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No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Topics to be discussed will range from the determination of who won the match, through biomechanics, free-fall of flexible bodies and aerodynamics, to the flight of ski jumpers and similar unnatural phenomena. Prerequisites: AM 11 and AM 34 or their equivalents, or permission of the instructor. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The themes of scaling and self-similarity provide the simplest, and yet the most fruitful description of complicated forms in nature such as the branching of trees, the structure of human lungs, rugged natural landscapes, and turbulent fluid flows. This seminar is an investigation of some of these phenomena in a self-contained setting requiring little more mathematical background than high school algebra. Topics to be covered: Dimensional analysis; empirical laws in biology, geosciences, and physics and the interplay between scaling and function; an introduction to fractals; social networks and the "small world" phenomenon. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The courses mentioned below are senior seminars. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Undergraduate College College Applied Mathematics Department Return to Previous New Search
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In a host of applications, from satellite communication to compact disc technology, the storage, retrieval, and transmission of digital data relies upon the theory of coding and information for efficient and error-free performance. This course is about choosing representations that minimize the amount of data (compression) and the probability of an error in data handling (error-correcting codes). Prerequisite: A knowledge of basic probability theory at the level of AM 165 or MA 161. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Originally developed by C.E. Shannon in the 1940s for describing bounds on information rates across telecommunication channels, information and coding theory is now employed in a large number of disciplines for modeling and analysis of problems that are statistical in nature. This course provides a general introduction to the field. Main topics include entropy, error correcting codes, source coding, data compression. Of special interest will be the connection to problems in pattern recognition. Includes a number of projects relevant to neuroscience, cognitive and linguistic sciences, and computer vision. Prerequisites: High school algebra, calculus. MATLAB or other computer experience helpful. Prior exposure to probability theory/statistics helpful. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Equations that arise from the description of fluid motion are born in physics, yet are interesting from a more mathematical point of view as well. Selected topics from fluid dynamics introduce various problems and techniques in the analysis of partial differential equations. Possible topics include stability, existence and uniqueness of solutions, variational problems, and active scalar equations. No prior knowledge of fluid dynamics is necessary. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Large, sparse systems of equations arise in many areas of mathematical application and in this course we explore the popular numerical solution techniques being used to efficiently solve these problems. Throughout the course we will study preconditioning strategies, Krylov subspace acceleration methods, and other projection methods. In particular, we will develop a working knowledge of the Conjugate Gradient and Minimum Residual (and Generalized Minimum Residual) algorithms. Multigrid and Domain Decomposition Methods will also be studied as well as parallel implementation, if time permits. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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This course is designed for undergraduate students in mathematics who have an interest in the life sciences. No biological experience is necessary, as we begin by a review of the relevant topics. We then examine a number of case studies where mathematical tools have been successfully applied to biological systems. Mathematical subjects include differential equations, topology and geometry. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Plasmas can be big, as in the solar wind, or small, as in fluorescent bulbs. Both kinds are described by the same mathematics. Similar mathematics describes semiconducting materials, the movement of galaxies, and the re-entry of satellites. We consider how all of these physical systems are described by certain partial differential equations. Then we invoke the power of mathematics. The course is primarily mathematical. Prerequisites: AM 34 or 36, MA 18 or 20 or 35, and PH 6 or PH 8 or EN 51. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Mulitgrid methods are a very active area of research in Applied Mathematics. An introduction to these techniques will expose the student to cutting-edge mathematics and perhaps pique further interest in the field of scientific computation. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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This course will deal with advanced concepts in numerical linear algebra. Among the topics covered: Singular Value Decompositions (SVD) QR factorization, Conditioning and Stability and Iterative Methods. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The mathematics of speculation as reflected in the securities and commodities markets. Particular emphasis placed on the evaluation of risk and its role in decision-making under uncertainty. Prerequisite: basic probability. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The course will deal with the mathematics of speculation as reflected in the securities and commodities markets. Particular emphasis will be placed on the evaluation of risk and its role in decision making under uncertainty. Prerequisite: basic probability. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Introduction to fluid dynamics as applied to the mathematical modeling and simulation of ocean dynamics and near-shore processes. Oceanography topics include: overview of atmospheric and thermal forcing of the oceans, ocean circulation, effects of topography and Earth's rotation, wind-driven currents in upper ocean, coastal upwelling, the Gulf Stream, tidal flows, wave propagation, tsunamis. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Introduction to reaction models for biomolecules, activation and formation of macro-molecules, stochastic simulation methods such as Langevin models and Brownian dynamics. Applications to blood flow, platelet aggregation, and interactions of cells with blood vessel walls. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The course will not be a systematic survey but will focus on specific topics in the history of mathematics such as Archimedes and integration. Oresme and graphing, Newton and infinitesimals, simple harmonic motion, the discovery of 'Fourier' series, the Monte Carlo method, reading and analyzing the original texts. A basic knowledge of calculus will be assumed. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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This course is designed to introduce students to the use of mathematical models in biology as well as some more recent topics in computational biology. Mathematical techniques will involve difference equations and dynamical systems theory, ordinary differential equations and some partial differential equations. These techinques will be applied in the study of many biological applications such as: (i) Difference Equations: population dynamics, red blood cell production, population genetics; (ii) Ordinary Differential Equations: predator¿prey models, Lotka¿Volterra model, modeling the evolution of the genome, heart beat model/cycle, tranmission dynamics of HIV and gonorrhea; (iii) Partial Differential Equations: tumor growth, modeling evolution of the genome, pattern formation. Prerequisites: AM 33 and 34 (APMA 0330 and 0340). 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
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The aim of the course is to illustrate through the examination of unsolved (but elementary) problems the ways in which professional applied mathematicians approach the solution of such questions. Ideas considered include: choosing the "simplest" nontrivial example; generalization; and specification. Ways to think outside convention. Some knowledge of probability and linear algebra helpful. Suggested reading. "How to solve it", G. Polya "Nonplussed", Julian Havil 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Undergraduate College College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Section numbers vary by instructor. Please check Banner for the correct section number and CRN to use when registering for this course. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Independent Study/Research Undergraduate College College Applied Mathematics Department Return to Previous New Search
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Introduces science and engineering graduate students to a variety of fundamental mathematical methods. Topics include linear algebra, complex variables, Fourier series, Fourier and Laplace transforms and their applications, ordinary differential equations, tensors, curvilinear coordinates, partial differential equations, and calculus of variations. 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
Introduces science and engineering graduate students to a variety of fundamental mathematical methods. Topics include linear algebra, complex variables, Fourier series, Fourier and Laplace transforms and their applications, ordinary differential equations, tensors, curvilinear coordinates, partial differential equations, and calculus of variations. 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
Provides the basis of real analysis which is fundamental to many of the other courses in the program: metric spaces, measure theory, and the theory of integration and differentiation. Please note, during the fall 2009 semester, interested students must register for MATH 2210 S01 (CRN 15311). 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule , Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A continuation of APMA 2110: metric spaces, Banach spaces, Hilbert spaces, the spectrum of bounded operators on Banach and Hilbert spaces, compact operators, applications to integral and differential equations. Please note, during the spring 2010 semester, interested students must register for MATH 2220 S01 (CRN 25319). 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule, Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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