Criterion 1

Teaching Excellence

Summary

Courses Taught 2000-2009

· MCS 118 (Calculus with Pre-Calculus Review 1A)

· MCS 119 (Calculus with Pre-Calculus Review 1B)

· MCS 122 (Calculus II)

· MCS 221 (Linear Algebra)

· MCS 222 (Multivariable Calculus)

· MCS 253 (Differential Equations)

· MCS 321 (Theory of Complex Variables)

· MCS 353 (Applied Analysis)

· MCS 357 (Discrete Dynamical Systems)

· MCS 358 (Mathematical Modeling)

· PHY 230 (Applied Mathematics for Physics and Engineering)

· PHY 370 (Advanced Mathematical Methods in Physics)

· FTS (Chaos and Culture)

Other Teaching Responsibilities 2000-2008

· Independent Study

o MCS 253, Differential Equations, 1 student, 1 credit (2001)

o MCS 353, Applied Analysis, 1 student, 1 credit (2002)

· Honors Theses

o 2 students (2002-2003)

o 1 student (2004-2005)

o 1 student (2008-2009)

· Academic Advising

o 43 students total

o 2 First Term Seminars

· Extracurricular Advising

o Advisor, 3 Mathematical Contest in Modeling teams, (2002,2003)

o Advisor, MCS Club (2003-2004)

Discussion

Since my promotion to Associate Professor in 2004 I have continued to innovate and grow as a teacher. I have modified techniques and developed new materials for familiar courses. I have taken on new courses and challenges. And I have developed new courses both singly and in collaboration with departmental colleagues. My excellence as a teacher of mathematics does not come just from my mastery of the material, but rather from a continued concern of how best to engage and motivate my students.

Probably the most effective way to engage students is to be enthusiastic about the material. I believe that I am exceptionally passionate about mathematics at all levels and this comes through in the classroom. In MCS 118 one student commented on my course evaluations that “Mr. LoFaro is the best math teacher I have ever had, hands down. He is not only incredibly knowledgeable on his material, but also enthusiastic and excited about his job, as well. I cannot praise LoFaro enough; he has expanded my mental horizons beyond anything I could have ever expected.” But sometimes I may go to far with my enthusiasm. According to one student I “can be too passionate, at times, almost obnoxious.”

Of course passion is not enough; it must be complimented by preparedness and materials that allow the students to become engaged in the material. In my materials for promotion to Associate Professor I discussed the importance of engaging students in the material and some of the tools I was using to accomplish this task. Since then, I have further developed some of these methods. Students have a tendency to use a math textbook as a source of problems and worked examples and do not read the text before coming to class. In the past we used a web-based program to assign what we called “prep problems.” This system worked, but it was pretty inflexible because it took a significant amount of time to publish the questions and was cumbersome to adjust when the schedule inevitably varied. Thus this was usually done before the semester started. I now use a written “problem of the day” at the start of many class periods. I find that this still prompts the students to read the material, but gives me the flexibility to prepare questions that address either the current topic or to review and reinforce previous ideas and techniques that will be needed during that class period.

In our department we try to emphasize that mathematics is best learned by “thinking and doing, not watching and listening.” As a consequence, we try to mix traditional lecture with in-class problem solving sessions. I have significantly increased the amount of time I devote to this more active approach, especially in 100 and 200 level courses. As a consequence, I have also developed a larger repository of worksheets, activities, and projects for these classes. This is especially true in MCS 118/119 “Calculus with Precalculus Review.” Barbara Kaiser and I developed this course together and we have small group classroom activities most every class period. We think that this is especially important in a course that is designed for students who are under-prepared for a college level calculus course and are more prone to the anxieties that come with this. Closely monitored classroom activities provide me with an opportunity to give one-on-one instruction to students who need additional direction and allow me to discover common misconceptions so that they can be addressed to the entire class.

I am a strong believer in the importance of in-depth projects and have always used them in the applied mathematics courses that are my specialty (MCS 253, 357, 358 and PHY 230). In this context, a project is much more than a word problem. It is generally a guided mathematical modeling project that utilizes the mathematical ideas that have been recently covered. These projects require students to model a physical phenomenon, analyze it mathematically, and then write (and sometimes present) a short report on the project. In fact, this process is almost the entire content of MCS 358, Mathematical Model Building. Last year, I began using projects in MCS 122 Calculus II and was very pleased with the outcome. The students seemed to enjoy the projects and I think that they helped me demonstrate the value of the material and how it might be applied in their future studies and endeavors.

