I have always been drawn to computers and games. Some of the fondest memories of my youth were receiving Pong (to play on a black and white TV), Mattel’s handheld Football II, the Intellivision gaming system, the 2k of RAM Timex Sinclair 100 (I saved files to a cassette player), and later the Commodore 64 (with a big old floppy drive). There were not many opportunities to use computers in the schools. In eighth grade we had a project in which we wrote a computer program using punch cards and in ninth grade I took the one computer course that was available.

After high school I attended St. Olaf College, which has a tradition of graduating robust classes of mathematics majors but did not have a computer science major at the time. I was thinking of mathematics and English as majors but eventually decided on just mathematics.

I enjoyed proving things, as is the brunt of the upper-level mathematics course work. In particular, there was something very satisfying in being able to show that something was absolutely true. My Ph.D. adviser, Jon Simon of the University of Iowa, once said that it’s the desire to take some small bit of the universe and make it perfect that drives the mathematician. Others postulate that coffee and cookies are the main fuel.

At the end of my undergraduate time, I had to figure out what to do with my life. I had toyed with the idea of high school teaching and enjoyed a teaching practicum I had taken at St. Olaf, but it did not feel quite right. In another course, I had done a short research project on sound compression and I enjoyed the freedom of working on something that no one ever had thought about. I imagined that graduate school might be interesting in this same way, so I headed to the University of Iowa. After passing through the qualifying exams, I decided that I wanted to work in topology (which is like geometry for hippies). I met with the different topology professors and eventually teamed up with Jon Simon. Jon had done some work on mathematical problems in chemistry, had a network of colleagues in different disciplines and was not afraid to use a computer in his research. In particular, Jon is a knot theorist (like knots in your shoes) and had been working on studying what knots look like when they are pulled tight. His research sounded like fun.

For my dissertation, I wanted to use a computer to simulate the tightening of knots. But we could not simulate real ropes on a computer since real ropes have, in some sense, an infinite amount of information and computers are finite. However, computers do like polygons, so my first task was to translate this tightening problem into something we could analyze with polygons and then show that what we get from computer simulations would correlate with the real ropes problem. I got to work on the mathematics, took a couple of programming courses, and later started to play around with writing code to simulate knot tightening. I really enjoyed combining computations with mathematics. I went to a couple of interdisciplinary conferences during these years and found the talks by researchers from other disciplines intriguing (even when I did not understand all of the details). I thought it would be enjoyable to do work that might have applications.

When I started my first professor job I did not have plans for a big research career. I thought that I would publish a paper related to my dissertation and maybe one or two follow-up papers. That would give me enough for tenure and then I would be in the clear. Research is a lot of work, with lots of ups and downs and long periods in which you feel like you are putting in a lot of effort and getting nothing in return. Balancing research with a new job, teaching new courses, adjusting to a new city, etc., seemed overwhelming, so the thought of spending a bunch of time on research was not appealing.

At the same time, I wanted to at least try to do research beyond my dissertation. I was afraid that if I did not try it right away then I probably never would. I did not know where to start, so I asked Jon what I should do to get more connected to the research community. He suggested emailing people that I had met at conferences to express interest in staying in touch. I did that.

I received several emails back but one in particular stood out. It came from Ken Millett from the University of California, Santa Barbara. He said he was interested in my work and suggested that maybe we could collaborate on a project. Ken is very well known in the mathematics community, so I was both thrilled and scared. After communicating by email for several months, Ken invited me to visit Santa Barbara over my spring break. I remember getting to the airport and thinking “I do not even know this guy and now I am going to spend a week with him at his house talking math.” But I went and I loved it. In fact, Ken and I are still collaborators to this day.

A couple of years later, Ken and I decided to organize a special session at a math conference. There were upcoming meetings in Hoboken, N.J., and Las Vegas. Ken suggested Hoboken but I thought that Las Vegas would be a better draw for our foreign invitees. We invited the top people in our field from all over the world hoping we could get at least a couple of international participants. To my surprise, nearly everyone said yes. This was one of the best things I ever did. It really connected me to the research community. It has been 12 years since I organized that first meeting and this November will mark the 15th meeting I have organized.

Around the same time as the first meeting, Ken encouraged me to apply for a National Science Foundation grant. I did not think I had a chance but figured that I would get some good feedback and that maybe I would have a better chance in the future. I applied to a program focusing on funding faculty at undergraduate institutions, so in my first proposal I included money to pay undergraduates to work with me. Much to my surprise, the project was funded.

