Our faculty members have a wide range of expertise and interests: applied graph theory, computation theory, differential equations and mathematical modeling, mathematics education, number theory, and statistics. That allows you to investigate diverse topics in pure and applied mathematics. You'll have opportunities to conduct and present research with professors on campus and with students and faculty from all around the country and even around the world.

Some recent student experiences:

- One of our students has had a paper published in the latest issue of the Rose-Hulman Undergraduate Mathematics Journal.
- Two Saint Michael's students collaborated with students from Pennsylvania, California, and Texas on a study to see how answering machines can correctly identify unknown words.
- One of our students participated in the prestigious Budapest program for mathematics in a semester abroad experience.
- At the University of Georgia, one of our students explored the mathematics behind the folding models of Origami.
- Another group of students analyzed a set of signatures using Fourier analysis and wavelet decomposition to distinguish which signatures were forged.
- Back on the Saint Michael's campus, a group of students used graph theory and geometry to provide optimal design strategies for self-assembling DNA nanostructures.
- One of our students was selected to help research the feasibility of designing a system capable of transferring from a low Earth orbit to a lunar orbit and possibly landing on the Moon.
- By taking part in a research experience, you will have the chance to present and publish your work, as some of our students have done. Recent examples include the American Journal of Undergraduate Research and the Journal of Applied Mathematics.

At St. Mike's, every class is taught by highly credentialed professors who know you by name. Many professors use classroom technology to capture their classes for students to review. To see an example, watch this lecture on Complex Analysis given by mathematics professor George Ashline.

## Math Learning Outcomes:

Mathematics majors are expected to acquire competence in calculus, linear algebra, and probability and statistics. Through these fields, students are to develop understanding and skills in mathematical reasoning, logical deduction, data analysis and interpretation, and problem solving at various levels and in various contexts.

Students will communicate effectively broader mathematical reasoning approaches and more specific problem solving steps.

Students will progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction, and formal proof. They are to formulate definitions and apply methods of direct and indirect proof.

Students will work with ideas and approaches representing the breadth of mathematical sciences, ranging from continuous to discrete and theoretical to applied.

Students will undertake an exploration of at least one advanced topic of their own choosing. This will require them to carefully read, analyze, and create mathematical arguments and draw on ideas and make connections with previous coursework.

Students will have experience with a variety of technological tools, such as computer algebra systems, visualization software, statistical packages, and computer programming languages.

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M.S., Ph.D. University of Notre Dame

B.S. St. Lawrence University

## Areas of Expertise:

Mathematics education and mathematics pedagogy; mathematical preparation of in-service and pre-service teachers; and complex analysis.

## Courses I Teach:

- Calculus
- Complex Analysis (view a classroom recording)
- History of Mathematics
- Linear Algebra
- Mathematics Education Seminar
- Number Theory
- Real Analysis

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Ph.D. University of North Carolina, Chapel Hill

M.S. University of Vermont

B.A. Bennington College

View my personal website

## Areas of Expertise:

Algebraic combinatorics, especially graph polynomials, and applied graph theory in statistical mechanics, computer chip design and bioinformatics.

## Courses I Teach:

Calculus I, II, III, Applied Graph Theory, Linear Algebra, Real Analysis, Abstract Algebra, Senior Seminar

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B.A, M.S. University of Vermont

## Areas of Expertise:

Mathematics education and mathematics pedagogy; mathematical preparation of in-service and pre-service teachers; abstract algebra.

## My Road to Saint Michael's:

I recently joined Saint Michael’s College from the University of Vermont where I worked on reviewing, revising, and increasing the rigor in the mathematics courses for early, elementary, and middle level education majors. I also worked on a department-wide study of the effectiveness of online homework systems in elements/ fundamentals of calculus courses. Prior to UVM, while working for the Vermont Mathematics Partnership, I led a team of mathematics educators and mathematicians in the design, development, and instruction of a professional development program for 5th-9th grade in-service mathematics teachers. The courses in this program included: Proportional Reasoning in the Middle Grades, Geometry in the Middle Grades, Making Informed Decisions, and Modeling Change.

