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MATH 648: Bayesian Statistical Inference
3.00 Credits
Bowling Green State University-Main Campus
Spring (even years). Introduction to the Bayesian approach to statistical inference. Discussion of modeling subjective information about parameters using a prior distribution. Computation of the posterior distribution for many standard statistical inference problems. Comparison of the Bayesian approach with the "classical" approach. Discussion of different strategies available for the numerical computation of Bayesian integrals. Illustration of the use of Bayesian methods in different fields of application.
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MATH 648 - Bayesian Statistical Inference
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MATH 650: Statistical Consulting
1.00 - 4.00 Credits
Bowling Green State University-Main Campus
Individualized instruction and in-depth experience in all phases of statistical consulting. Prerequisite: background in mathematical statistics, regression, and design of experiments. Graded S/U.
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MATH 650 - Statistical Consulting
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MATH 651: Topology I
3.00 Credits
Bowling Green State University-Main Campus
Topological spaces, separation properties, product and quotient topologies, compactness, connectedness, homotopy, fundamental group and covering spaces, Seifert-VanKampen theorem, geometry of simplicial complexes. Prerequisites: MATH 565, MATH 503, and consent of instructor.
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MATH 651 - Topology I
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MATH 661: Complex Analysis I
3.00 Credits
Bowling Green State University-Main Campus
Complex numbers, analytic functions and differentiation, elementary functions, power series, complex integration with applications to function theory. Prerequisites: MATH 565 and consent of instructor.
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MATH 661 - Complex Analysis I
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MATH 665: Real Analysis I
3.00 Credits
Bowling Green State University-Main Campus
Infinite sequences and series of real numbers, theory of metric spaces, Riemann and Riemann-Stieltjes integral. Prerequisites: MATH 565 and consent of instructor.
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MATH 665 - Real Analysis I
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MATH 666: Real Analysis II
3.00 Credits
Bowling Green State University-Main Campus
Further topics on Riemann-Stieltjes integral, sequences and series of functions, further topics in metric spaces, Lebesgue measure and integral. Prerequisite: MATH 665.
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MATH 666 - Real Analysis II
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MATH 668: Iterative Solution of Nonlinear Equations in Several Variables
3.00 Credits
Bowling Green State University-Main Campus
Model problems in nonlinear equations. Gateau derivatives, F-derivatives, and convex functionals. Contractions and the continuity property. Iterative methods. Minimization methods: paraboloid methods, descent methods, conjugate-direction methods. Steplength algorithm. Convergence factors. Continuation methods. Convergence under partial ordering. Prerequisites: MATH 332, and either advanced calculus or equivalent, and programming experience.
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MATH 668 - Iterative Solution of Nonlinear Equations in Several Variables
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MATH 669: Approximation Theory
3.00 Credits
Bowling Green State University-Main Campus
Polynomial interpolation and its limitations. Piecewise linear approximation. Piecewise Cubic Interpolation. B-splines and their stable evaluation. B-spline series. Smoothing and least square approximation. Surface approximation by tensor product. Orthogonal polynomials and infinite-order methods. Prerequisite: MATH 551.
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MATH 669 - Approximation Theory
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MATH 670: Advanced Readings in Mathematics or Statistics
1.00 - 4.00 Credits
Bowling Green State University-Main Campus
Independent reading and study in the mathematical or statistical literature. Prerequisite: consent of instructor.
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MATH 670 - Advanced Readings in Mathematics or Statistics
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MATH 671: Survival Analysis
3.00 Credits
Bowling Green State University-Main Campus
Survisor, hazard, and cumulative hazard functions; phenomena of censorship and types of censoring; likelihood functions, maximum likelihood and asymptotic theory; nonparametric inferences in the presence of censored data; product-limit estimator; estimator and tests associated with the survivor function. Regression models; Cox proportional hazard model and partial likelihood; accelerated failure time models. Prerequisite: MATH 641.
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MATH 671 - Survival Analysis
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