Right now, I am amidst my fourth NSF grant.

This funding has helped to launch my research career. In addition to providing computing equipment and opportunities to travel to conferences to see old colleagues and meet new ones, it has been instrumental in including undergraduates in my research. Through the years, 31 undergraduates have been supported by these grants (many of them for two or more years), including 12 since I arrived at UST in 2006. Over a third of these students have gone on to graduate school.

While it is fun to have the students go on to graduate school, a research experience is valuable for any student. As such, I have worked with students with varying interests, majors, and abilities. It is always satisfying to see these students develop as they tackle difficult problems, and I always learn more from the students than they learn from me. In fact, seven of my publications have undergraduate coauthors.

This summer I had a special experience. I took six students to Dennison University in Granville, Ohio, for the UnKnot 2012 Conference. One of my former students, Tom Wears of Longwood University, also participated in the conference. I gave a one-hour invited lecture and three of my students gave contributed talks. It was particularly satisfying to see my current students interact with Tom, possibly peering into their futures.

The focus of my research always has been on studying knotting in objects imbued with some physical properties, beginning with the tightening problem from my dissertation. The tightening work continues today although the focus has changed a little. About 10 years ago, I began a collaboration with Jason Cantarella from the University of Georgia to improve the software to tighten knots, resulting in the program RidgeRunner. Since then, we have written three papers with one more submitted. The most recent work is a collaboration with Jason and two physicists Tom Kephart (Vanderbilt University) and Roman Buniy (Chapman University). Kephart and Buniy have proposed that subatomic particles called glueballs are tightly knotted and linked, tube-like objects. In creating a catalog of tight knots and links, we are (in theory) creating a catalog of these subatomic glueballs.

In the early 2000s, I also shifted my main focus from understanding the structure of tight knots to understanding the structure of polymers. Polymers (like rubber, styrofoam, proteins, and DNA) are long chemical chains and can

be modeled by polygons with some physical properties. We wanted to study what the polymers looked like when they were moving about at random, focusing on knotted polymers. For example, we wanted to know whether the polymers could most easily be placed inside the shape of a pencil, rugby ball, a basketball, M&M candy, etc. This work has been in collab- oration mainly with Ken and Andrzej Stasiak (a molecular biologist from the University of Lausanne, Switzerland who I first met as a graduate student).

A few years ago, I saw a very interesting talk by Joanna Sulkowska (then a physics post-doc at the University of California San Diego and currently of the University of Warsaw) about proteins. Proteins are chains of amino acids that perform many functions within cells. They are created as linear chains and then fold into their functional form (called the native state). These proteins need to fold reprocibly to the same form (some diseases, for example, come from misfolded proteins), and preferably quickly. Some proteins have knotting in their native states. Since knotting should complicate the folding process and make it slower, why would proteins form knots? In particular, is this an accident of nature or does the knotting serve some purpose? The answers to these questions are unknown, so Ken, Andrzej, Joanna, Jose Onuchic (Joanna’s post-doc adviser at UC San Diego, now at Rice University) and I decided to search for answers. Our resulting paper appeared in the Proceedings of the National Academy of Sciences, a high impact journal spanning all of the sciences. Our paper made a bit of a buzz on the Internet too. After the release of a press statement, the story was covered by Wired.com.

These types of cross-disciplinary collaborations now drive my research and continued learning. My collaborators and I combine our skills to tackle problems that none of us could solve on our own. Indeed, the whole is greater than the sum of the parts (which is a tough proposition for a mathematician). These many years later, I am still drawn to computers and games. However, instead of playing Pong on a black and white TV, I now play with supercomputers.

*Eric Rawdon is associate professor of mathematics in the College of Arts and Sciences.*

From Exemplars, a publication of the Grants and Research Office.

“ANALYSIS: Does being pope give you an inside track to sainthood?” Religion News Service, April 23. Theology professor Massimo Faggioli is quoted.

Faggioli was interviewed by Al Jazeera America about the canonization of Pope John XXIII and Pope John Paul II on April 24.

“Obituary: Terence Nichols University of St. Thomas professor,” Star Tribune, April 24.

“Campus beat: Emily Dickinson marathon at St. Thomas plans 1,789 poems in 13 hours,” Star Tribune, April 25. English professor Erika Scheurer is quoted.

