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Course Criteria
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4.00 Credits
Prerequisite: A grade of C or better in MTH 281 or MTH 283, a grade of C or better in at least one mathematics course numbered 300 or above or permission of instructor. This course deals with the fundamentals of complex analysis, including basic properties of complex numbers, analytic functions, harmonic functions, integration, Taylor and Laurent series, residue calculus, conformal mapping, and their applications.
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4.00 Credits
Prerequisite: At least one mathematics course numbered 300 or above. This course is a survey of combinatorial methods, including binomial coefficients and other special numbers, recurrence relations, calculus of finite differences, and generating functions, emphasizing exact evaluation of combinatorial sums in closed form. The course includes use of a computer algebra system, such as Maple or MATLAB.
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4.00 Credits
Prerequisite: MTH 347 with a grade of “C” or better or permission of instructor. The course covers techniques of modeling data that are collected sequentially. Topics include a review of basic ideas of modeling a continuous variable, time series regression, autocorrelation, decomposition methods, exponential smoothing, ARMA (Autoregressive Moving Average) models, and ARIMA (Autoregressive Integrated Moving Average) models. The course uses a statistical programming language. Data from a variety of fields will be studied. Counts toward the statistics minor; does not count toward the minor, B.A., or B.S. in Mathematics.
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4.00 Credits
Prerequisites: MTH 281 or MTH 283, MTH 284 or MTH 288, and a 300-level mathematics course. This course covers general probability (set functions, basic axioms, independence); Bayes' theorem; univariate probability distributions (probabilities, moments, variance, mode, percentiles, transformations); multivariate probability distributions (central limit theorem, joint conditional and marginal distributions - probabilities, moments, variance, covariance); discrete and continuous time Markov chains; and selected applications. Course makes extensive use of appropriate software.
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4.00 Credits
Prerequisite: MTH 347 with a grade of “C” or better or permission of instructor. The course covers techniques of modeling data for data that are categorical rather than continuous in nature. Topics include joint, marginal, and conditional probabilities, relative risk, odds ratios, generalized linear models, logistic regression, multi-category logit models, and loglinear models. The course utilizes data examples from the fields of biology, medicine, health, epidemiology, environmental science, and psychology; it uses a statistical programming language and counts toward the statistics minor; it does not count toward the minor, B.A. or B.S. in Mathematics.
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4.00 Credits
Prerequisites: MTH 281 or MTH 283, MTH 286, and at least one mathematics course numbered 300 or above. This course focuses on the calculus, linear algebra, and geometry of curves and surfaces, as well as applications to engineering and science. Material covered includes the curvature and torsion of curves, Gaussian and mean curvatures of surfaces, minimal surfaces, geodesics, holonomy, and the Gauss-Bonnet theorem. Optional material includes applications of the calculus of variations to geometry and of minimal surface theory to soap film formation. The course makes extensive use of a computer algebra system, such as Maple.
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4.00 Credits
Prerequisite: A grade of C or better in a course of level 300 or above in one of the following disciplines, MTH, CIS, EEC, EET, ESC; or instructor permission. This course presents advanced topics in number theory. Topics may include primality testing, prime number generation, integer factorization, discrete logarithms, elliptic curves and advanced cryptographic protocols, and other topics chosen by the instructor.
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4.00 Credits
Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above. Topics include systems of differential equations, local and global behavior of a vector field in the plane, discrete dynamical systems, structural stability, the Poincare-Bendixon theorem, bifurcations, chaos, and strange attractors. The course includes use of a computer algebra system, such as Maple or MATLAB.
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4.00 Credits
Prerequisites: MTH 281 or 283, or permission of the instructor. This course covers basic mathematical interest theory and time value of money, annuities, loan repayment, bonds, equations of value and yield rates, interest rate sensitivity, stocks and financial markets, arbitrage, term structure of interest rates and derivatives. It is designed to prepare students for the SOA Exam FM/CAS Exam 2 (Financial Mathematics Exam).
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4.00 Credits
Prerequisite: At least one mathematics course numbered 300 or above, or permission of instructor. This is a detailed study of a selected topic in advanced mathematics. The topic will vary, depending on instructor. It may be taken for credit more than once, but no single topic may be repeated. Please consult the Mathematics Department for current information.
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