Course Offerings
MAIT offers one or more core courses each semester, along
with a selection of electives and special topics.
Schedules, rooms, and time listings may be found at the University
registration website www.testudo.umd.edu.
Core Program
MAIT 613 Advanced Applied Linear Algebra (3)
(based on the Trefethen or Higham books) Tools and techniques of computational linear
algebra for applications. Topics include: linear systems and least squares problems,
error analysis, accuracy and stability, matrix decompositions, iterative solvers, Krylov
subspace methods, symmetric and non-symmetric eigenvalue problems, singular value decomposition
MAIT 623 Modern Mathematical Methods of Signal and Image Processing I (3)
(based on the first half of "A Wavelet Tour of Signal Processing" by Stéphane Mallat)
Introduction to current signal/image processing techniques, including wavelets and frames,
in the context of applied and numerical harmonic analysis. Topics include time-frequency
and time-scale representations, sub-band filterbanks, and applications to compression and denoising.
MAIT 633 Applied Fourier Analysis (3)
Theory, practice, and implementation
(MATLAB) of Fourier analysis with applications in signal processing.
Topics include the Fourier transform for periodic and non-periodic
functions in continuous and discrete time, generalized functions,
sampling theorems, fast computational algorithms for transforms
and convolutions, filterbanks and multirate systems
MAIT 669 Independent Masters Project (3-6)
The masters project is intended to
allow students to apply advanced mathematical methods to practical, real-world
problems. Projects will be supervised individually by faculty members
associated with the MAIT Program. The nature of the
project is flexible and will be determined jointly by the student and faculty
supervisor. Ideally, working professional students should be able to use a work-related
project for this purpose. The work involved should be equivalent to a 3 credit regular course.
A detailed final written report describing the project must be prepared by the
student and approved by the faculty supervisor.
Electives
MAIT 615 Quantum Information, Detection, and Computation (3)
Introduction to information processing tasks implemented on fundamentally
quantum mechanical systems. Topics include background physics, mathematics,
and information theory, quantum cryptography, teleportation, super-dense
coding, quantum computation, Shor's algorithm, quantum error correction,
quantum limits in detection and estimation.
MAIT 624 Modern Mathematical Methods of Signal and Image Processing II (3)
(based on the second half of "A Wavelet Tour of Signal Processing" by Stéphane Mallat)
Advanced studies with state of the art signal/image processing techniques in the context
of applied and numerical harmonic analysis. Topics include stable signal representation
techniques (for noise reduction) and erasure channel problems, second-generation wavelets,
geometric sub-division schemes for multi-dimensional problems, level set approaches,
applications in estimation and analysis of sensor data, non-uniform sampling methods.
MAIT 626 Statistical Pattern Recognition and Classification (3)
(texts of Tribishani and Hastie; "Introduction to Statistical Learning Theory")
This is a new course. Mathematical and statistical tools for decision making
based on categorization of patterns present in data. Topics include regression,
feature extraction, dimensionality reduction, parametric and non-parametric
approaches to decision, estimation, and classification problems.
MAIT 627 Fast Multipole Methods (3)
Introduction to the fast multipole method, a matrix compression
computational scheme analyzing wide classes of structured operators
arising in physics, data analysis, and visualization. Topics include:
single and multi-level FMM, iterative solvers, non-uniform interpolation
schemes, Fast Gauss Transform, solutions of Laplace and Helmholtz equations.
MAIT 660 Scientific Computing for Advanced Industrial Mathematics
(3)
Fundamental techniques in scientific computation with an introduction
to the theory and software of each topic. Topics may include data
analysis, signal and image processing with control, non-traditional
mathematical modeling, Fourier and wavelet transform methods, second
generation wavelets for graphics, inverse problems and scattering.
Special Topics
Special topics courses are intended to expose students to the latest developments
in mathematical applications. As such, the content will vary depending on
the instructor and the current state-of-the-art in the subject areas. New 679
courses will be added as areas of interest arise.
MAIT 679A Mathematical Methods in Nanotechnology (3)
MAIT 679B Introduction to Biomathematics and Applications (3)
MAIT 679C Fast Acquisition Techniques in MRI (3)
MAIT 679D Sigma-Delta Methods in Communications and Radar (3)
MAIT 679E Computational Time-Frequency Analysis (3)
The aim of the course will be to cover the algorithms
and the discrete
transforms necessary to do time-frequency analysis to detect hidden
signatures, perform speech recognition, and improve synthetic imaging
schemes such as inverse synthetic aperture radar. Topics will include the
uncertainty principle, the discrete Fourier transform, the periodicity
transforms, the short-time Fourier transform, the spectrogram, the Gabor
representation, the ambiguity function, Cohen's classes of time-frequency
distributions, the symplectiv transformations, chirplets, the wavelet
transform, the Radon transform, and the ridgelet transform. Focus will be
on how to appropriately discretize the analytically derived transforms
with applications in mind.
MAIT 679F Frames and Applications (3)
MAIT 679G Harmonic Analysis and Waveform Design
(3)
This course will focus on recent advances in
waveform design using tools
from the area of Harmonic analysis. Topics include the design and
properties of different families of constant amplitude
zero-autocorrelation code (CAZAC) sequences, both periodic and
aperiodic,
in single and multidimensional settings.
MAIT 679M Introduction to Financial Mathematics (3)
MAIT 679R Design and Analysis of RADAR Signals (3)
MAIT 679T
Target Tracking and Filtering (3)
This advanced topics course will present the latest
advances in tracking
technology. The course begins with a review of probability theory,
followed by a discussion of the Bayesian estimation techniques. The
Kalman
filter and its extensions are then introduced and studied. Related
techniques including non-linear filters, modified gain techniques,
Wiener
filters, coordinate systems, and adaptive methods will also be
covered.
Advanced techniques in particle filtering, as well as tracking
problems
such as neighbor association and target re-acquisition will also be
treated.
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