“Emily Dickinson poetry marathon kicks off at St. Thomas,” Minnesota Public Radio, April 25. Scheurer is quoted.

“Minnesotans win major arts awards; St. Paul Art Crawl begins,” MinnPost, April 25. The Emily Dickinson poetry marathon is mentioned.

“Canonisation de Jean XXIII et Jean-Paul II: unifier l’Église,” Le Presse, April 25. Faggioli is quoted. (The article is written in French.)

“Papal canonizations a lesson in subtle art of Catholic politics,” Reuters, April 25. Faggioli is quoted.

“Tinder Users Hope To Swipe Their Way To New Love,” WCCO, April 30. Communication and Journalism professor Carol Bruess is quoted.

“Vatican to debate teachings on divorce, birth control, gay unions,” Los Angeles Times, April 30. Faggioli is quoted.

“From a refugee camp to the halls of higher learning,” MinnPost, May 6. Incoming Mathematics professor and St. Thomas alumna Sousada Chidthachack is featured.

**Opus College of Business**

“Home values bounce back around metro,” Star Tribune, April 26. Director of real estate programs Herb Tousley is quoted.

“Outside consultant: How to gauge success of marketing efforts,” Star Tribune, April 27. Marketing adjunct professor Michael Hoffman is quoted.

“New Numbers on Twin Cities Housing,” KARE 11, April 29. A report compiled by the Shenehon Center for Real Estate is referenced.

“Wolves’ owner Glen Taylor supports Sterling punishment,” KARE 11, April 30. Ethics and Business Law professor John Wendt is quoted.

“Hardware stores create their own Angie’s List,” Star Tribune, May 3. Marketing professor Dave Brennan is quoted.

“Data breach and Canada overshadow Steinhafel’s Target legacy,” Minneapolis/St. Paul Business Journal, May 5. Brennan is quoted.

“Target may take months to pick new CEO,” Minneapolis/St. Paul Business Journal, May 5. Brennan is quoted.

**School of Engineering**

“SciGirls,” WUOC, April 27. School of Engineering professor AnnMarie Thomas is featured.

“Medical marijuana: Is a study the solution?” Star Tribune, April 30. Commentary by adjunct professor Frank Freedman.

School of Law

“Canon law professor Dr. Charles Reid discusses Nienstedt deposition,” KARE 11, April 22. School of Law professor Charles Reid is quoted.

“Archbishop Nienstedt’s testimony spurs calls for reform,” Star Tribune, April 24. Reid is quoted.

“Andrew, Brodkorb, others join Star Tribune as bloggers,” Star Tribune, April 28. School of Law professor Nekima Levy-Pounds is mentioned.

“No ‘search warrant’ to be found in rule,” Star Tribune, April 28. Director of academic achievement Scott Swanson is quoted.

“BOTCHED EXECUTION: Okla. failure reignites capital punishment debate,” KMSP, April 30. School of Law professor Mark Osler is quoted.

**In other news **

“Opus Group founder Gerry Rauenhorst dies at 86,” Minneapolis/St. Paul Business Journal, April 25.

“Gerald Rauenhorst, Twin Cities developer and St. Thomas benefactor, dies at 86,” Pioneer Press, April 26.

“Opus founder Gerry Rauenhorst dies,” Star Tribune, April 26.

“Historic Celebration at the Vatican,” KARE 11, April 28. Photos taken by Bernardi Campus director Thanos Zyngas are shown.

“Campus Rape Addressed by White House Task Force, Local Colleges,” KSTP, April 30. Student Affairs director of strategic student initiatives Rachel Harris, as well as several St. Thomas students, is quoted.

“Former Congressman Jim Oberstar dies at 79,” MinnPost, May 3. Oberstar is St. Thomas’ 1998 Distinguished Alumnus.

“Jim Oberstar, longtime Iron Range congressman, dies at 79,” Pioneer Press, May 3.

]]>You may recall the “application sections” in your introductory mathematics courses: velocity and acceleration, compound interest, force balance, center of mass. Most of the applications you likely encountered were from the fields of physics, engineering and economics. Except for population growth, it is unlikely that any applications in your math courses came from biology. Until recently, many biologists also viewed themselves as pure experimentalists with no need for mathematics in their field, but advances in experimental techniques have generated huge amounts of data, and without mathematical modeling and analysis it would be impossible for biology to make sense of all these data.

