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Courses

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NWC Graduates

MAPS-REU

Daniel Sweet
Memorial Fellowship


IMA 2015: Modern Harmonic Analysis and Applications

OPSF 2016: Orthogonal Polynomials and Special Functions

NWC Courses



The Norbert Wiener Center prides itself on providing its graduate students with state-of-the art education in mathematics and applied mathematics. Faculty at the NWC teach courses ranging from the rudimentary analysis courses required for graduate qualifying exams, to the highly-focused topics courses.

Below is a list of recent courses taught by Norbert Wiener Center Faculty.

Fall 2015

  • MATH634 - Harmonic Analysis
    John J. Benedetto

    Syllabus

    1. The fundamental relation between Fourier analysis and number theory in topics such as the FFT, spectral synthesis, the p-adics, uniform distribution, Kroneckerís theorem, the HRT conjecture and the Riemann zeta function.
    2. Carleson's theorem for Fourier series and recent related research.
    3. Algebraic and geometric fundamentals of harmonic analysis, e.g., factorization and automorphisms of group algebras and the characterization of idempotent measures.
    4. Beurling algebras, weighted norm inequalities, spectral analysis.
    5. Statements and discussions of specific open problems and general unresolved issues: the uncertainty principle, MRI and non-uniform sampling, the Fuglede conjecture and the results of Tao, deterministic compressive sensing and the results of Bourgain, ambiguity functions and Wigner distributions, waveform design and the construction of sequences in terms of Weilís solution of the Riemann hypothesis for finite fields, the characterization of the space of absolutely convergent Fourier transforms.

Spring 2015

  • MATH631 - Real Analysis II
    Kasso Okoudjou

    Course Page
    Abstract measure and integration theory, metric spaces, Baire category theorem and uniform boundedness principle, Radon-Nikodym theorem, Riesz Representation theorem, Lebesgue decomposition, Banach and Hilbert Spaces, Banach-Steinhaus theorem, topological spaces, Arzela-Ascoli and Stone-Weierstrass theorems, compact sets and Tychonoff's theorem.
  • Math858R - Selected Topics in Analysis: Sparse and Low Rank Representations: Analytical Methods and Industrial Applications
    Radu Balan

    Course page
    Topics inlude:
    Approximation Principles: Non-parametric vs. parametric models, linear vs. nonlinear, deterministic vs. stochastic estimation.
    Linear models: Stochastic approach: Karhunen-Loev decmposition; PCA; ICA Deterministic approach: case studies: spectral approximations; Fix- Strang conditions for shift-invariant spaces; Blind source separation for sparse signals
    Model Selection: Classic principles: Akaike information criterion; Bayesian information criterion; Minimum description length Sparse Models
    Nonlinear Models Matrix Completion Problem Phaseless reconstruction

Fall 2014

  • MATH630 - Real Analysis I
    Kasso Okoudjou

    Course Page
    Lebesgue measure and the Lebesgue integral on R, differentiation of functions of bounded variation, absolute continuity and fundamental theorem of calculus, Lp spaces on R, Riesz-Fischer theorem, bounded linear functionals on Lp, measure and outer measure, Fubini's theorem.
  • MATH858F - Selected Topics in Analysis: Time-Frequency and Wavelet Analysis - Theory and Applications
    John Benedetto

    Topics include: Time-frequency (Gabor) analysis on R^d and the role of the Heisenberg group, Short-time Fourier Transform, Wavelet theory on R^d, Time-frequency and wavelet uncertainty principles, the Bailan-Low phenomenon, Compressive sensing, Time-frequency and Wavelet frames, frame multiresolution analysis.

Spring 2014

  • Math858C - Selected Topics in Analysis: Geometric Multiresolution Representation
    Wojciech Czaja

    A survey through multiresolution representations that capture geometric information. The "lets", including shearlets, curvelets, ridgelets, and contourlets, are discussed and analyzed.
  • Math858R - Selected Topics in Analysis: Sparse and Low Rank Representations: Analytical Methods and Industrial Applications
    Radu Balan

    Course page
    Topics inlude:
    Approximation Principles: Non-parametric vs. parametric models, linear vs. nonlinear, deterministic vs. stochastic estimation.
    Linear models: Stochastic approach: Karhunen-Loev decmposition; PCA; ICA Deterministic approach: case studies: spectral approximations; Fix- Strang conditions for shift-invariant spaces; Blind source separation for sparse signals
    Model Selection: Classic principles: Akaike information criterion; Bayesian information criterion; Minimum description length Sparse Models
    Nonlinear Models Matrix Completion Problem Phaseless reconstruction

Fall 2008





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Norbert Wiener Center
Department of Mathematics
University of Maryland
College Park, MD 20742
Phone: (301) 405-5158
The Norbert Wiener Center is part of the College of Computer, Mathematical, and Natural Sciences.