I began my undergraduate career as a biology major, before realizing that I was not cut out for laboratory work (the odd unidentifiable smell, the lack of human interaction, and a strong fear of Bunsen burners all contributed to my downfall in the lab). I became a mathematics major with every intention of eventually becoming a teacher of mathematics. I am passionate about teaching mathematics and helping all students succeed in mathematics. I am a true “mathophile” but my real love is in helping students who have struggled with mathematics in the past realize that they can do high-level mathematics. Prior to coming to Saint Michael’s in 2011, I taught at the University of Vermont for four years.

# Jim Hefferon, PhD

Professor of Mathematics

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B.S., M.S., Ph.D. University of Connecticut

My background is in the theory of computation.

Courses I Teach:

- Calculus
- Numerical Methods
- Statistics
- Theory of Computing

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M.S., Ph.D. Rutgers University

B.S. St. John's University

## Areas of Expertise:

Differential equations; nonlinear dynamics; chaos and fractals; reaction-diffusion systems; mathematical models in chemistry, physiology, population dynamics

## Courses I Teach:

- Applied Mathematics
- Calculus I and II
- Differential Equations
- Discrete Mathematics

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M.Sc., Ph.D. McGill University

B.Sc. University of British Columbia

## Areas of Expertise:

Algebraic Number Theory; Algebraic K Theory

## Courses I Teach:

- Abstract Algebra
- Calculus I,II,III
- Linear Algebra
- Probability and Statistics

My favorite class to teach is Calculus III. I very much like the material, which is the interplay of geometry and calculus. The power of mathematics to solve hard problems really begins to be evident in this class. And at this point, the students are for the most part very mathematically smart, motivated, and interested in the material.

## My Saint Michael's:

Saint Michael's students are bright, polite, outgoing, and usually willing to learn. What more could a professor ask for? The smaller class sizes and the relatively relaxed relationship one can have with one's students are also things I appreciate along with the overall friendly atmosphere of the students and the faculty.

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Ph.D. University of South Carolina

M.S. The University of Vermont

B.S. DePaul University

## Areas of Expertise:

Applied statistical techniques for environmental sciences, biostatistics, and sports; Statistical education; Statistical consulting.

## Courses I Teach:

- Applied Regression Analysis
- Applied Statistical Methods
- Calculus I
- Elementary Statistics
- Probability and Statistics
- Seminar in Mathematics

You’ll have the chance to become involved in research both on and off campus. Several projects enable students to participate in and present their work at academic and professional conferences on campus and around the country. (See specific examples under "What You’ll Learn"). Student research topics have included origami, Galois groups, computer chip layouts, DNA nanostructures, space robotics, HIV infection models, and professional soccer league possession analysis.

Some of our students have been able to research, study, and present at such schools and venues as Brigham Young University, Mathematical Association of America meetings such as the summer MathFest, and the NASA Goddard Space Flight Center.

Our students and faculty have received grants and funding for their research from the Vermont Consortium for Language and Academics, The Vermont Genetics Network, The Louisville Institute, Vermont EPSCoR, National Security Agency, NASA, the National Science Foundation and other comparable agencies.

### Present at HRUMC, a great regional undergraduate conference

Most of our majors participate in the annual Hudson River Undergraduate Mathematics Conference (HRUMC). This one-day conference celebrates undergraduate mathematics research with students and faculty from across the Northeast, and provides students with the experience of attending and presenting at a professional mathematics meeting. There are also exciting plenary talks by nationally renowned mathematicians, and career and graduate school panel discussions. This is a great opportunity to meet a wide range of other students also excited about mathematics. Each year, several of our students present their advanced work in mathematics, computer science, statistics, and more.

### Take advantage of summer learning opportunities

Many of our students take part in Research Experience for Undergraduates (REU) programs over the summer. These opportunities enable our students to learn the fundamentals of mathematics research and to explore the many applications of math in the real world. Our students have recently participated in programs at Texas A&M, University of Georgia, George Washington University, Northern Arizona University, Claremont Colleges, and Princeton University/the Institute for Advanced Study.