Last year, I taught a section of Applied Math and Modeling with a focus on mathematical biology. Often when students learn and interpret mathematics through the lens of an application, the mathematics becomes more intuitive and meaningful. My goal with this course was, first and foremost, to teach students how to write accurate, yet tractable, mathematical models. A mathematical model describes some phenomenon from the real world in the form of a mathematical formula or equation. Once the model is formulated, it can be analyzed using a huge variety of techniques, depending on the type of model and what information we want to gain from its analysis.

The second goal of my course was to introduce students to some of these analytical techniques. Because many biologists are interested in how properties change with time, many of the mathematical models in the course took the form of differential equations, which involve derivatives that describe rates of change. What do math students tend to want to do when they see an equation? Solve it; however, solving differential equations, especially those that arise in biological applications, is difficult; furthermore, while biologists are interested in changes in time, they often are interested in what happens after a long, long time. It turns out that many mathematical techniques do not require solving differential equations that allow mathematicians to determine what will happen to a system after a long, long time. Using these techniques, students were able to predict whether two interacting species that are introduced into an ecosystem (say, a predator wolf and its prey, a rabbit) will coexist after 20 years or to predict whether one, or both, of these species will become extinct. Students were able to predict how far along the California coast an initially small population of sea otters will spread, given food and environmental conditions. Students also were able to determine what the minimum susceptibility of individuals must be in order for a certain percentage of a population to die from an outbreak of severe acute respiratory syndrome. Biology provided these students with a unique way to understand the mathematical analysis methods that they were learning.

Upper-level mathematical biology courses such as mine have become more popular in undergraduate education over the past 10 years. Mathematical biology has been an active area of research for much longer, and it too has increased in popularity over the past 15 years. Mathematical biology is a huge field in itself with many different areas of application within biology. Researchers are using math to investigate topics such as how refusing vaccines for one’s children affects the probability of a measles outbreak, or how fluid flow affects the formation of biofilms, which are films of bacteria that can grow in moist places, such as rocks in streams, sewers – and showers!

Recently, I have been working on models that predict how a single biological cell interacts with its environment. Cell-environment interaction is extremely important because it affects many processes in the body, including wound healing, immune response and the development of cancer. As a result, there are huge amounts of experimental data available. Some experiments aim to determine how the cell changes its attachments to the surrounding environment, while others aim to elucidate what biochemical reactions must occur within the cell so that it attaches. Without mathematical modeling and analysis, there would be no way to begin to understand how these components all work together.

While I view mathematical biology as a rich and beautiful field, my main goal is to use this field to expose students to the power of mathematics as a tool – a tool that these students can take with them to whatever future endeavors they choose and a tool that can better help them understand the world around them.

Read more from CAS Spotlight.

I’m not the person my students think I am. You see, I teach courses in applied statistics, and when students see the Ph.D. that follows my name, they assume that I am a socially awkward, humorless statistician or mathematician who will emphasize theorems and proofs over practical applications of the material. While I can’t contradict the assumption of social awkwardness, I have two confessions to make: 1) I am a former allied health professional, and 2) I don’t consider my courses to be “math” courses; instead, they are courses in quantitative literacy. I emphasize real-world applications (over theorems and proofs) to facilitate hands-on engagement in the research process, problem solving and decision making. In our data-driven world, few skills are more important than quantitative literacy. I know this firsthand, as a health professional who was caught off guard by lack of quantitative literacy.

Let me explain.

In my first profession, I was an occupational therapist (OT). OTs are allied health professionals who collaborate with doctors, nurses, social workers and other therapists to treat people who are injured, ill or have disabilities. As an OT, I worked in both inpatient and outpatient settings with patients recovering from significant physical events such as stroke, heart attack, amputation or joint replacement, as well as cognitive and psychological disorders such as dementia, schizophrenia or bipolar disorder.

My OT education focused on identifying and developing plans for effectively treating physical and psychological disorders. I took courses in anatomy, physiology, physical injuries and disabilities, neuroscience and psychosocial disorders. I learned to identify and treat myriad conditions in infants, children, adolescents, adults and seniors. Through several internships, I tried out my textbook and classroom learning on real patients under the supervision of experienced therapists.

My education wasn’t solely patient and treatment focused. Research articles robust with statistical analyses and interpretations were threaded throughout my classwork, and I completed one course in applied statistics and one course in health science research methods; nevertheless, while I read about health science research methods and statistical analysis as an undergraduate, I engaged in very little of it! Perhaps as a result, I graduated with an OT degree under the impression that these components of my education were simply boxes to be checked before graduation rather than critical skills for effective practice as an OT.

