Undergraduate Research
Background
There is a broad spectrum of possibilities for undergraduate research in mathematics at ASU. Research might be funded and/or it might be for course credit. It might be an individual project, or it might be a component of a much larger project. It might also be built into a regular catalog course.
The basic goal of research is to discover new things. In undergraduate mathematical research, sometimes these things were already known to the mathematical world at large, but not known to the researcher at the start. Sometimes, the discoveries are in fact new to the world. Working mathematicians need to focus on the latter. Both types of research are good experiences for undergraduate students. Projects may also involve computations related to open questions in mathematics, or involve topics in mathematics education.
NSF Summer Research Experiences for Undergraduates
The National Science Foundation funds math departments to run summer Research Experiences for Undergraduates (REU) sites. There is a competitive selection process. Students who are selected spend the summer at the REU site. Normally, students attend an REU site at a University different from where they are enrolled during the regular school year. They are compensated for travel expenses, and room and board for the trip.
Once at the REU site, faculty supervise the research. They may have students working individually, or in small groups. Usually, sites will have particular areas of mathematics studied for the research. By the end of the summer, the students will have written final reports on their research. Many present their findings at a special poster session at the large joint annual meetings of the math societies (e.g., AMS, MAA, SIAM).
Each site has a person you may contact for more information on the application process, and how that site is run.
NSF Research Experiences at Home Institutions
The National Science Foundation also funds certain faculty to supervise undergraduate research experiences in conjunction with the faculty member's research grant. Availability at ASU varies over time. Watch for posting in the undergraduate math office, and on the math major e-mailing list for opportunities.Research in MAT 445
In Spring 2001, MAT 445 Theory of Numbers, will be conducted so that students will do mathematical research as part of the course. In fact, research is the main theme of the course. Students will be directed to specific problems, perform numerical experiments, and conjecture theorems in number theory. Then, students try to turn their conjectures into theorems (by proving them), and write up the results. It is a great way to gain an understanding of how mathematics can be discovered/created, and have an introduction to mathematical research. Along the way, the standard theorems and techniques of number theory will be learned. -->
Research with ASU Math Faculty
Research can be conducted under the supervision of a faculty member in the ASU math school. If the faculty member's research is supported by external funding, there may be some support available for students. In other cases, the research may warrant course credit.
A student may arrange to do research with any faculty member in the School of Mathematical and Statistical Sciences at the rank of assistant professor or higher. Below we list some of the School of Mathematical and Statistical Sciences faculty who have projects suitable for undergraduates.
- Dieter Armbruster
- Dynamical systems. A project relating to the synchronization of fireflies treated as coupled integrate and fire oscillators.
- Hélène Barcelo
- Enumerative and/or algebraic combinatorics.
- Marilyn Carlson
- Mathematics education.
- Anne Gelb
- Projects in numerical medical imaging and numerical partial differential equations.
- Glenn Hurlbert
- Combinatorics, graph theory and optimization.
- Don Jones
- Projects in differential equations, fluid dynamics, mathematical biology and scientific computations.
- John Jones
- Projects in algebraic number theory and in the teaching of abstract algebra. Both projects involve some computer programming.
- Matthias Kawski
- Java projects: Interactive visualization projects that range from simple Java applets for undergraduate classes all the way to challenging projects that support NSF-supported research in differential geometric control theory. Each project, whether intended as a learning or research tool, involves programming, but the emphasis is always on mathematics. Objectives for students are to learn, and do more mathematics, participate in cutting edge research, learn valuable job skills and to work on mesmerizing projects.
- Yang Kuang
- Mathematical biology.
- Juan Lopez
- Projects in fluid dynamics, dynamical systems, scientific computations and computer graphics. NSF REUsupport available for spring 2001.
- Alex Mahalov
- Algebraic geometry with applications to differential equations: a pure mathematics project but with unexpected applications. A highly interdisciplinary project involving data analysis, computations and visualization for environmental fluid dynamics.
- Hans Mittelmann
- Projects in optimization and scientific computing which typically involve some computer programming.
- Rosemary Renaut
- Medical imaging research
- Hal Smith
- Projects in mathematical biology, dynamics, differential equations.
- Sergei Suslov
- Orthogonal polynomials, special functions, integral transforms and their applications.
- Bruno Welfert
- Projects in numerical methods for solving ordinary and partial differential equations with applications to fluid dynamics, electromagnetics, finance, civil engineering and stochastic processes.
- Michelle Zandieh
- Mathematics education.
