemiology (the mathematical and/or statistical modeling of the spread of infectious disease within a population, in order to better understand and predict patterns of infection) at the University of Minnesota. Clearly, the link between math and science is inextricable, and Kemper wants to explore those links.
Dr. Melissa Shepard, who has a Ph.D. from the University of Minnesota, is exploring some links of her own. Shephard’s interests lie in algebraic topology (“rubber sheet geometry” – the study of properties of a figure that remain invariant under allowable transformations of the figure). Shepard loves doing this type of research because “it’s beautiful.” As you listen to the enthusiasm in her voice and peruse the colorful computer graphics on her screen, you are intrigued. However, this is stuff well beyond Algebra III.
Although game theory (the study of mathematical games including questions of the existence of solutions and the development of procedures for finding them) is not her specific area of interest, Shepard led me through some interesting math games (mathematical models that include more than one player, well-defined possible actions, strategies for each player, and an assignment of payoffs to players dependent on their collective actions) such as NIM and the Four Color Problem. Moreover, Shepard is excited to see more women entering a domain that was almost exclusively male for many years. She says, “Men and women working in the field bring a sense of realism.”
Dr. Jeff McLean gave me my own sense of realism regarding the shortcomings of my mathematics education. McLean, holder of a Ph.D. from Ohio University and a closet pure mathematician, is fascinated by the marriage of math and philosophy. In a delightfully freewheeling conversation, we contemplated meta-mathematical questions, such as: Is math invented or discovered? (This reminded me a little of that “if the tree falls in the forest and no one is there so does it make a sound” question that I always found exasperating.) Does one type of geometry have a higher priority over another? I had little to offer since fractions still give me plenty of trouble. Undaunted, McLean even gave me a short lesson on some of the mysteries of paired prime numbers (a prime is a whole number not divisible without a remainder by any whole number other than itself and one). Clearly, he is profoundly committed to the “scholarship of teaching” and is proud to assert that the department certainly has scholarship standards, but “teaching is our priority.”
McLean believes that technology has had a major influence on mathematics education. The Mathematics Department has a state-of-the-art computer lab and students come equipped with graphing calculators that do the job more quickly than a No. 2 pencil. McLean asserts, “Technology has allowed us to change the way we teach and where we spend our time.”
According to Kemper, because St. Thomas is not focused on “ivory tower research” the department has been challenged by the question: How will my students use math? The department took that challenge seriously and responded accordingly in a unique way, through the Center for Applied Mathematics (CAM) established in 1990 through an institutional endowment. The center’s staff works with the business community to “define and pursue problems in all areas of mathematics.” Naturally, Kemper sees this partnership as appropriate due to St. Thomas’ strong business leanings.
Dr. Patrick Van Fleet, who has a Ph.D. from Southern Illinois University-Carbondale, has directed CAM since 1998. Student-faculty teams have worked on problems in biomedical engineering, epidemiology, life and casualty insurance, vessel traffic control, nonlinear optics, meteorology and (multi) wavelets. Some completed student projects sound daunting. Amy Lowell ’02 made sense of “Mechanical Chaos.” Keith O’Brien ’04 pursued “The Ward Tornado Vortex Chamber.” Scott Wehrenbeg ’02 and Ben Peyton ’02 analyzed “Applications of Markov Chain Monte Carlo Methods to Survival Analysis.”
As its literature states, “CAM’s goal is to increase awareness of the use of mathematics beyond the academic community.” The research projects they promote, the lecture series they offer each year, and their visiting scholar program help them to achieve that goal.
Dr. Kurt Scholz, who has a Ph.D. from UCLA, and Dr. Doug Dokken, a Ph.D. from the University of Minnesota, offer apt examples of professors involved beyond the academic community. They have engaged in several research projects with the National Weather Service and collaborated on an algorithm (a step-by-step problem solving procedure) to predict snowfall depth from radar reflectivity data.
Now they are running computer simulations of severe storms, using real data to model the progression of storms on a newly acquired Alpha ES40 computer. According to Scholz, “Using rather sophisticated modeling programs, ARPS (Advanced Regional Prediction System) developed by the University of Oklahoma, we are able to ‘reconstruct’ the progression of storms and the development of tornadoes.”