Not long after graduation, I began working for the Minnesota Department of Public Health. I became involved in a state-funded grant intended to reduce high-risk behavior (e.g., alcohol and drug use, suicide and sexual promiscuity) by adolescents. Over a three-year period, our team established baselines of high-risk behavior, formed appropriate community- and school-based intervention, and continued to collect and analyze data that examined the impact of our efforts; importantly, the results of our efforts were reported to state officials and agencies, as well as the community we served.

My ability to contribute to the data collection, analysis and interpretation was limited. Although I had completed required statistics and research courses as an undergraduate, my actual abilities to engage in the research process were modest. It became clear to me that the quantitative classes I had taken were not simply boxes to be checked prior to graduation. Developing the ability to use statistical concepts in professional practice was important not just in theory, but in practice. Until I developed these skills, my ability to make a difference in the lives of others through my professional OT practice was restricted.

As such, I began my second career in applied statistics and research methodology. In my Biostatistics course at UST, I strive

to help undergraduates entering fields such as biology, medicine, ecology and psychology engage fully in the research process. My students and I don’t simply read about research or solve equations. We formulate important questions, develop testable hypotheses, design appropriate data collection procedures, use appropriate statistical tools and learn to communicate results to different audiences.

I help students develop quantitative literacy so that, regardless of their chosen fields, they will be prepared to use data and statistical concepts and tools to make a difference in the world around them.

Each semester I begin my biostatistics class by disabusing students of their misperceptions. Most importantly, I tell them, “No, this is not a math class. It is a class in data-driven problem solving and decision making … and whether you realize it now or not, it will be one of the most important classes you will ever take.”

Read more from CAS Spotlight.

The Barry M. Goldwater Scholarship and Excellence in Education Program was established by Congress in 1986 to honor Sen. Barry M. Goldwater (R-Ariz.), who had served 30 years in the U.S. Senate. The program was designed to foster and encourage outstanding students to pursue careers in mathematics, the natural sciences and engineering. This year the program awarded 283 scholarships for the 2014-15 academic year to undergraduate sophomores and juniors from the United States.

Dr. Kyle Zimmer, associate professor of biology who is St. Thomas’ Goldwater program chair, said, “The Goldwater Scholarship is a national competition and is one of the most competitive, prestigious awards an undergraduate in the STEM fields can receive.”

Gentle, a St. Michael, Minn., native, said, “As a research chemist or a professor at a research institution, I hope to lead and mentor teams in the development of new materials, such as materials for solar cell technology. Overall, I hope to contribute to solving world problems such as the global search for feasible renewable energy.” After she graduates, she plans to pursue a Ph.D. in materials chemistry, and is leaning toward a career in academia or as a research chemist in industry.

Millholland, a physics and applied mathematics double major from Madison, Wis., said, “Although I am unsure exactly which area of research I plan to pursue, I am interested in the application of computationally intensive modeling techniques to the field of quantum cosmology. This field involves the study of quantum mechanical descriptions of the formation and evolution of the early universe.” After graduation she’d like to attend graduate school in astrophysics or particle physics and someday teach at the university level.

Sathe, of Hopkins, Minn., plans to pursue a Ph.D. in biomedical engineering, conduct research in biomedical science and teach at the university level.

The Goldwater Scholars were selected on the basis of academic merit from a field of 1,166 mathematics, science, computer science and engineering students who were nominated by the faculties of colleges and universities nationwide. A total of 172 of the scholars are men, 111 are women, and virtually all intend to obtain a Ph.D. as their degree objective. Twenty-two scholars are mathematics majors, 191 are science and related majors, 63 are majoring in engineering, and seven are computer science majors. Many of the scholars have dual majors in a variety of mathematics, science, engineering, and computer disciplines.

The one- and two-year scholarships will cover the cost of tuition, fees, books, and room and board, up to a maximum of $7,500 per year.

Recent Goldwater scholars have been awarded 80 Rhodes Scholarships, 117 Marshall Awards, 112 Churchill Scholarships and numerous other distinguished fellowships. Since 1998, 23 St. Thomas students (including Gentle and Millholland) have received Goldwater Scholarships.

Since 1989, the Barry M. Goldwater Scholarship and Excellence in Education Foundation has awarded 7,163 scholarships worth approximately $46 million.

