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Course Criteria
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3.00 Credits
Linear spaces, linear operators, and functionals, necessary conditions, transversality, corner conditions, HamiltonJacobi theory, direct methods, eigenvalue problems, isoperimetric problems, theory of the second variation, differential forms and n-dimensional manifolds, applications to differential equations, conservation laws, dynamic programming, and Pontryagin maximum principle, application in physics, engineering economics. Prerequisite: Math 311.
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3.00 Credits
Continuation of Math 435. Prerequisite: Must be preceded by Math 435.
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3.00 Credits
Continuation of Math/Econ 337. Topics include martingales and measures, stopping times, discrete and continuous time finance, Brownian motion, Ito calculus, stochastic differential equations, Black-Scholes-Merton formula, numerical procedures. Prerequisite: Math 337 or Econ 337. (Co-listed with Econ 437)
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3.00 Credits
Selected topics in non-Euclidean, solid, projective, and fractal geometry. Prerequisite: Math 330.
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1.00 Credits
An instructional unit based on material learned in Math 440 will be designed by each student. These units will be class tested. The unit and results of class testing will be presented both in written and oral format. Prerequisite: Math 440.
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3.00 Credits
Complex plane, complex function theory, elementary Riemann surfaces, conformal mapping, complex integration, infinite complex series and sequences, calculus of residues with applications. Prerequisite: Math 311.
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3.00 Credits
Argument principle and consequences; harmonic functions and Dirichlet's problem; infinite products; entire, meromorphic and rational functions; analytic continuation; symmetry principle; conformal mapping; functions of several complex variables. Prerequisite: Preceded by Math 451.
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3.00 Credits
Fourier series, norm and pointwise convergence of Fourier series, the conjugate and maximal functions, analytic functions in the unit disk and Hardy spaces, interpolation of linear operators and the Hausdorff-Young-Riesz Theorem, Sidon sets. Prerequisites: Math 315 and Math 351.
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3.00 Credits
Fourier integrals, almost-periodic functions on the real line, Banach algebras, Wiener's Tauberian Theorem and the prime number theorem, the Paley-Wiener Theorems, band-limited functions and Shannon's Theorem, the continuous wavelet transform, discrete wavelet transforms and frames, orthonormal bases of wavelets and multi-resolution analysis. Prerequisite: Must be preceded by Math 461.
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3.00 Credits
An introduction to linear optimization and its engineering applications; problem modeling, search-based optimization, the simplex method for solving linear problems, multi-objective optimization, discrete dynamic programming. Applications of optimization in the fields such as transportation, project management, manufacturing and facility location will be discussed. Prerequisites: Stat 213 or equivalent and (Eng Mg 382 or Math 203 or Math 208). (Co-listed with Eng Mgt 465)
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