Research Areas
Algebra
Modern algebra has its roots in the mathematics of the ancient world,
arising out of the basic problem of solving equations. Following an
explosive development in the twentieth century, it is now a vibrant,
multi-faceted and wide-ranging branch of mathematics, having ties with
almost every field of mathematics and computer science. The interests of the
Algebra group at Northeastern include algebraic geometry, commutative
algebra, representation theory and homological algebra, with connections to
combinatorics, singularities, Lie groups and topology. [more info...]
Analysis
Analysis is a broad branch of mathematics that encompasses many fields,
generally sharing a basis in calculus. In our Department, research in analysis includes a
wide range of fields and subjects, from differential equations to ergodic theory. [more info...]
Combinatorics and Discrete Mathematics
Discrete mathematics is perhaps the fastest growing area of modern mathematics.
It has a wealth of real world applications, especially in computer science, which have
greatly contributed to its rapid growth. The Mathematics Department has an active
research group in combinatorics, the central field of discrete mathematics.
The faculty in our Combinatorics Group work in a variety of areas including
algebraic combinatorics, discrete and combinatorial geometry, and graph theory. [more info...]
Topology
Topology is the mathematical study of those properties that
are preserved through continuous deformations of objects.
Topology began with the study of curves, surfaces,
and other objects in the plane and three-space. It can be
used to abstract the inherent connectivity of objects
while ignoring their detailed form. Topology can be divided into algebraic topology, differential
topology, and geometric topology. All three areas of research are represented in the Mathematics Department. [more info...]
Probability and Statistics
The field of Probability and Statistics encompasses a broad array of topics in pure
and applied mathematics, and has applications in almost every field of scientific research.
The theoretical foundations of Probability Theory were developed in the early twentieth
century by Kolmogorov and other workers, and this led to an explosion of applications
in every scientific field. By its nature the field is driven by real-world applications,
and this is reflected in the work of the members of the Probability and Statistics group,
whose research ranges from applied Statistics to inter-disciplinary research to pure mathematics. [more info...]
Interdisciplinary
Mathematics has, since ancient times, been associated with many
disparate areas of human inquiry, ranging from art and philosophy to science and
engineering. This fruitful interchange has led to important mathematical discoveries,
and has also stimulated the development of whole new fields of study. This tradition
continues today in the Mathematics Department, where a wide variety of interdisciplinary
research is conducted, both singly and in collaboration with researchers in
other departments and universities. [more info...]
Last modified September 14, 2005
|
