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Course Criteria
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3.00 Credits
Prerequisite: MAT 361 and 367. A thorough treatment of the solution of initial and boundary value problems of partial differential equations. Topics include classification of partial differential equations, the method of characteristics, separation of variables, Fourier analysis, integral equations and integral transforms, generalized functions, Green's functions, Sturm-Liouville theory, approximations, numerical methods.
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3.00 Credits
Prerequisite: MAT 336. Use of algebraic techniques to study arithmetic properties of the integers and their generalizations. Primes, divisibility and unique factorization in integral domains; congruences, residues and quadratic reciprocity; diophantine equations and additional topics in algebraic number theory.
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3.00 Credits
Prerequisite: MAT 325, 335, and 361. Introduction to the theoretical foundations of numerical algorithms. Solution of linear systems by direct methods; least squares, minimax, and spline approximation; polynomial interpolation; numerical integration and differentiation; solution of nonlinear equations; initial value problems in ordinary differential equations. Error analysis. Certain algorithms are selected for programming.
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3.00 Credits
Prerequisite: CSC 112 or 121 and MAT 335. Methods and applications of optimizing a linear function subject to linear constraints. Theory of the simplex method and duality; parametric linear programs; sensitivity analysis; modeling and computer implementation.
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3.00 Credits
Prerequisite: MAT 435. Theory and applications of discrete optimization algorithms. Transportation problems and network flow problems; integer programming; computer implementation.
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3.00 Credits
Prerequisite: MAT 275 and 336. A study of the basic concepts of general topology. Metric spaces, continuity, completeness, compactness, connectedness, separation axioms, product and quotient spaces; additional topics in point-set topology.
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3.00 Credits
Prerequisite: MAT 365 or 411. Theory of curves and surfaces in Euclidean space. Frenet formulas, curvature and torsion, arc length; first and second fundamental forms, Gaussian curvature, equations of Gauss and Codazzi, differential forms, Cartan's equations; global theorems.
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3.00 Credits
Prerequisite: MAT 335 and 361. Advanced study of ordinary differential equations. Existence and uniqueness; systems of linear equations, fundamental matrices, matrix exponential; series solutions, regular singular points; plane autonomous systems, stability and perturbation theory; Sturm-Liouville theory and expansion in eigenfunctions.
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3.00 Credits
MAT 261 and STT 315. The formulation, analysis and interpretation of probablistic models. Selected topics in probability theory. Conditioning, Markov chains, and Poisson processes. Additional topics chosen from renewal theory, queuing theory, Gaussian processes, Brownian motion, and elementary stochastic differential equations.
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3.00 Credits
Prerequisite: MAT 361 or 435 or MAT/STT 465. Techniques of problem recognition and formulation, and mathematical solution and interpretation of results. Each student will construct a mathematical model under the supervision of the Applied Mathematics Advisory Committee and report on the investigation in written and oral form. Seminar format.
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