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Course Criteria
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1.00 - 4.00 Credits
Credit Hours: 1 to 4
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4.00 Credits
The course is intended to provide a mathematical perspective on one or more topics chosen from algebra, geometry, and/or topology. Topics may include combinatorial matrix theory, classification of surfaces, Lie groups, Galois theory, geometric analysis, computational geometry, homology, and/or fixed point theorems. Prerequisites/Corequisites: Prerequisites: vary with topic. When Offered: Spring term even-numbered years. Credit Hours: 4
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4.00 Credits
A careful study of measure theory, including abstract and Lebesgue measures and integration, absolute continuity and differentiation, L^p spaces, Fourier transforms and Fourier series, Hilbert spaces and normed linear spaces. Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor. When Offered: Spring term even-numbered years. Credit Hours: 4
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4.00 Credits
A basic course in the concepts of linear functional analysis, including such topics as linear functionals, bounded linear operators, unbounded linear operators, graphs, adjoints, spectral theory of linear operators, and applications to differential equations and mathematical physics. Prerequisites/Corequisites: Prerequisites: MATH 4210, MATH 4300, or permission of instructor; MATH 6200 or equivalent also desirable. When Offered: Fall term annually. Credit Hours: 4
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4.00 Credits
A continuation of material presented in MATH 6220. Covers such topics as inverse and implicit function theorems, fixed point theorems, Riesz bases, distributions and Sobolev spaces, variational methods, degree theory, and applications to differential equations. Prerequisites/Corequisites: Prerequisite: MATH 6220 or equivalent or permission of instructor. When Offered: Spring term odd-numbered years. Credit Hours: 4
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4.00 Credits
A basic graduate course covering Cauchy's Theorem, residues, infinite series and products, partial fractions, conformal mapping and the Riemann mapping theorem, analytic continuation, zeros and growth of analytic functions, approximation by rational functions, Phragmen-Lindelof Theorems, inverse-scattering theory, elliptic functions, and Riemann Surfaces. Prerequisites/Corequisites: Prerequisites: MATH 4210 and MATH 4300 or equivalent or permission of instructor. When Offered: Fall term odd-numbered years. Credit Hours: 4
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4.00 Credits
A basic graduate course introducing the fundamental concepts of modern evolution equations theory in the setting of ordinary differential equations. Topics include existence and uniqueness, integral equations, stability of equilibria, stable manifolds, Floquet theory, Poincare-Bendixson theory, bifurcation theory, center manifolds, normal forms, averaging theory, Hamiltonian mechanics and calculus of variations, chaotic dynamics, KAM theory, and soliton theory. Prerequisites/Corequisites: Prerequisite: MATH 4400 or permission of instructor. When Offered: Spring term even-numbered years. Credit Hours: 4
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4.00 Credits
Mathematical foundations and/or applications of ordinary differential equations. Possible topics include: stability and chaos in dynamics, mathematical methods of classical mechanics, stochastic differential equations, and soliton equations. Listing of topics offered to date. Prerequisites/Corequisites: Prerequisites: Vary with topic. When Offered: Spring term odd-numbered years. Credit Hours: 4
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4.00 Credits
A course dealing with the basic theory of partial differential equations. It includes such topics as properties of solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables; linear and nonlinear first order equations; existence and uniqueness theory for general higher order equations; potential theory and integral equations. Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor. When Offered: Fall term annually. Credit Hours: 4
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4.00 Credits
Mathematical foundation and/or applications of partial differential equations. Possible topics include soliton theory and applications, wavelets and PDEs, scattering theory, hyperbolic conservation laws. Prerequisites/Corequisites: Prerequisites: vary with topic. When Offered: Spring term annually . Credit Hours: 4
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