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MAT 5600: Introduction to Analysis I. Cr
4.00 Credits
Wayne State University
Prereq: MAT 5070 or consent of instructor. Completeness, convergence, compactness and continuity in the context of Euclidean spaces; applications to differential calculus. (T)
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MAT 5600 - Introduction to Analysis I. Cr
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MAT 5610: Introduction to Analysis II. Cr
3.00 Credits
Wayne State University
Prereq: MAT 5600. Integration, point-wise and uniform convergence of sequences and series of functions; power series; introduction to analytic functions; Fourier series; possible additional topics. (T)
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MAT 5610 - Introduction to Analysis II. Cr
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MAT 5700: Introduction to Probability Theory. Cr
4.00 Credits
Wayne State University
Prereq: MAT 2030, 2250 or 2350. Only two credits after MAT 2210 or MAT 6150. Probability spaces, combinatorial analysis; independence; discrete and continuous random variables; expectations; normal, Poisson and binomial distribution; joint, marginal and conditional distribution functions; law of large numbers; central limit theorems. (T)
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MAT 5700 - Introduction to Probability Theory. Cr
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MAT 5710: Introduction to Stochastic Processes. Cr
3.00 Credits
Wayne State University
Prereq: MAT 5700 or consent of instructor. Non-measure-theoretic introduction to the theory of stochastic processes and its applications, with emphasis on Markov processes and stationary processes with both discrete and continuous parameters. (B)
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MAT 5710 - Introduction to Stochastic Processes. Cr
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MAT 5740: The Theory of Interest. Cr
3.00 Credits
Wayne State University
Prereq: MAT 2020 and 2250. Concrete problems used to explore concepts in the theory of interest, including measurement of interest, annuities, yield rates, amortization, bonds, and stochastic approaches. Students prepare for certain professional actuarial examinations. (Y)
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MAT 5740 - The Theory of Interest. Cr
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MAT 5770: Mathematical Models in Operations Research. Cr
3.00 Credits
Wayne State University
Prereq: MAT 2030, 2250, and 2210 or 5700 or consent of instructor. Deterministic and probabilistic mathematical modeling of real-world problems. Topics include linear and nonlinear programming; queues; inventories; decision processes. (B)
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MAT 5770 - Mathematical Models in Operations Research. Cr
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MAT 5800: Introduction to Mathematical Statistics. Cr
4.00 Credits
Wayne State University
Prereq: MAT 5700. A one-semester course for senior undergraduate and master's degree students. Introduction to basic mathematical theory of statistics. Topics include sample distributions, estimation theory, data analysis and sample statistics, testing hypothesis, two sample cases, analysis of variance, regression analysis, Bayesian inference. (Y)
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MAT 5800 - Introduction to Mathematical Statistics. Cr
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MAT 5830: Applied Time Series. Cr
3.00 Credits
Wayne State University
Prereq: college courses in probability and statistics equivalent to MAT 5700 and MAT 5800, or consent of instructor. Time series models, moving average, autoregression, and more general models; point estimators, confidence intervals, and forecast in the time domain. Statistical analysis in the frequency domain; spectral density and periodogram. (B)
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MAT 5830 - Applied Time Series. Cr
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MAT 5870: Methods of Optimization. Cr
3.00 Credits
Wayne State University
Prereq: MAT 2350. Introduction to basic mathematical theory and computational methods of optimization; optimality conditions in various optimization problems and numerical methods of optimization. (Y)
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MAT 5870 - Methods of Optimization. Cr
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MAT 5890: Special Topics in Mathematics
3.00 Credits
Wayne State University
Prereq: MAT 2030, and 2250 or 2350. Material currently of interest to students and faculty. Topics to be announced in Schedule of Classes. (I)
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MAT 5890 - Special Topics in Mathematics
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