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Course Criteria
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3.00 Credits
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, central limit theorem, Poisson process, and multivariate Gaussian distribution. Prereq., APPM 2350 or MATH 2400. Credit not granted for this course and ECEN 3810 or MATH 4510.
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3.00 Credits
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., APPM 3310 or MATH 3130. Same as APPM 5120 and MATH 4120.
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3.00 Credits
Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions. Prereqs., APPM 2350 and 2360 or 2380 (min grade C-). Coreq., APPM 3110. Same as APPM 5350.
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3.00 Credits
Introduces methods of complex variables, contour integration, and theory of residues. Applies solving partial differential equations by transform methods, Fourier and Laplace transforms, and Reimann-Hilbert boundary-value problems. Also applies conformal mapping to ideal fluid flow and/or electrostatics. Prereqs., APPM 2350 and 2360, or 3310 (min grade C-) or instructor consent. Same as APPM 5360.
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3.00 Credits
An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics can vary: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Prereqs., APPM 2350 and 2360. Recommended prereqs., APPM 3310, 4350 and 4650. Same as APPM 5380.
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3.00 Credits
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness; tests of simple and composite hypotheses, linear models, and multiple regression analysis. Analyzes variance distribution-free methods. Prereq., MATH 4510 or APPM 3570. Same as APPM 5520 and MATH 4520.
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3.00 Credits
Single and multivariable regression, forecasting using regression models, time series models, and modeling with MA, AR, ARMA, and ARIMA models, forecasting with time series models, and spectral analysis. Prereqs., APPM 3570 or MATH 4510, and APPM 4520 or MATH 4520. Same as APPM 5540, MATH 4540.
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3.00 Credits
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Prereq., APPM 3570 or equivalent. Same as APPM 5560.
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3.00 Credits
Covers discrete and continuous probability laws, random variables; expectations; laws of large numbers and central limit theorem; estimation, testing hypothesis, analysis of variance, regression analysis, and nonparametric methods. Emphasizes applications with an introduction to packaged computer programs. Prereq., APPM 1360 or equivalent Calculus 2 course. Same as APPM 5570.
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3.00 Credits
Combines statistical methods with practical applications and computer software. Develops commonly used statistical models such as analysis of variance as well as linear and logistic regression. The statistical models are implemented and interpreted in the context of actual data sets using available statistical software. Continuation of APPM 4570. Prereq., APPM 4570 or any course in statistics. Same as APPM 5580.
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