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452
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Partial Differential Equations
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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. Prerequisite: 351. (Quant)
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454
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Principles of Real Analysis
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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: 220, 240. (Quant)
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456
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Functions of a Complex Variable
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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: 253. (Quant)
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459
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Topology
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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 J-terms. Prerequisite: 220, 240. (Quant)
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462
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Numerical Analysis
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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: 240, computer science 150. (Same as computer science 462.) (Quant)
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471
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Abstract Algebra I
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Introduction to the basic structures of abstract algebra: groups, subgroups, cosets, isomorphisms, factor groups, homomorphisms, rings, integral domains, fields, ideals, and polynomial rings. Prerequisites: 220, 240. (Quant)
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472
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Abstract Algebra II
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Topics may include simple groups, Sylow theorems, divisibility in integral domains, generators and relations, field extensions, splitting fields, solvability by radicals, Galois theory, symmetry, and geometric constructions. Offered on demand. Prerequisite: 471. (Quant)
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