Courses
RITs
NWC Graduates
MAPSREU
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 stateofthe 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 highlyfocused 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 padics, uniform distribution, Kronecker’s 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 nonuniform 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 Weil’s 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, RadonNikodym theorem, Riesz Representation theorem, Lebesgue decomposition, Banach and Hilbert Spaces, BanachSteinhaus theorem, topological spaces, ArzelaAscoli and StoneWeierstrass 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: Nonparametric vs. parametric models, linear vs. nonlinear, deterministic vs. stochastic estimation.
Linear models: Stochastic approach: KarhunenLoev decmposition; PCA; ICA
Deterministic approach: case studies: spectral approximations; Fix
Strang conditions for shiftinvariant 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, RieszFischer theorem, bounded linear functionals on Lp, measure and outer measure, Fubini's theorem.
MATH858F  Selected Topics in Analysis: TimeFrequency and Wavelet Analysis  Theory and Applications John Benedetto
Topics include: Timefrequency (Gabor) analysis on R^d and the role of the Heisenberg group, Shorttime Fourier Transform, Wavelet theory on R^d, Timefrequency and wavelet uncertainty principles, the BailanLow phenomenon, Compressive sensing, Timefrequency 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: Nonparametric vs. parametric models, linear vs. nonlinear, deterministic vs. stochastic estimation.
Linear models: Stochastic approach: KarhunenLoev decmposition; PCA; ICA
Deterministic approach: case studies: spectral approximations; Fix
Strang conditions for shiftinvariant 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