With the help of the National Weather Service in Chanhassen and others, they have begun working with the weather data from the Granite Falls tornado of July 25, 2000. Scholz explains, “ Using ARPS, we can enter weather soundings, measuring wind velocity, temperature and humidity at various elevations and obtain a realistic simulation of the weather pattern. The Granite Falls tornado is particularly interesting because it developed so quickly and caught everyone by surprise.” With Scholz and Dokken putting their collective heads together, any future tornadoes had better beware.
Scholz and Dokken explored their common interests even further while on sabbatical at the Institute for Mathematics and its Applications at the University of Minnesota. They devoted an entire year to “Mathematics in the Geosciences” (any of the sciences that deal with the earth). According to Scholz, “Hundreds of visitors from all over the world, from industry and academia, are participating in numerous seminars and workshops.” In the context of this research, Dokken is continuing to explore hydrodynamics, fluid dynamics, dynamic meteorology and microphysics parameterization for atmospheric models (microphysics parameterization – a mathematical model of a physical process that takes place on a microscopic scale). Dokken says, “It is the interaction between these areas, in the context of severe spring and summer weather events, that I find fascinating.” Obviously, Scholz and Dokken are committed to work exploring the link between mathematics and earth science.
The department’s Actuarial Science Program uses mathematical skills to access risks. (Classic definition: An actuary is a person who can pursue a straight line from an unwarranted assumption to a foregone conclusion.) It further explores the link between mathematics and business. It is one of only two such programs in Minnesota. Dr. Heekyung Kang Youn, who has a Ph.D. from the University of Minnesota, is director of the program. She explains: “Actuaries use past information (statistics) to predict future risks and value the risks. In terms of valuation of a risk, an actuary has to predict future occurrences of unpredictable events such as deaths (when), car accidents (when and how severe), unemployments, retirements, as well as future investment returns of the premiums collected.”
If you have never met an actuary, you are not alone. There are only about 20,000 actuaries in North America. Along with the course work required, actuaries must pass a series of professional exams before they are certified. Youn found that her analytical skills acquired as a mathematician were indispensable for actuarial work. According to Youn, “Mathematical training is useful because of the direct application of the content material as well as the ability to analyze a complex problem and to set it in a bigger context.” Actuaries are in high demand, particularly in the abundant insurance company market of the Twin Cities. Luckily, the Actuarial Science Program is more than happy to train them.
Last, but certainly not least, I was able to engage in an e-mail interview last spring with Dr. Chehrzad Shakiban, holder of a Ph.D. from Brown University and chair of the mathematics department since 1997. In 2001 she was on sabbatical in Lausanne, Switzerland. Shakiban was the first woman hired in a full-time math position and is proud to report that the department has grown to 15 full-time members, six of whom are women. Shakiban, who was born and raised in Iran, asserts, “We are the most diverse department at St. Thomas and represent a number of different nationalities.” She is committed to working with minority students and those with financial need to the tune of a $400,000 grant she received from the National Science Foundation. The resulting 29 scholarships will ensure that students can complete their major in mathematics, engineering or computer science.
Shakiban’s Lausanne endeavors are head-spinning. She and her husband, Dr. Peter Olver from the University of Minnesota, are writing a book, Fundamentals of Applied Mathematics, a junior-senior advanced undergraduate level textbook. Then in her spare time, she is applying the research she has been doing in “computer vision” (a field of mathematics that deals with programming computers to recognize visual objects, understand images – including their shapes – and analyze those images) in the study of mechanical properties of DNA. According to Shakiban, “Very little is known about DNA structure, its topology and dynamics. The research I am doing at Polytechnique Federal De Lausanne (EPFL) in Switzerland is in modeling techniques to study DNA structure in a large-scale. Computer vision is then used to understand and characterize the models that are produced by numerical methods at EPFL.” Certainly, Shakiban is pursuing a unique path whose significance could be far-reaching.
The professors in our Mathematics Department have followed many paths to get to this university, arriving at St. Thomas in search of questions and answers. They have also come to teach. Their minds compel them to see the universe differently than my one-dimensional mind sees it.
However, they awakened me to the fact that my finite view of all things mathematical was limited by my finite thinking. The myriad of interests and areas of research of the people in the department speak to the well-cultivated minds that thrive there. Yes, the minds in the math department are beautiful, but what is most captivating is the anticipation they have to meet and instruct the equally beautiful minds of the students that come their way.
Marla Kauzlarich-Borer, a full-fledged member of the math anxiety club, works in the Communication Studies Department. She is an adjunct instructor in English at St. Thomas.