Applied Mathematics
Introduction
The language, tools and theorems of mathematics are applied in a vast range of disciplines within engineering and computer science, the physical sciences, the biomedical sciences, management and economics, psychology, etc. As a field of study and research applied mathematics lies at the boundary between mathematics and its applications. Applied mathematics involves the application of interesting mathematical tools to significant applied problems and the development of new mathematics adapted to particular applications.
The Applied Mathematics Group
The applied mathematics group includes about a quarter of the full time faculty members of the department, with about 11 individuals of whom 2 hold joint appointments with other departments. Currently there are also 7 associate members from other departments and a number of retired professors who to various degrees maintain active involvement with the applied mathematics group. There are particularly active interactions between the applied mathematics group and its graduate students with members of the School of Computer Science, the Department of Atmospheric and Oceanic Sciences and the Centre for Applied Mathematics in Bioscience and Medicine. Members of the group are have been very active in the Centre de Recherche Mathematiques (CRM) and its Applied Mathematics Laboratory, based at McGill, which facilitates collaboration between the mathematicians or Montreal's four universities and brings a steady stream of world class mathematicians to the city, as well as funding some postdoctoral positions. At the graduate student level the Institut des Sciences Mathematiques (ISM) supplies some postdoctoral and graduate student funding, and also enables students to take advanced courses from any of the city's universities through its programmes in all areas of mathematics including its Applied and Computational Mathematics programme.
Appointments in recent years have led to the development of two distinct research concentrations in the applied mathematics group. One grouping works on different aspects of differential equations (partial, stochastic, and delay) and applications with the majority of their research being characterized by the use of a blend of analysis with computation. This group has recently been strengthened by the appointments of Gantumur Tsogtgerel in 2009, and Rustum Choksi and Jean-Christophe Nave in 2010. The other grouping is in Discrete Mathematics with emphasis on Discrete Optimization and Algorithmic Game Theory. The research agendas of our current faculty in both areas are largely application driven. These are and will continue to be extremely important and fertile areas of applied mathematics research into the long-term future, and our plan is to continue to build on both groups.
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| Numerical simulations of the mixing of a passive tracer by a turbulent two-dimensional fluid, above — with no rotation and below — on a rapidly rotating planet such as Jupiter. Clickable images. | |
Current Research Areas in Applied Mathematics
- Differential Equations and Numerical Analysis
with a particular
emphasis on different classes of differential equations (partial,
stochastic, delay) and dynamical systems, usually linked to
specific areas of application. Present areas of expertise
include:
- computational fluid dynamics (Peter Bartello, Sherwin Maslowe, Jean-Christophe Nave, Jian-Jun Xu)
- dynamical systems and delay equations (George Haller, Tony Humphries, Leon Glass, Michael Mackey).
- numerical analysis of differential equations (Peter Bartello, Tony Humphries, Jean-Christophe Nave, Gantumur Tsogtgerel)
- numerical linear algebra and its applications (Xiao-Wen Chang, Chris Paige)
- partial differential equations and applied analysis (Rustum Choksi, Eliot Fried)
- Discrete Mathematics
There is a very active Discrete
Mathematics group at McGill comprised of researchers and
students from mathematics and other departments, working in a
wide variety of areas, including:
- Graph Theory and Combinatorics (Bruce Reed, Bruce Shepherd, Adrian Vetta)
- Network Optimization (Bruce Shepherd, Mohit Singh, Adrian Vetta)
- Algorithmic Game Theory and Economics (Adrian Vetta, Bruce Shepherd)
- Probability and Probabilistic methods (Louigi Addario-Berry, Luc Devroye, Bruce Reed)
- Mathematical & Theoretical Physics (Gantumur Tsogtgerel, Charles Roth)
- Optimisation (David Avis , Neville Sancho, Bruce Shepherd, Mohit Singh, Adrian Vetta). This area has broad applications to many disciplines and is popular with graduate students across the Science and Engineering Faculties. The group currently offers courses in continuous and discrete optimization, combinatorial optimization, computational geometry, operations research and approximation algorithms.
Research Seminars
Current Seminar Series
- CRM-McGill Applied Mathematics seminar, current semester.
- Discrete Mathematics and Optimization seminar.
- Centre for Applied Mathematics in Bioscience and Medicine Seminar/Workshop Series.
Archive of Previous Seminars
Links
- Centre de Rechereche Mathematiques (CRM) and the CRM Applied Mathematics Laboratory
- Institut des Sciences Mathematiques (ISM) and its Applied and Computational Mathematics programme.
- McGill University and