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Course Criteria
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1.00 Credits
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.
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1.00 Credits
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.
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1.00 Credits
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.
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1.00 Credits
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.
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1.00 Credits
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).
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1.00 Credits
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.
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1.00 Credits
Course description unavailable
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1.00 Credits
Filtering (estimation of a "state process" from noisy data) is an important area of modern statistics. It is of central importance in navigation, signal and image processing, control theory and other areas of engineering and science. Filtering is one of the exemplary areas where the application of modern mathematics and statistics leads to substantial advances in engineering. This course will provide a student with the working knowledge sufficient for cutting edge research in the field of nonlinear filtering and its practical applications. Topics will include: hidden Markov models, Kalman and Wiener filters, optimal nonlinear filtering, elements of Ito calculus and Wiener chaos, Zakai and Kushner equations, spectral separating filters and wavelet based filters, numerical implementation of filters. We will consider numerous applications of filtering to speech recognition, analysis of financial data, target tracking and image processing. No prior knowledge in the field is required but a good understanding of the basic Probability Theory (APMA1200 or APMA2630) is important.
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1.00 Credits
Section numbers vary by instructor. Please check Banner for the correct section number and CRN to use when registering for this course.
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1.00 Credits
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.
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