### Learn from presentations by visiting math experts

We host a variety of talks and lectures by distinguished guests and alumni as a part of our regular Colloquium Series. Some recent titles include: "Counting Self-Intersection Points of Loops on Surfaces," "Symmetry and the Monster: Mathematics as the Ultimate Complex System," "Graphs and Symmetry," "Differences in Global Mathematics Education," "Mathematics of Juggling", "Chaos and the Mathematics of Prediction," and "The Shape of Space." Our Alumni Panels offer the chance for our math students to hear from and talk with math alumni who are using their degrees in different ways. Panelists share their career paths and/or graduate school experience, and give advice to students. Saint Michael’s also co-hosts a joint Combinatorics Seminar Series with the University of Vermont that brings together academic and industry researchers to discuss the theory and applications of combinatorics.

### Become a member of Pi Mu Epsilon

Saint Michael's is home to the Vermont Alpha Chapter of Pi Mu Epsilon (PME), the National Mathematics Honors Society. PME currently has over 340 chapters at colleges and universities throughout the United States. Math students who meet the requirements can be inducted into the society during their junior or senior year. We have regular events, such as an annual induction ceremony and reception, special speakers, and recognition at graduation.

### Take seminars and special topics courses in mathematics

Our spring semester math seminar courses offer opportunities to study and present on compelling topics in the math field. Our two most recent seminars focused on environmental issues related to water and the mathematics of games. Our fall semester special topics courses provide the opportunity to study mathematical fields not considered in our normal course sequence. Future topics planned are topology, graph theory, and population dynamics.

Mathematics majors are attractive to a wide variety of business and industrial firms, especially if the major is combined with some coursework in computer science, a natural science, economics or business; many find work in the actuarial field or as analysts in the computer or communications industry. You might prepare to teach at the secondary school level by simultaneously completing education courses, including a semester of student teaching, which leads to state certification.

Many of our students go directly into the work force upon graduation. IBM, Pfizer, UBS, Travelers Insurance, the NSA, and Liberty International Underwriters are just a few of the companies at which Saint Michael's math alumni now work. Our graduates are computer analysts, actuaries, consultants, and high school math teachers. They are also college professors, administrators, and researchers at places like UMass, UVM, and Sandia National Labs.

A number of our students pursue advanced degrees. As a math major at Saint Michael's, you can prepare for graduate programs in pure or applied mathematics or in statistics. You can also prepare for medical school, law school, or graduate work in mathematics intensive fields such as bioinformatics or economics by combining the math major with other Saint Michael's courses in education, computer science, a natural science, economics or business.

Our graduates excel in a range of professional fields including:

- Business, Finance, and Investment Banking
- Accounting and Tax Services
- Mathematics Education
- Actuarial Analysis
- Medical School
- Computer Science and Software Development
- Data and Statistical Analysis
- Operations and Administration
- Research and Development
- Careers in mathematics intensive fields such as bioinformatics and economics

Our alumni attend graduate school in mathematics, statistics, and other fields at the University of Minnesota, Clarkson University, Colorado State University, North Carolina State University, the University of Notre Dame, the University of Maine, and the University of Vermont, to name only a few.

Many graduates of the Mathematics Department are rapidly advancing in their careers and educational skills. The following pages contain profiles in which alumni provide their current job titles and career descriptions, or career and educational plans for the future. The featured alumni also reflect on how their Saint Michael's education has prepared them for their professions. Their diverse stories are grouped under more general category links, which are listed below. Click on the links to read their individual accounts.

For alumni who are interested in sharing their information with Saint Michael's, contact George Ashline, Chair and Professor of Mathematics, at gashline@smcvt.edu.

## Alumni Report on their Math Careers

Many graduates of the Mathematics Department are rapidly advancing in their careers and educational skills. The following pages contain profiles in which alumni provide their current job titles and career descriptions, or career and educational plans for the future. The featured alumni also reflect on how their Saint Michael's education has prepared them for their professions. Their diverse stories are grouped under more general category links, which are listed below. Click on the links to read their individual accounts.

For alumni who are interested in sharing their information with Saint Michael's, contact George Ashline, Professor of Mathematics, at gashline@smcvt.edu.

### Career Pursuits of Mathematics Alumni