Two subprograms in the Applied Mathematics groups are Physical Applied Mathematics and Combinatorics and Computer Science. Research in `physical' applied mathematics covers a broad range of fields of application including physics, chemistry, materials science, biology, and related fields of engineering, as reflected in the Physical Mathematics Seminar. Our general goal is to develop mathematical models and simulation techniques with direct relevance for real-world problems in science and engineering. We view applied mathematics as an an interdisciplinary science, which actively participates in new discoveries in the more traditional fields. We also see theory, experiment and computation as equally important components of scientific research, so we maintain two experimental laboratories, the traditional Fluid Dynamics Laboratory as well as a Dry Fluids Laboratory, and the Applied Mathematics Computational Laboratory.

The Navy Center for Applied Research in Artificial Intelligence (NCARAI) has been involved in both basic and applied research in artificial intelligence since its inception in 1982. NCARAI, part of the Information Technology Division within the Naval Research Laboratory , is engaged in research and development efforts designed to address the application of artificial intelligence technology and techniques to critical Navy and national problems. The research program of the Center is directed toward understanding the design and operation of computer systems capable of improved performance based on experience; efficient and effective interaction with other systems and with humans; sensor-based control of autonomous activity; and the integration of varieties of reasoning as necessary to support complex decision-making. The emphasis at NCARAI is the linkage of theory and application in demonstration projects that use a full spectrum of artificial intelligence techniques. The NCARAI includes the Immersive Simulations section, the Intelligent Multimodal/Multimedia Systems section, the Intelligent Systems section, and the Interface Design and Evaluation section.

We are taking part in creating a new discipline within engineering; a discipline dedicated to solving the problems arising from the complexity of the human society, from the activities and aspirations of the human beings. Unlike other disciplines of engineering, our problems do not originate in physics or chemistry. Our problems originate from economics and history and such, and the only tools we have at our command are derived from mathematics, in fact, the mathematics of the last 50 years. Princeton University is an educational institution, not an institution for training individuals to perform certain tasks. ORFE is liberal engineering education par excellence: you are not trained for any particular task, you are educated in a whole range of intellectual activities, and you are free to choose the work that you like or the paths that you want to explore. To that end, we give our graduates a strong background in mathematics and engineering, and they accumulate an understanding of economics and other complex human activities. We are sure that upon graduation, our students are ready to meet the challenges of the world.

The Pacific Institute for the Mathematical Sciences (PIMS) was founded and is maintained by the five main universities in Western Canada (Simon Fraser University, University of Alberta, University of British Columbia, University of Calgary, University of Victoria) with the objectives of: Promoting research in mathematics; Strengthening ties and collaboration between the mathematical scientists in the academic community, in the industrial and business sector, and in government; Enhancing education and training in mathematical sciences, and broadening communication of mathematical ideas; and Creating strong mathematical partnerships and links within Canada and with organizations in other countries, focusing on the nations of the Pacific Rim.

Over a century ago, Maurice Couette created a simple device to measure the viscosity of a fluid. He placed the fluid between two concentric cylinders and measured the amount of torque required to turn the inner cylinder. As one increases the rotation rate of the inner cylinder, more torque is required. However, at a certain rotation rate, the variation of torque with cylinder speed changes abruptly. This occurs at the onset of an instability, the sudden change of the pattern of fluid flow as a parameter is varied. In this case, a series of circulating cells known as Couette-Taylor vortices emerge in the fluid flow . The presence of this instability places limits on the utility of Couette's viscometer. Many fluid instabilities have such practical consequences; for instance, the presence of fingering instabilities during oil extraction can mean that half of the oil in a reservoir is left in the ground. At the Center for Nonlinear Dynamics, we study fluid instabilities and pattern formation in many fluid systems.

Research in quantum field theory in the Mathematics Department covers the canonical quantization, the renormalization of Yang-Mills theory, quantum gravity, and string theory with an emphasis on the role of supersymmetry. Recent work involves the AdS/CFT correspondence (from which results on the strong coupling limit of certain 4-dimensional gauge theories can be obtained from calculations in classical 5-dimensional supergravity) and the renormalizability and high-precision experimental verification of the standard model.

The School of Mathematics is an international center of research and postdoctoral training in many diverse aspects of mathematics including pure mathematics, combinatorics, mathematical physics and applied mathematics. Fifty to sixty mathematicians are invited to the School each year to study with the Faculty and to pursue research projects of their own. A small number of memberships for a longer period of time are also available. Funding for candidates comes from a variety of sources. Some mathematicians are funded by the Institute, others receive financial aid from their home institutions, and a portion receive grants from governments or foundations.

SAMSI is a national institute whose vision is to forge a new synthesis of the statistical sciences and the applied mathematical sciences with disciplinary science to confront the very hardest and most important data- and model-driven scientific challenges. SAMSI achieves profound impact on both research and people by bringing together researchers who would not otherwise interact, and focusing the people, intellectual power and resources necessary for simultaneous advances in the statistical sciences and applied mathematical sciences that lead to ultimate resolution of the scientific challenges.

Our research is in the fundamentals of statistics and data mining as well as methodology for the real-world problems motivated by the massive data sets at AT&T. As a direct descendant of the Bell Labs Statistics group, we have a rich history aging back to Walter Shewhart's invention of control charts, and John Tukey's pioneering work in theoretical statistics and data analysis. We are an industry leader in fraud detection methodology, and with some of the largest data sets in the world, we are pioneers in models for data mining on massive data sets.

Search and browsw the library. Mathmatics topics: Algebra, Analysis, Arithmetic/Early Math, Calculus (Single Variable), Calculus (Multivariable), Communicating Math, Differential Equations, Discrete Math, Dynamical Systems (Chaos, Fractals...), Geometry, History and Biography, Logic/Foundations, Number Theory, Numerical Analysis, Operations Research, Pre-Calculus (Functions, Inequalities, Trigonometry), Probability/Statistics, Topology, Applications/Connections. Educational materials. Teaching issues/strategies.

The overall goal of this project is to develop flexible topological methods which will allow the analysis of data which is difficult to analyze using classical linear methods. Data obtained by sampling from highly curved manifolds or singular algebraic varieties in Euclidean space are typical examples where our methods will be useful. We intend to develop and refine two pieces of software which have been written by members of our research group, ISOMAP (Tenenbaum) and PLEX (de Silva-Carlsson). ISOMAP is a tool for dimension reduction and parameterization of high dimensional data sets, and PLEX is a homology computing tool which we will use in locating and analyzing singular points in data sets, as well as estimating dimension in situations where standard methods do not work well. We plan to extend the range of applicability of both tools, in the case of ISOMAP by studying embeddings into spaces with non-Euclidean metrics, and in the case of PLEX by building in the Mayer-Vietoris spectral sequence as a tool. Both ISOMAP and PLEX will be adapted for parallel computing. We will also begin the theoretical study of statistical questions relating to topology. For instance, we will initiate the study of higher dimensional homology of subsets sampled from Euclidean space under various sampling hypotheses. The key object of study will be the family of Cech complexes constructed using the distance function in Euclidean space together with a randomly chosen finite set of points in Euclidean space.

Yale University computational mathematics program covers areas related to fast computation and processing.

The Department of Statistics at Yale University consists of 7 faculty members, 2 staff, and about 25 graduate students. We have active research programs in statistical information theory, statistical genetics and bioinformatics, bayesian methods, statistical computing, graphical methods, model selection, asymptotics, and other topics. Our faculty and students are also active in collaborative research with other departments throughout the university, including computer science, biological sciences, social sciences, physical sciences, engineering, bioinformatics, economics and applied mathematics.