For more information about the Goldwater Scholarships, contact Zimmer, (651) 962-5244.

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At Northwestern, the Department of Engineering Sciences and Applied Mathematics is part of the School of Engineering, and, as a result, I was required to take engineering courses, such as statics and dynamics, fluid mechanics and operations research, in addition to the courses required for my applied mathematics major. Of the engineering courses, I mostly enjoyed mechanics, so when I decided to stay at Northwestern and get a Ph.D. in applied math I knew that I wanted conduct research in an area that combined mathematical modeling, mechanics and scientific computing, which is a branch of applied math that utilizes computer programming to solve mathematical models to ultimately understand the nonmathematical problem at hand. Out of this came my Ph.D. thesis on using the level set method, a type of computational method that allows one to track the motion of interfaces, to simulate fracture due to cyclic loading.

So, how did I get from research in fracture mechanics to mathematical biology? On Jan. 7, 2002, Professor Howard Levine gave our weekly applied mathematics colloquium on modeling the vascularization of cancerous tumors. I was in awe. At that point, mathematical biology was not as popular as it currently is, and I had no idea that you could apply mathematics to biology. Since at that time I was finishing my Ph.D. and was on the job market, I decided to focus my job search to postdoctoral research positions in mathematical biology. This is how I ended up at the University of Minnesota working with Professor Hans Othmer. As a postdoctoral research associate, I realized that not only can one apply mathematical principles to biological problems, but that mechanics plays an important but poorly understood role in biological processes.

Mathematical biology is a huge field ranging from mathematical modeling of disease spread over large geographical areas using continuum population models to modeling protein transport during cellular division using discrete particle dynamics models. I work to mathematically model the movement and growth of single cells and soft tissues. Many of the models I use to understand growth and movement are based on principles of deformable body mechanics. Traditionally, biology has been considered to be an experimental science in which mainly qualitative observations are important. Over the last one to two decades, the need for quantitative analysis in biological fields has significantly increased. The way I see it, there are two major reasons for this. First of all, oftentimes a biological experiment can address one small aspect of a much larger and more complex process. For example, there are experiments that are aimed at understanding how proteins are transported during cell division and other experiments whose goal is to understand the magnitude of forces required to divide a cell. But, how does protein transport affect these forces? Mathematical models can incorporate data from multiple experiments and lead us to a better understanding of the interplay between various subprocesses. Second, many experiments, especially those that require manipulation of mechanical properties on a cellular level, are extremely difficult to perform. Simulations based on mathematical models can provide insight as to what might happen in a biological system on which an experiment cannot be done.

While I have worked on mathematical models aimed at understanding the interplay between the biochemistry and mechanics involved in a growing vertebrate limb, the effect of mechanical stresses on growing tumor, and the stresses that form in a brain that is growing within an abnormally developed skull, I have spent the majority of my time attempting to gain a better understanding of how mechanical interactions with the environment affect the movement of single cells in that environment. Surprisingly, the mathematical models describing all of these systems are very similar. Through the Center for Applied Mathematics Summer Research Program and through an NSF grant that several of my colleagues and I have received, I have been very fortunate to work with several talented and hard-working St. Thomas students on these mechanical models of cell movement. One group of students developed and programmed a model in which the goal was to investigate how the strength of attachments a cell makes with a flat surface affects the way that it moves over that surface. Another group worked on modeling cell movement through a series of deformable barriers meant to replicate the collagen fibers in the human body. The goal of this project was to understand how the mechanical properties of collagen fibers affect the ability of a cell to move about. Through both of these projects we have learned that mechanical properties of the cell and its surroundings have a huge effect on a cell’s ability to move. Through a joint project with an industrial partner, I am in the process of extending this student work to learn more about the interplay between mechanical properties of the cell and intracellular biochemical processes.

My work with students on these projects has been especially rewarding. Both groups mentioned above have presented their research at professional research conferences and have had a taste of what it means to be a researcher. Through their research projects both groups have grown in their mathematical intuition, computational programming and problem-solving skills. Most rewarding to me, both groups of students have developed an appreciation of the usefulness of mathematics in helping us understand how (nonmathematical) things work.

