Mathematics

Programs Offered: M.S., Ph.D.
http://math.tufts.edu
617.627.3235

The Master of Science (M.S.) in mathematics is for students interested in careers in fields including teaching, financial services, statistical research, medical technology, aerospace, and software development.

Students pursuing the M.S. must complete nine courses including required courses in real analysis, complex analysis, algebra, and geometry/topology. These classes can be complemented by advanced courses, which have recently included offerings in surface dynamics, smooth ergodic theory, mathematical neuroscience, algebraic geometry, and measure-theoretic probability. In addition, students pursuing the M.S. are required either to write a thesis or to pass three qualifying exams. Those who choose the thesis explore a specific topic in mathematics under the direction of a faculty member.

Current areas of faculty research include geometric group theory and topology, dynamical systems, representation theory, algebraic and differential topology, algebraic geometry, harmonic analysis, stochastic processes, imaging, tomography and inverse problems, neural models and networks, and fluid dynamics.

The M.S program typically takes two years to complete.

The Doctor of Philosophy (Ph.D.) in mathematics is for students interested in careers in areas such as university research and teaching, technology, and finance.

An individualized course of study, the Ph.D. program builds on introductory graduate courses chosen from real analysis, abstract algebra, geometry and topology, numerical methods, and partial differential equations (the last two offered in alternate years). The program's advanced courses are based on the interests of current Ph.D. students and have included offerings such as surface dynamics, smooth ergodic theory, mathematical neuroscience, algebraic geometry, and measure-theoretic probability.

The program concludes with a dissertation, which is expected to make a substantial original contribution to the field of the student's specialty and meet the standards of quality exemplified by current mathematical research journals. Recent dissertation titles have included, Right-Angled Coxeter Groups and CAT(0) Spaces, Haar-Based Multi-Resolution Stochastic Processes, and The Axonal Plexus: A Description of the Behavior of a Network of Axons Connected by Gap Junctions.

Current areas of faculty research include geometric group theory and topology, dynamical systems, representation theory, algebraic and differential topology, algebraic geometry, harmonic analysis, stochastic processes, imaging, tomography and inverse problems, neural models and networks, and fluid dynamics.

Doctoral students have the opportunity to teach at Tufts. Initially, they may run tutorials or lead review sessions, but usually they teach a full section of a mathematics course.

The department is also a contributing member of the IGERT soft material robotics program. This program, funded by the National Science Foundation, supports Ph.D. students working on projects that combine expertise in more than one department. This support is awarded on a competitive basis. If you wish to be considered for this program you must select the IGERT Soft Material Robotics option when you apply. Additional information on these fellowship awards and soft material robotics at Tufts is available by visiting the IGERT Soft Material Robotics website.

Mathematics: Faculty

James Adler
Ph.D., University of Colorado
Scientific computing

Thomas Barthelmé
Ph.D., University of Strasbourg
Dynamical systems

Bruce M. Boghosian
Ph.D., University of California, Davis
Fluid dynamics

Christoph Börgers
Ph.D., New York University
Mathematical biology

Jens Christensen
Ph.D., Louisiana State University
Integral geometry and harmonic analysis

Moon Duchin
Ph.D., University of Chicago
Geometry, topology, groups, dynamics

Fulton Gonzalez
Ph.D., Massachusetts Institute of Technology
Harmonic analysis

Mauricio Gutierrez
Ph.D., Brandeis University
Group theory

Marjorie Hahn
Ph.D., Massachusetts Institute of Technology
Probability

Boris Hasselblatt, Chair
Ph.D., California Institute of Technology
Dynamical systems

Misha Kilmer
Ph.D., University of Maryland
Numerical linear algebra

Scott MacLachlan
Ph.D., University of Colorado, Boulder
Computational partial differential equations

Alberto Lopez Martin
Ph.D., Universität Zürich
Algebraic geometry

George McNinch
Ph.D., University of Oregon
Algebraic groups

Zbigniew H. Nitecki
Ph.D., University of California, Berkeley
Dynamical systems

Eric Todd Quinto
Ph.D., Massachusetts Institute of Technology
Tomography and functional analysis

Kim Ruane, Director of Graduate Studies
Ph.D., Florida State University
Geometric group theory

Montserrat Teixidor i Bigas
Doctorat, Universitat de Barcelona
Algebraic geometry

Loring Tu
Ph.D., Harvard University
Algebraic geometry

Sabir Umarov
Ph.D., Moscow Power Engineering Institute (Technical University)
Probability

Genevieve Walsh
Ph.D., University of California, Davis
Geometry and topology

Richard Weiss
Dr. rer. nat., Technische Universität Berlin
Group theory