Mathematics
Majors and Minor
Faculty and professional interests
Andrew Leahy, chair
Group representation theory, history of mathematics
Mary Vlastnik Armon (on leave Spring 2013)
Number theory, analysis
Kevin Hastings (on leave Spring 2013)
Probability, statistics, operations research, financial mathematics
Dennis Schneider
Real and complex analysis, functional analysis
Brent Solie
Group theory, combinatorics
Pedro Teixeira
Commutative algebra
The Department of Mathematics offers a rigorous core curriculum that challenges students to think abstractly, recognize and generalize patterns, communicate ideas, and define and solve problems. In addition, mathematics students can explore exciting developments in this rapidly changing field through special topics courses and independent research in areas such as game theory, chaos, and cryptography.
Mathematics students begin with a solid foundation in calculus, linear algebra and mathematical structures before proceeding to a variety of advanced courses and independent work. All mathematics majors are also required to finish an independent research project leading to a public presentation before they graduate. Some opt for a year-long honors project in the department instead. Recent research and honors projects have dealt with a wide array of topics such as measure theory and financial mathematics, analytic and numerical solutions to partial differential equations, and factorization algorithms and their application to computer security.
Faculty research encompasses a range of both pure and applied areas of mathematics, and advanced projects are often driven by both student and faculty interests. For instance, faculty interest in the history of mathematics has led to student projects in projective geometry. Faculty interest in number theory has led to student projects in computer security and distributed computing. Faculty interest in stochastic processes has led to student projects modeling everything from epidemics to stock prices. In addition, students have assisted with curriculum development projects centered around Mathematica, a computing environment for doing mathematics that is used extensively in introductory as well as advanced mathematics courses.
The department also offers a major in the area of Financial Mathematics. This field of study focuses on the properties of investment objects, investor's and firm's attitudes toward risk, and the consequences to individual investor behavior as well as that of the whole market. It is a subject of much current interest, both theoretical and practical, which combines mathematical reasoning with economic insights.
Mathematics majors have completed distinguished graduate programs in mathematics, computer science, statistics, economics, biomathematics, engineering and operations research. Other graduates have become respected teachers, or have been sought out by computer and consulting firms, insurance companies, investment companies, banks and government agencies.
The departmental curriculum contributes to the College's Key Competency Requirements as follows:
- Writing Key Competency - MATH 300, 321, 331, and 341 serve as writing-intensive courses for majors
- Speaking Key Competency - MATH 361, 399, or a completed honors project serve as speaking-intensive courses for majors
- Information Literacy and Informed Use of Technology - Mathematics majors become proficient in the state-of-the-art computer algebra system Mathematica for numerical, symbolic, and graphical problem solving.
Departmental Learning Goals
Students completing a major in Mathematics will be able to:
- Reason logically and demonstrate complex problem-solving skills
- Demonstrate competency in the core of the discipline
- Communicate effectively in the language of the discipline
- Demonstrate a knowledge of how to use technology to support investigation
Students completing a major in Financial Mathematics will:
- Apply the concept of randomness appropriately to financial modeling
- Demonstrate understanding of the nature of financial quantities and the mathematical and economic relationships between them
- Combine economic reasoning with mathematical rigor to solve problems
- Write and speak correctly in the language of the discipline of Financial Mathematics