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MATH 8304: Topics in Analysis
3.00 Credits
University of Colorado Boulder
Presents advanced topics in analysis including Lie groups, Banach algebras, operator theory, ergodic theory, representation theory, etc. Prereqs., MATH 8330 and 8340, or instructor consent.
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MATH 8304 - Topics in Analysis
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MATH 8330: Functional Analysis
3.00 Credits
University of Colorado Boulder
Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations, and spectral theorem for bounded self-adjoint operators), and Banach algebras (the Gelfand theory). See also MATH 8340. Prereqs., MATH 6310 and 6320. Undergraduates must have approval of the instructor.
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MATH 8330 - Functional Analysis
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MATH 8340: Functional Analysis
3.00 Credits
University of Colorado Boulder
Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations, and spectral theorem for bounded self-adjoint operators), and Banach algebras (the Gelfand theory). See also MATH 8330. Prereq., MATH 8330. Undergraduates must have approval of the instructor.
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MATH 8340 - Functional Analysis
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MATH 8370: Harmonic Analysis
3.00 Credits
University of Colorado Boulder
Examines trigonometric series, periodic functions, diophantine approximation, and Fourier series. Also covers Bohr and Stepanoff almost periodic functions, positive definite functions, and the L1 and L2 theory of the Fourier integral. Applications to group theory and differential equations. See also MATH 8380. Prereq., MATH 5150 and 6320. Undergraduates must have approval of the instructor.
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MATH 8370 - Harmonic Analysis
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MATH 8410: Mathematical/ Computational Fluid Dynamics
3.00 Credits
University of Colorado Boulder
Mathematical treatment of basic Navier-Stokes partial differential equations describing fluid dynamics, including the Euler and Stokes equations as approximations for high and low speed flows. Emphasizes both analytical considerations and computational methods. Prereq., instructor consent. Undergraduates must have approval of the instructor.
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MATH 8410 - Mathematical/ Computational Fluid Dynamics
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MATH 8420: Mathematical/ Computational Fluid Dynamics
3.00 Credits
University of Colorado Boulder
Mathematical treatment of basic Navier-Sokes partial differential equations describing fluid dynamics, including the Euler and Stokes equations as approximations for high and low speed flows. Emphasizes both analytical considerations and computational methods. Prereq., instructor consent. Undergraduates must have approval of the instructor.
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MATH 8420 - Mathematical/ Computational Fluid Dynamics
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MATH 8714: Topics in Logic 1 and
3.00 Credits
University of Colorado Boulder
Topics in Logic 1 and
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MATH 8714 - Topics in Logic 1 and
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MATH 8815: Ulam Seminar
1.00 - 3.00 Credits
University of Colorado Boulder
May be repeated up to 3 total credit hours.
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MATH 8815 - Ulam Seminar
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MATH 8900: Independent Study
1.00 - 3.00 Credits
University of Colorado Boulder
Undergraduates must have approval of the instructor. May be repeated up to 6 total credit hours.
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MATH 8900 - Independent Study
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MATH 8990: Doctoral Dissertation
1.00 - 10.00 Credits
University of Colorado Boulder
All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog.
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MATH 8990 - Doctoral Dissertation
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