*Magdalena Stolarska is assistant professor of mathematics at the College of Arts and Sciences and associate director of the Center for Applied Mathematics.*

*From Exemplars, a publication of the Grants and Research Office.*

I have spent much of the last 12 years teaching various topics in statistics, research methods and measurement to undergraduate and graduate students at St. Thomas and elsewhere. My students typically have been hard working and eager to learn. They came to class and took notes. They learned the steps of important processes. Their nodding heads indicated that they understood the material as it was being presented to them. And yet, these bright and capable students often had difficulty applying course material in novel or ambiguous but true-to-life contexts. Despite the clarity of my explanations or the number of times I demonstrated how to apply concepts and processes, students often didn’t know what to do with what they knew.

I came to understand that *remembering* and *understanding* are necessary, but not sufficient, for the kind of “knowing” that allows one to think critically and solve complex problems. This realization seemed particularly problematic, as it is precisely this type of“knowing” our students need now, in our increasingly technical and competitive world.

While this need for knowing exists in all disciplines, it may be especially urgent for the Science, Technology, Engineering and Mathematics (STEM) disciplines. In 1996, the Advisory Committee to the National Science Foundation, responding to a call to improveundergraduate STEM education, published “Shaping the Future: New Expectations for Undergraduate Education in Science, Mathematics, Engineering, and Technology.” One of its recommendations called for faculty teaching undergraduate STEM courses to “build inquiry, a sense of wonder and the excitement of discovery, plus communication and teamwork, critical thinking, and lifelong learning skills into learning experiences.”

At St. Thomas, STEM faculty members have taken to heart the call to actively engage students through critical thinking and collaborative problem solving.

In spring 2010, Kris Wammer, associate professor of chemistry, organized a two-day workshop on the use of Peer-Led Team Learning (PLTL) in entry-level STEM courses. PLTL involves groups of six to 12 students who take the same course (e.g., Chemistry111) and work with trained peer-facilitators to address problems that facilitate conceptual understanding of course material and the development of problem-solving skills. The workshop was well attended by biology, chemistry, mathematics, computer and information sciences, geology, physics and engineering faculty. At its conclusion, faculty decided to initiate a PLTL program for students taking introductory STEM coursesat St. Thomas.

After an intense summer of planning, the PLTL program was ready to launch: A program structure consisting of a coordinator, four departmental liaisons and 16 to 20student peer-facilitators was agreed upon; shortterm funding to support a program coordinator and pay peer-facilitators for the 2010-2011 academic year was secured from the dean of the College of Arts and Sciences and the Biology Department; discipline-specific peer-facilitators were recruited and trained; concept-focused, problem-based activities were developed by departmental liaisons for use by peer-facilitators in small-group sessions; formal PLTL program evaluation procedures were devised; and a name for the PLTL program was created: the STEM Learning Community (LC) Program.

In fall 2010, STEM LCs emphasizing collaboration, active learning, problem solving and critical thinking were introduced. Each semester since then, STEM LCs have been offered to about 300 chemistry students, 200 biology students, 130 calculus students and 90 statistics students, most of whom are first-year college students at St. Thomas. Between 180 and 240 students participate in the STEM LCs each semester.

Research on the use of collaborative learning strategies in undergraduate STEM education suggests that they are a highly effective strategy for promoting the kind of “knowing” that is expected of STEM professionals. Evaluation of the STEM LC programat St. Thomas indicates that benefits for participants and peer-facilitators are many: learning effective study skills; acquiring depth of understanding; gaining skills in collaboration; and developing confidence in problem-solving abilities. As one STEM LCparticipant noted, “I learned different ways of approaching a problem, and if I didn’t understand something, the group was able to help.” Another participant stated, “I study more efficiently and more often” as a result of this experience.

Mithra Marcus, clinical professor of chemistry, is excited by the impact of the STEM LC program on her students. She noted, “This program has helped my students think critically about course material rather than just focus on memorizing facts.” Such an emphasis has translated into improved learning outcomes for participants. Significantly higher exam scores have been achieved by LC participants in all of the courses in which LCs are offered. In the case of chemistry, STEM LC participants scored more than five points higher, on average, than their peers on a standardized, nationally normed chemistry examination.

Through my own involvement with the STEM LC program, I am reminded that my job is not to simply tell students what is important to know. If I truly want my students to beactive learners, critical thinkers and effective problem solvers, I must find ways for them to connect with one another and with the material in deep and meaningful ways. The STEM LC program appears to offer an effective strategy for doing just that.

Read more from CAS Spotlight

]]>“I mainly have been studying clouds and how they’re organized on different time and length scales,” Stechmann said. “I’m trying to understand the various aspects of weather and climate that aren’t understood now. I want to improve the models that are used to predict weather and climate.”

