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Course Criteria
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3.00 Credits
Combinatorics, probability models (binomial, Poisson, normal, gamma, etc.) Stochastic independence, generating functions, limit theorems and types of convergence, bivariate distributions, transformations of variables. Markov processes, applications. Prerequisite: multivariable calculus and linear algebra. Except for students with extremely strong backgrounds, 218 should be taken prior to 247.
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3.00 Credits
Distribution theory, order statistics, theory of point estimation and hypothesis testing, normal univariate inference, Bayesian methods, sequential procedures, regression, nonparametric methods. Students interested in applications may take 218L. Prerequisite: 247.
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3.00 Credits
Development of the first order predicate calculus and fundamental metamathematical notions.
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3.00 Credits
Major developments in mathematics from ancient times to the early 20th century. Emphasis both on the historical perspective and the mathematics; assignments include many exercises and theorems. Prerequisite: multivariable calculus, and either linear algebra or 223. Especially recommended for teacher candidates.
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3.00 Credits
Applications of algebra to reliability and secrecy of information transmission. Error-correcting codes, including linear, Hamming, and cyclic codes, and possibly BCH or Reed-Solomon codes. Cryptography, including symmetric-key, DES and RSA encryption. Prerequisite: linear algebra.
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3.00 Credits
Modeling microeconomic problems of supply and demand, profit maximization, and Nash equilibrium pricing. Auctions and bargaining models. Statistical models and data analysis. Computational experiments. Prerequisite: multivariable calculus.
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3.00 Credits
Advanced treatment of multivariable calculus. Differentiation of functions of several variables, including inverse and implicit function theorems. Vector differential calculus. Integration of functions of several variables. Vector integral calculus, including Stokes’ theorem. Prerequisite: multivariable calculus and linear algebra. No credit for students who have completed 229.
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3.00 Credits
Properties of real numbers, compactness and completeness. Limits, sequences and series, uniform convergence, and power series. Basic properties of functions on the real line, and the elementary theory of differentiation and integration. Emphasis on methods of proof used in advanced mathematics courses.
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3.00 Credits
Complex numbers, analytic and elementary functions, transformations of regions. Complex integrals, Cauchy’s integral theorem and formula, Taylor and Laurent series. The calculus of residues with applications, conformal mappings. Prerequisite: multivariable calculus.
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3.00 Credits
Mathematical modeling with applications in biology and medicine. Basic mathematical modeling tools such as linear regression, differential equations, matrix and statistical analysis, probability theory, and computer simulation. Mathematical models in population dynamics, epidemiology, immunology, diffusion phenomena, pharmacokinetics, neurophysiology, and biochemistry of cells. Prerequisite: linear algebra and differential equations.
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