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MATH 633: Algebra I
3.00 Credits
Bowling Green State University-Main Campus
Groups, rings, fields, and other algebraic structures. Prerequisite: MATH 503.
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MATH 633 - Algebra I
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MATH 634: Algebra II
3.00 Credits
Bowling Green State University-Main Campus
Continuation of MATH 633.
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MATH 634 - Algebra II
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MATH 638: Linear Algebra
3.00 Credits
Bowling Green State University-Main Campus
Vectors and matrices, quadratic forms, positive definite matrices, convexity, classical inequalities, generalized inverses. Prerequisite: consent of instructor.
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MATH 638 - Linear Algebra
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MATH 641: Probability Theory I
3.00 Credits
Bowling Green State University-Main Campus
Axiomatic foundations of probability theory; discrete and continuous type random variables and their distributions; random vectors and their functions; special probability distributions including multivariate normal; generating functions; limiting moment generating functions; weak law of large numbers and central limit theorem. Simple random sampling; sampling from univariate and bivariate normal; exact sampling distributions. Prerequisite: MATH 565 or consent of instructor.
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MATH 641 - Probability Theory I
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MATH 642: Mathematical Statistics II
3.00 Credits
Bowling Green State University-Main Campus
Theory of point estimation; sufficiency, completeness, unbiased estimation, Cramer-Rao inequality. Maximum likelihood estimation, Bayes and minimax procedures; Neyman-Pearson theory of testing hypotheses; power function, most powerful and uniformly most powerful tests. Theory of confidence estimation and interrelationship with tests of hypotheses; shortest length confidence intervals; likelihood ratio tests; nonparametric procedures. Prerequisite: MATH 641.
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MATH 642 - Mathematical Statistics II
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MATH 643: Mathematical Statistics III
3.00 Credits
Bowling Green State University-Main Campus
Fall, Spring. Transformations of random vectors, affine and orthogonal transformations multivariate normal vectors, the delta-method, variance stabilizing transformations; optimal predictors; sufficiency, completeness, and estimation; asymptotic optimality properties of estimators with particular emphasis on the asymptotic normality of maximum likelihood estimators; Neyman-Pearson theory; locally most powerful tests of hypotheses; basic theory of linear models; and the analysis of discrete data including logistic regression. Prerequisite: MATH 642.
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MATH 643 - Mathematical Statistics III
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MATH 644: Stochastic Processes
3.00 Credits
Bowling Green State University-Main Campus
Stochastic models including discrete and continuous time; Markov chains and Brownian motion; introduction to topics: Guassian processes, queues, theory of dams and storage, epidemic models, branching processes, renewal processes. Prerequisite: MATH 641.
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MATH 644 - Stochastic Processes
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MATH 645: Statistical Distribution Theory
3.00 Credits
Bowling Green State University-Main Campus
Distributions, their transformations and characterizations, exact sampling distributions; approximate distributions; Gram-Charlier and Edgeworth series; Monte Carlo method; asymptotics including delta method. Prerequisite: MATH 641 or consent of instructor.
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MATH 645 - Statistical Distribution Theory
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MATH 646: Nonparametric Statistical Inference
3.00 Credits
Bowling Green State University-Main Campus
Statistical models in nonparametric settings; equal-in-distribution relation and its applications; nonparametric statistics based on counting and ranking; U-statistics and asymptotics; evaluating and comparing performance of nonparametric alternative hypotheses; nonparametric point and interval estimation; linear rank statistics and their asymptotic theory; locally most powerful rank tests; applications to one- and two-sample settings. Prerequisite: MATH 642, or MATH 641 and MATH 542.
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MATH 646 - Nonparametric Statistical Inference
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MATH 647: Sequential Statistical Inference
3.00 Credits
Bowling Green State University-Main Campus
Sequential parametric estimation; stopping rules and stopping variables; lower-bound for variance of an estimate; Wald's equation; Wald's sequential probability ratio test and its properties. Fundamental Identity of Sequential Analysis; fixed-width confidence estimation; special sequential tests of composite hypotheses. Prerequisite: MATH 642, or both MATH 641 and MATH 542.
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MATH 647 - Sequential Statistical Inference
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