Text D. Applied Mathematics Research

 

1. Read and translate the text into Ukrainian at home. If you were a student of Applied Mathematics department at MIT, which field would you choose? Present your reasons to the whole group.

Department of applied mathematics look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.

Applied Mathematics Fields

• Combinatorics

• Computational Biology

• Physical Applied Mathematics

• Computational Science & Numerical Analysis

• Theoretical Computer Science

• Theoretical Physics

 

Combinatorics

Combinatorics involves the general study of discrete objects. Reasoning about such objects occurs throughout mathematics and science. For example, major biological problems involving decoding the genome and phylogenetic trees are largely combinatorial. Researchers in quantum gravity have developed deep combinatorial methods to evaluate integrals, and many problems in statistical mechanics are discretized into combinatorial problems. Three of the four 2006 Fields Medals were awarded for work closely related to combinatorics: Okounkov's work on random matrices and Kontsevich's conjecture, Tao's work on primes in arithmetic progression, and Werner's work on percolation.

The department has been on the leading edge of combinatorics for the last forty years. The late Gian-Carlo Rota is regarded as the founding father of modern enumerative/algebraic combinatorics, transforming it from a bag of ad hoc tricks to a deep, unified subject with important connections to other areas of mathematics. The department has been the nexus for developing connections between combinatorics, commutative algebra, algebraic geometry, and representation theory that have led to the solution of major long-standing problems. They are also a leader in extremal, probabilistic, and algorithmic combinatorics, which have close ties to other areas including computer science.

 

Computational Biology

Computational biology and bioinformatics develop and apply techniques from applied mathematics, statistics, computer science, physics and chemistry to the study of biological problems, from molecular to macro-evolutionary. By drawing insights from biological systems, new directions in mathematics and other areas may emerge.

The Mathematics Department has led the development of advanced mathematical modeling techniques and sophisticated computational algorithms for challenging biological problems such as protein folding, biological network analysis and simulation of molecular machinery.

Mathematical modeling and computer algorithms have been extensively used to solve biological problems such as sequence alignment, gene finding, genome assembly, protein structure prediction, gene expression analysis and protein-protein interactions, and the modeling of evolution. As a result, researchers are now routinely using homology search tools for DNA/protein sequence analysis, genome assembly software for world-wide genome sequencing projects, and comparative genome analysis tools for the study of evolutionary history of various species. All of these widely used tools were developed, at least in part, by MIT Mathematics Department faculty, instructors and former students. Techniques and tools developed by computational biologists are widely used to drive drug development by pinpointing targets, screening molecules for biological activity, and designing synthetic molecules for specific uses.

Exciting problems in this field range include the protein folding challenge in bioinformatics and the elucidation of molecular interactions in the emerging area of systems biology. Mathematicians will likely make significant contributions to these fundamental problems.