Weather forecasters use certain equations to see what the atmosphere will look like in the future. Stechmann wants to create the correct equations and different strategies for solving them on a computer.

“It all goes back to an independent study I did at St. Thomas,” he said. His senior year, Stechmann took an independent-study course, Fluid Dynamics and Numerical Methods for Fluid Dynamics, taught by Doug Dokken, Kurt Scholz and Mikhail Shvartsman.

“I started off at St. Thomas as a pre-med student but then I got to know some of the older students majoring in math and I just really liked it. I enjoyed the challenge,” Stechmann said. “I really liked doing physics, math and chemistry [his three majors at St. Thomas] so when I went to grad school I chose weather and climate classes because it employed all three.” Stechmann earned a Ph.D. in mathematics at Courant Institute of Mathematical Sciences, New York University, last May.

He received two fellowships for his postdoctoral research at UCLA: A mathematical sciences fellowship from the National Science Foundation and a climate and global change fellowship from the National Oceanographic and Atmospheric Association.

In a few years when he’s done with his postdoctoral research,he hopes to teach and do research as a tenure-track professor.

“I’d like to come back to Minnesota, but you usually can’t be so picky,” said Stechmann, a Red Wing native.

**Colleen Duffy ’03 **– *Assistant Professor *At the University of Wisconsin-Eau Claire, Colleen Duffy knows that students enter her classroom with different levels of appreciation for math.

“There are students who dislike math and when they are done with class, they dislike math less,” she said. “A lot of students come in thinking math is interesting. I can share with them the cool parts of math and it’s great to see the light come on when they finally understand something. Math majors are really excited about math, and I help them explore it further.”

This is the profession Duffy envisioned many years ago. In high school, she helped her friends with their math homework, competed on the math team and completed math independent-study classes. So it was natural for her to major in mathematics at St. Thomas. She also majored in Spanish and minored in physics.

“I was friends with everyone on the faculty. They helped me get into graduate school and helped me succeed,” Duffy said.

“Cheri Shakiban was my adviser so I did a lot of research projects with her that greatly helped me in my Ph.D. program. I did applied research projects such as studying the stability of structures.” One project was inspired by the study of the historic collapse of the Tacoma Bridge in Washington. The suspension bridge collapsed in 1940 due to wind-induced vibration.

“We looked at a variety of structures to determine under what forces the structures would collapse. I set up a system of equations to see what happens if you change the number a little bit – is it still stable or will it collapse?”

Her independent study in abstract algebra with Melissa Shepard Loe helped her decide to concentrate in algebra in graduate study. Duffy earned a Ph.D. in mathematics from Rutgers, The State University of New Jersey, last May.

Duffy teaches three classes a semester at UW-Eau Claire. Her research focuses on noncommutative algebra.

**Tom Dahl ’01 **- *Actuary *It’s risky business, but that’s what an actuary loves. Tom Dahl deals with the financial impact of risk and uncertainty. He is an actuary at Federated Mutual Insurance Co.’s home office in Owatonna.

Federated specializes in business insurance; Dahl is one of four employees who works in the actuarial health insurance division.

One of his responsibilities is pricing. As most Americans are aware, health insurance costs continue to rise. Dahl explained,“Pricing is based on what it cost last year. We look at trends and we project how much it will cost the next year. We set our premiums so we’ll be able to make a small profit or at least break even.”

Dahl enjoys his work at Federated. “I get to see all phases of the health insurance process and I have a lot of autonomy in my work. I have friendly co-workers,” he added.

When he started his freshman year at St. Thomas, he knew that he would major in actuarial science. Later he tacked on a major in math.

“I always liked math,” Dahl said. His cousin worked for State Farm Insurance and suggested Dahl might like actuarial work, so in high school he participated in a mentorship program with St. Thomas alumnus Joe Paul ’88, an actuary.

His adviser at St. Thomas, Heekyung Youn, who taught several of his classes, helped him find an internship. For two years he interned at Mercer Consulting and worked with state Medicaid programs. He was hired at Mercer in Minneapolis after graduation and worked there until 2004.

“Then I decided that I didn’t want to live in the Twin Cities anymore. I needed a break so I moved to Owatonna for the Federated job. It’s a more relaxed pace of life – no rush hour! It takes me four minutes to drive to work ,” said Dahl, a Moorhead native.

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