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Course Criteria
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4.00 Credits
4 hours Elements of Euclidean and non-Euclidean geometries: incidence, betweenness, separation, congruence, and parallel postulates. Geometry of physical space. Historical development. A proof oriented course. Prerequisites: MATH 220, 240. (Quant)
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3.00 Credits
Credit arr. On-the-job learning experience. The plan must be presented for departmental approval before the experience begins.
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1.00 - 4.00 Credits
1, 2 or 4 hours
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4.00 Credits
4 hours An introduction to initial and boundary value problems associated with certain linear partial differential equations (e.g., Laplace, heat and wave equations). Fourier series methods, including the study of best approximation in the mean and convergence, will be a focus. Sturm-Liouville problems and associated eigenfunctions will be included. Numerical methods, such as finite difference, finite element, and finite analytic, may be introduced, including the topics of stability and convergence of numerical algorithms. Prerequisites: MATH 351. (Quant)
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4.00 Credits
4 hours The mathematics of real functions, emphasizing rigorous analytical proofs. Sets, real number properties, cardinality, topology of the reals, limits of a function, continuity, differentiation, integration, sequences, series. Prerequisites: MATH 220, 240. (Quant)
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4.00 Credits
4 hours Extending calculus to functions of a complex variable. Complex numbers, limits, derivatives, Cauchy- Riemann equations, analytic functions, contour integrals, Cauchy integral formula. Taylor series, Laurent series, residues, conformal mappings, and applications. Offered in alternate years. Prerequisite: MATH 253. (Quant)
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4.00 Credits
4 hours An introduction to general, or point-set, topology. Topological spaces and continuous functions. Order, metric, product, and subspace topologies. Limit points, connectedness, compactness, countability axioms, separation axioms, Urysohn lemma and metrization theorem. Usually offered in alternate January terms. Prerequisite: MATH 220, 240. (Quant)
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4.00 Credits
4 hours Roots of equations and solutions of systems of linear equations, interpolation and approximation, differences and numerical integration, and numerical solutions of ordinary differential equations. Offered in alternate years. Prerequisites: MATH 240, CS 150. (Same as CS 462.) (Quant)
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4.00 Credits
4 hours Introduction to the basic structures of abstract algebra: groups, subgroups, cosets, isomorphisms, factor groups, homomorphisms, rings, integral domains, fields, ideals, and polynomial rings. Prerequisites: MATH 220, 240. (Quant)
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