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Course Criteria
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3.00 Credits
Computer arithmetic. Solution of nonlinear equations. Interpolation. Numerical integration and differentiation. Solution of linear equation systems. Eigenvalue problem, least square, chebyshev, trigonometric and rational function approximation. Numerical solution of differential equations.
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3.00 Credits
Topics in graph theory, including connectivity, matchings, graph algorithms, network flows, graph matrices, isomorphisms, Eulerian and Hamiltonian graphs, spanning trees, decompositions, shortest paths, the matrix-tree theorem, colorings of graphs, planarity and embeddings, Kuratowski's theorem, matroids, and selected applications. Courses must be taken in sequence.
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3.00 Credits
Introduction to methods of statistical analysis and methods for teaching statistics. Descriptive statistics, organization of data, sampling techniques, sampling distributions, methods of statistical inference, estimation, hypothesis testing, regression, and correlation. Computer-assisted analysis. With departmental approval may be repeated for credit.
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2.00 Credits
See department for course description.
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3.00 Credits
Topics from nonlinear analysis, harmonic analysis, analytic functions, ordered vector spaces, analysis on Lie groups, and operator theory.
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3.00 Credits
Advanced theory of dynamial systems and partial differential equations including the basics of partial differential equations, boundary value problems for elliptic equations, the Cauchy problem, and parabolic equations. Topics selected from Hamiltonian systems, waves and shocks, variational methods, control theory.
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3.00 Credits
Topics from singular and simplicial homology and cohomology theories, fundamental group and covering spaces, CW complexes and elements of homotopy theory, algebraic theory of manifolds, introduction to differential topology and vector bundles, applications. Courses must be taken in sequence.
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3.00 Credits
Topics from groups, semigroups, rings, fields, algebras, and homological algebra.
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3.00 Credits
Sets, spaces, and measures. Probability distributions. Random variables. Dependence. Limit theorems. Birth and death processes and Markov processes. Mathematical statistics, hypothesis testing, and sequential analysis. Selected applications. Courses must be taken in sequence.
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3.00 Credits
Topics in the history of mathematics education including an examination of the current research trends in mathematics education.
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