As mentioned previously, Barbara Kaiser and I together proposed and developed the two-semester sequence Calculus with Precalculus Review (MCS 118-119). The department felt that a having traditional precalculus course (that did not fulfill a general education requirement) and then having these students take MCS 121 (Calculus I) might not be as successful as having an integrated course that taught calculus but approached precalculus material in a “just in time” manner. The course is structured so that every major calculus topic is revisited multiple times throughout the two semesters. For example, when MCS 119 begins in the spring we will begin by discussing derivatives and their applications. In this revisit, however, we will introduce some applications that we did not discuss in MCS 118. Derivatives will be discussed two additional times during the semester when we discuss exponential functions and again when we discuss trigonometry. We believe that this approach allows sufficient time and practice to master calculus while at the same time teaches important precalculus ideas when they are needed.

I continue to take on new teaching challenges. Several years ago I had the opportunity to teach the PHY 370 (Advanced Mathematical Methods in Physics). This was a great learning opportunity for me as I regularly teach PHY 230 (Applied Mathematics for Physics and Engineering) and it was extremely helpful to me to see how the material in the lower level course is built upon in the upper division one. I am currently teaching MCS 321 (Theory of Complex Variables) for the first time at Gustavus and although I have taught most of this material at previous institutions, it will be a welcome challenge and change.

In addition to classroom teaching responsibilities I have been active in advising and the direction of Honors Theses. Honors Theses are not terribly common in the MCS Department and I have directed four of these since coming to Gustavus. Of particular note is the thesis by Tim Dorn that led to the publication of a joint paper in the journal Genetics.

Criterion 2

Professional Activities

Summary

Please refer to my Annotated Bibliography for a summary of publications and presentations over the last ten years. My CV contains a complete listing of all publications and presentations during my career as well as a listing of professional activities.

Discussion

The structure of my Annotated Bibliography reflects my dual interests in mathematical research in applications of dynamical systems and in the development of projects and software to be used in undergraduate instruction of dynamical systems and differential equations. I view both of these facets of my professional agenda as equally important and there is a clear synergy between them.

A quick reading of my research publications might suggest that my research agenda is not very focused. Applications described in these papers include population genetics, neuroscience, and computer science. However, the mathematical tools used in all of these papers are the unifying thread. In each of these papers I use the tools of dynamical systems to analyze the given model. Each model is a system that varies over time (a dynamical system) and the objective in each of these papers was to determine the long-term behavior (or convergence) of the system. For example, the paper “Authority rankings from HITS, PageRank, and SALSA: existence, uniqueness, and effect of initialization” considers various methods for ordering the web pages found when doing a web search. We determine conditions under which each of the given algorithms will converge to a ranking that is independent of an initial seeding and is meaningful in the context of a web search. A second common question that is addressed in these papers is “how does the convergence change if parameters in the model are changed.” This is known as bifurcation theory. In the paper “Population Models of Genomic Imprinting II. Maternal and Fertility Selection” we use these ideas to show that in one particular model of genomic imprinting a bifurcation occurs that causes the behavior of the system to bifurcate from a stable equilibrium solution (in this case a fixed allele frequency vector) to an oscillatory solution (where the allele frequencies will vary over time.)

In the Research Presentations section of my Annotated Bibliography I refer to a pair of presentations on the evolution of cooperation. This work differs somewhat from my earlier research in that the system being modeled is a dynamical system with some intrinsic randomness (or stochasticity). The system models the interactions of two populations: the first will never cooperate while the second will cooperate with another individual until that individual takes advantage of them. The model equations combine both game theory (in the form of the Prisoner’s Dilemma) and population genetics (game payoffs are interpreted as fitnesses). I have proven that in the absence of randomness, the dynamics of a population that consists of mostly non-cooperators will, over time, tend to a solution that contains no cooperators. In other words, without randomness, cooperation cannot evolve. Simulations and basic analysis of the stochastic model suggest that there are certain conditions on the game payoffs that make the evolution of cooperation more likely. However, I have not been able to prove that this is correct and hence have chosen not to publish this work.

I believe that my work has been well received in the mathematical modeling and dynamical systems community. This is reflected by the acceptance of these papers in high quality journals in their fields. In addition, I have had the opportunity to present my work at a wide variety of institutions and conferences both locally and nationally (as well as internationally in Spain and while on sabbatical in New Zealand).

