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Course Criteria
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3.00 Credits
Prerequisite: MATH 6301 or consent of department. Reliability of coherent systems, distributions in reliability, classes of life distributions, maintenance and replacement policies, availabilities, competing risks, reliability hypothesis testing, estimation of reliability functions, regression models for reliability data, and fault tree analysis.
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3.00 Credits
Prerequisite: consent of the department. Theory and practice of effective statistical consulting. Communication with clients, problem solving, and report writing. May be repeated for credit. Students may not count more than six semester hours credit for MATH 6370 toward a degree in Mathematics.
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3.00 Credits
Prerequisite: MATH 4371 or 4311 or consent of department. Measure theoretic origins, infinite dimensional probability spaces, modes of convergence, laws of large numbers, central limit theorems; certain topics from infinitely divisible laws, stochastic processes, separability, martingales and semi-martingales, ergodic theory, systems theory and stopping rules.
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3.00 Credits
Prerequisite: credit or concurrent registration in MATH 4311 or the consent of the department. A brief introduction to financial derivatives, normal random variables, geometric brownian motion, stochastic differentiation, stochastic integration, ito's lemma, the Black-Scholes PDE and its solution.
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3.00 Credits
Prerequisite: MATH 6311 or consent of the department. Biostatistical design of medical studies, one- and two-sample inference, counting data, nonparametric, distribution-free and permutation models: robust procedures, simple and multiple regression, multiple comparisons, cross-over designs, discrimination and classification, and other topics.
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3.00 Credits
Prerequisite: MATH 6311 and 6312 or consent of department. Failure times, censoring mechanisms, failure rates, survival functions, product limit estimators, covariates, Cox model, partial likelihood, exponential regression, rank tests, and other topics.
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3.00 Credits
Prerequisite: MATH 6311, 6312 or consent of department. Presentations of longitudinal data, general linear models for longitudinal data, parametric models for covariance structure, analysis of variance methods, marginal models, random effects models, methods for discrete longitudinal data.
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3.00 Credits
Prerequisite: consent of department.
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3.00 Credits
Prerequisite: MATH 4411. Analytic continuation, reflection principle, argument principle, Rouche's theorem. Convergence of sequences, series, and infinite products of analytic functions. Entire functions, conformal mappings, Riemann mapping theorem, Riemann surfaces, gamma function, Riemann zeta function.
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3.00 Credits
Prerequisite: MATH 4102 or consent of department. MATH 6450 is prerequisite to MATH 6451. Measure theory, integration, types of convergence, absolute continuity, function spaces.
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