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No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
This course introduces techniques useful for solving many nonlinear partial differential equations, with emphasis on elliptic problems. PDE from a variety of applications will be discussed. Contact the instructor about prerequisites. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course will cover an introduction of the L_p theory of second order elliptic and parabolic equations, finite difference approximations of elliptic and parabolic equations, and some recent developments in the Navier¿Stokes equations and quasi¿geostrophic equations. Some knowledge of real analysis will be expected. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
This is an advanced seminar course. We will cover several topics in high order numercial methods for convection dominated problems, including methods for solving Boltzman type equations, methods for solving unsteady and steady Hamilton¿Jacobi equations, and methods for solving moment models in semi¿conductor device simulations. Prerequisite: AM 255 or equivalent knowledge of numerical analysis. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Genomics is revolutionizing biology and biomedicine and generated a mass of clearly relevant high-D data along with many important high-D discreet inference problems. Topics: special characteristics of discrete high-D inference including Bayesian posterior inference; point estimation; interval estimation; hypothesis tests; model selection; and statistical decision theory. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The theory of large deviations attempts to estimate the probability of rare events and identify the most likely way they happen. The course will begin with a review of the general framework, standard techniques (change-of-measure, subadditivity, etc.), and elementary examples (e.g., Sanov's and Cramer's Theorems). We then will cover large deviations for diffusion processes and the Wentsel-Freidlin theory. The last part of the course will be one or two related topics, possibly drawn from (but not limited to) risk-sensitive control; weak convergence methods; Hamilton-Jacobi-Bellman equations; Monte Carlo methods. Prerequisites: AM 263 and 264. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Various general techniques have been developed for control and system problems. Many of the methods are indirect. For example, control problems are reduced to a problem involving a differential equation (such as the partial differential equation of Dynamic Programming) or to a system of differential equations (such as the canonical system of the Maximum Principle). Since these indirect methods are not always effective alternative approaches are necessary. In particular, direct methods are of interest. We deal with two general classes, namely: 1.) Integration Methods; and, 2.) Representation Methods. Integration methods deal with the integration of function space differential equations. Perhaps the most familiar is the so-called Gradient Method or curve of steepest descent approach. Representation methods utilize approximation in function spaces and include both deterministic and stochastic finite element methods. Our concentration will be on the theoretical development and less on specific numerical procedures. The material on representation methods for Levy processes is new. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course will provide presentation of the biology and mathematical models/algorithms for a variety of topics, including: (1) The analysis and interpretation of tandem mass spectrometry data for protein identification and determination of signaling pathways, (2) Identification of Phosphorylation sites and motifs and structural aspects of protein docking problems. Prerequisites: The course is recommended for graduate students. It will be self-contained; students will be able to fill in knowledge by reading material to be indicated by the instructor. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
SPDEs is an interdisciplinary area at the crossroads of stochastic processes and partial differential equations (PDEs). The topics of the course include: geneses of SPDEs in real life applications, mathematical foundations and analysis of SPDEs, numerical and computational aspects of SPDEs, applications of SPDEs to fluid dynamics, population biology, hidden Markov models, etc. Prerequisites: familiarity with stochastic calculus and PDEs (graduate level). 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Topics that will be covered include: WKB method: zeroth and first orders; turning points; Perturbation theory: regular perturbation, singular perturbation and boundary layers; Homogenization methods for ODE's, elliptic and parabolic PDE's; Homogenization for SDE's, diffusion processes in periodic and random media; Averaging principle for ODE's and SDE's. Applications will be discussed in class and in homework problems. Organizational meeting will take place on Tuesday, September 8, 2009 at 10 am, Room 110, 182 George Street. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
This course gives an introduction to the the basic concepts of a posteriori estimates of finite element methods. After an overview of different techniques the main focus will be shed on residual based estimates where as a starting point the Laplace operator is analyzed. Effectivity and reliability of the error estimator will be proven. In a second part of the course, students will either study research articles and present them or implement the error estimates for some specific problem and present their numerical results. Recommended prerequisites: basic knowledge in finite elements, APMA 2550, 2560, 2570. An organizational meeting will be held Tuesday, September 8th from 10-12 noon at 37 Manning Street, Room 104. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The purpose of the course is to lay the foundation for the development and analysis of numerical methods for solving systems of ordinary differential equations. With a dual emphasis on analysis and efficient implementations, we shall develop the theory for multistage methods (Runge-Kutta type) and multi-step methods (Adams/BDF methods). We shall also discuss efficient implementation strategies using Newton-type methods and hybrid techniques such as Rosenbruck methods. The discussion includes definitions of different notions of stability, stiffness and stability regions, global/local error estimation, and error control. Time permitting, we shall also discuss more specialized topics such as symplectic integration methods and parallel-in-time methods. A key component of the course shall be the discussion of problems and methods designed with the discretization of ODE systems originating from PDE's in mind. Topics include splitting methods, methods for differential-algebraic equations (DAE),deferred correction methods. and order reduction problems for IBVP, TVD and IMEX methods. Part of the class will consist of student presentations on more advanced topics, summarizing properties and known results based on reading journal papers. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The courses mentioned below are graduate level seminars. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Explores classical and recent results in information theory. Topics chosen from: multi-terminal/network information theory; communication under channel uncertainty; side information problems (channel, source, and the duality between them); identification via channels; and multi-antenna fading channels. Prerequisite: AM 171 or basic knowledge of information theory. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
We will focus on two main topics in mathematical study of the kinetic theory: (1) The new goal method to study the trend to Maxwellians; (2) various hydrodynamical (fluids) limits to Euler and Navier-Stokes equations. Main emphasis will be on the ideas behind proofs, but not on technical details. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Course will address some basic multiscale computational methods such as: multigrid solvers for physical systems, including both geometric and algebraic multigrid, fast integral transforms of various kinds (including a fast Radon transform), and fast inverse integral transforms. Basic problems in computer vision such as global contour detection and their completion over gaps, image segmentation for textural images and perceptual grouping tasks in general will be explained in more details. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Solving large systems of linear equations: The course will use the text of Treften and BAO that includes all the modern concepts of solving linear equations. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
We discuss the construction and general theory of multistep and multistage methods for numerically solving systems of ODE's, including stiff and nonlinear problems. Different notions to stability and error estimation and control. As time permits we shall discuss more advanced topics such as order reduction, general linear and additive methods, symplectic methods, and methods for DAE. Prerequisites: AM 219 and AM 255 or equivalent. Some programming experience is expected. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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