The second thrust of my scholarly activity is summarized in the Pedagogical Publications section of my Annotated Bibliography. Throughout my career I have been extremely active in developing, implementing, and assessing projects and software for use in differential equations and dynamical systems courses. This began at Washington State University with the award of two National Science Foundation grants for the project “IDEA: Internet Differential Equations Activities” (http://www.sci.wsu.edu/idea/). Although the NSF funding for this project expired years ago, my collaborator Kevin Cooper and I continue to monitor and update the site as technology advances and new ideas and projects arise. More recently, Kevin and I were asked to author nine projects that are included in the differential equations text book Differential Equations with Boundary-Value Problems 6th ed. by D.G. Zill and M.R. Cullin and published by Brooks/Cole.

I am currently involved in the NSF funded CODEE project. CODEE is a consortium of colleges and universities that are collaborating on making projects and tools such as the ones I have developed easily available to a wide audience of teachers. The primary investigator of this project is Darryl Yong of Harvey Mudd College. I have been asked to write a brief paper describing strategies for assigning, motivating, and grading modeling projects in differential equations courses. I will also be involved in training others in using the CODEE resources at upcoming national and regional math conferences.

My work in the pedagogy of differential equations education has been extensive and continues to be an integral facet of my career. I helped develop one of the first web sites that provided instructors with both differential equations projects and the software to help understand the dynamics of these models. I participated in the development of an award-winning piece of software (ODE Architect) that was one of the first to bring multimedia tools to an educational audience. I continue to write projects that are published in textbooks and journals. I believe that the breadth and depth of this work clearly demonstrates that I am a recognized expert in this area.

Criterion 3

College Leadership

Summary

College-wide Committees and Leadership

· Director, Rydell Professor Program (2005-present)

· Provost Council (2007-present)

· Instructional Infrastructure Advisory Committee – Chair (2005-2007)

· Academic Operations Committee (2005-2008)

· Curriculum Committee (2004-2005)

· Faculty Development Committee (2003-2004)

· Faculty Committee on Student Life (2001-2003)

Other College-wide Activities

· Faculty Mentor (2007-present)

· International Student Host Family (2006-2008)

· Nobel Conference Host (2005)

· Task Force on High-Risk Alcohol Use (2002-2003)

· Hughes Grant Planning Committee (2002-2003)

· Rydell Professor Faculty Host (2002)

· Facilitator, Freshman Wilderness Experience (3 times)

· Judicial Board member (various times)

Departmental Committees and Responsibilities

· Math Placement Exams (2001-present)

· Math Contest in Modeling Faculty Sponsor (2002-present)

· Departmental Search Committee (2008)

· Departmental Library Liaison (2000-2003)

· Math Club Faculty Advisor (2003-2004)

· Department Colloquium organizer (2001-2002)

Discussion

The summary above demonstrates that I have established a significant pattern of leadership in college and departmental governance. I have served on and chaired important faculty committees, have been active in departmental duties, and have taken on some less formal college-wide responsibilities as well.

In my estimation, the most significant of my responsibilities is the Directorship of the Rydell Professor program. I believe that I have made a very significant contribution to this program by first providing the continuity and leadership that was lost in a previous presidential transition, and then increasing the visibility of this program both on-campus and to the wider Gustavus community. Since taking the directorship of this program I have scheduled Rydell Professorships for Robert Gallo, Sylvester James Gates, Frans de Waal, and Curtis Marean. Last year we began what I hope is a new tradition to this program, a Twin Cities lecture that is co-sponsored by a local institution. Last year we partnered with the Minnesota Zoo and this year we will be partnering with the Science Museum of Minnesota. These lectures are intended to highlight one of the annual events that is unique to the Gustavus community. I believe that I have also increased the visibility of this program on our campus. Classroom visits are much more frequent than when I was a faculty host for Steve Smale and I have been arranging less formal activities with student groups who might benefit from interacting with the Rydell Professor in a less formal setting.

One of the most challenging aspects of this program is the recruitment of individuals to serve as Rydell Professor. The program is described as a “scholar-in-residence program designed to bring Nobel laureates and similarly distinguished scholars to the campus.” Although the honorarium is significant, I have found it difficult to recruit active research scholars to participate in the program due primarily to the extended nature of the visit. I have tried to be creative in dealing with this requirement, (for example, Sylvester James Gates made almost weekly visits during his spring semester) but I am still frustrated by the challenges in convincing a renowned research scientist to visit for an extended period. I have had more success with individuals who have already participated in a Nobel Conference, as they are already familiar with Gustavus and the intangible things that make this place special. Thus I regularly attend the Nobel Conference luncheons to try and spread the word to potential Rydell Professors. In addition, I try to be tangentially involved in the planning of upcoming Nobel Conferences to better inform my invitation process.

Because I direct the Rydell Professor program, Provost Mary Morton asked me to serve on the Provost’s Council, which includes the directors of similar programs on campus. This group meets approximately once per month to share ideas and confer on issues that impact upon our programs that do not necessarily fit into the academic structure of the college.

I have served on a number of faculty committees including chairing the Instructional Infrastructure Advisory Committee (IIAC). I believe that participating in faculty governance is an important aspect of academic life at this college and I take these responsibilities seriously.

My service to the department is equally important. I have annually managed the math placement examination and, with the help of Max Hailperin, oversaw the conversion of this exam from a test taken on-campus during summer registration to an online examination that is taken before students arrive for registration. Last year I was one of three department members who oversaw the hiring of our most recent tenure-track hire.

The list above also illustrates that I have been active in less formal service roles on campus. Of these activities, I most enjoy facilitating the Freshman Wilderness Experience trips to the Boundary Waters. This is a trip of approximately one week that has taken place the week prior to students arriving on campus. Two of the objectives of the trip is to help develop leadership skills and to instill a sense of confidence in the students who participate. I have done this trip three times and each time I have seen the students blossom and continue to succeed once they arrive on campus.

Criterion 4

The Mission of the College

Eight years ago, when I interviewed for this position, a student asked me “why do you want to work at Gustavus?” The response was easy and immediate: “why did you choose to attend Gustavus?” I then explained how I wanted to teach at a school with a sense of community, a place where faculty and students are involved in both academic and social issues. In the time since that first visit to this campus, I have come to believe that one of the defining characteristics of this campus is its sense of community.

The Gustavus Adolphus College Mission and Core Values Statement defines our sense of community. It asserts that we continually strive to be a community that seeks excellence and nurtures talents. It asks us to continually assess our teaching methods and develop innovative methodologies while retaining those techniques and ideas that work. It demands us to respect all members of the community and to engage the local and global community in ways that foster respect, leadership, and caring.

I hope that in the preceding sections I have made it abundantly clear that not only do I seek excellence in my teaching and research but that I instill in my students the same level of enthusiasm, excitement, and determination. In advanced mathematics courses I strive to provide my students with an in-depth understanding of the material that allows them to appreciate the beauty and depth of the material. In introductory courses my excitement about the material is also clearly evident. I strive to demonstrate not only the power of mathematics, but also the importance and utility of the problem-solving thought processes that can be developed and refined by solving complex mathematical problems. I chose to become the Director of the Rydell Professor Program primarily because I believe this program provides our community with the opportunity to engage in a meaningful and profound way with people whose work exemplifies excellence.

I have consistently refined my teaching methods and have introduced innovative courses and materials to the mathematics curriculum both here at Gustavus and throughout my discipline. The projects I’ve authored are the most visible form of innovation as these have been published on the web, in textbooks, and on CDs. But there is other, less visible, evidence of innovation. The use of software such as Maple in most every class I teach and the planning of an active-learning classroom in the MCS department are two such examples.

I have consistently involved myself in activities that foster respect, leadership, and caring in our community. When serving on Judicial Boards, or hosting international students, or taking incoming freshman to the Boundary Waters, I have used these opportunities to serve as catalysts for growth for both the students and myself. My favorite memory of my first Freshman Wilderness Experience trip embodies the personal and communal growth I hope to foster. Our first several portages were a mess. It seemed it took longer to decide who was going to carry what that it did to carry everything over the portage. On the second day out, on arriving at yet another portage, several of the students suggested a division of the packs and canoes so that the two people in each canoe could be responsible solely for their canoe and the things it carried. We had heavy packs and light packs, backpacks and Duluth packs, heavy canoes and light canoes. Yet the assignment of packs to canoes was flawless. This was remarkable. But what made it even more satisfying is a picture I took on a long portage of a student with one pack strapped to her back, a second pack strapped in front, paddles in each hand, and a smile of triumph across her face! She double-packed a long portage so her partner need only carry the canoe on what would be a long portage.

When I came to Gustavus I knew I needed to work in a community that cherished ideals such as these. After nine years on this campus I realize that this institution has instilled in me a greater understanding of what it means to be an active participant in a community and I hope that in the years to come this level of involvement will continue to grow.