These sessions as usual will be run by Professor Wang. And we will continue the free Pizza. But, you can also sign up for a one hour credit M 4801. For more information about the Putnam Exam, follow this link.
Math Biology will be offered MWF 9 in 322 Cherry Emerson (066A,322). Instructor is Christopher Klausmeier, of the School of Biology. The prereq is Calc II.
Differential Geometry will offered in the Fall. It hasn't been offered in three semesters, and was scheduled to be offered in the Spring 04 semester. But, we have another VIGRE postdoc Professor Tomaso Pacini, who is ideally suited to teach the course. We wanted to take advantage of his expertise (and give him a good introduction to GT teaching) so pushed the course up a bit.
Fourier Analysis will be a M 4803 course, taught by Professor Brody Johnson, who is a VIGRE postdoc. His sylabus and course description is:
Course Syllabus: An Introduction to Applied Fourier Analysis Professor Brody Johnson It is safe to say that in almost every engineering curriculum students encounter Fourier series in at least one of their engineering courses. In electrical engineering this frequently occurs in an advanced course on signals and circuits, while in mechanical engineering Fourier series are generally seen in a junior level course on vibration. Such exposure to Fourier series is extremely beneficial to the student, but often is too short for the students to develop much in the way of theoretical understanding. Moreover, in practice the students will generally work with discrete data and in place of Fourier series the relevant mathematical tool becomes the discrete Fourier transform. What follows is the syllabus for a junior/senior level mathematics course designed to provide students with a strong foundation in continuous and discrete Fourier methods as well as introduce the students to more advanced topics such as frames, wavelets, and subband coding as time permits. The course would develop rigorous mathematical theory, but would also incorporate applications. The course will benefit from substantial use of MATLAB (or an equivalent platform) and, in particular, at least one computer project should be expected. Possible Text(s): "An introduction to wavelet analysis," by David F. Walnut. Co-requisite: Calculus III. Topic Outline: 1. Linear algebra review: Vector spaces, bases, orthonormality, and the inner product. Functions as vectors. (1 week) 2. Sequences and series of functions: Point-wise convergence, uniform convergence, and convergence in norm. Uniform continuity of functions. (2 weeks) 3. Fourier Series I: Fourier coefficients, Bessel's Inequality, Riemann-Lebesgue Lemma, Parseval's Identity, point-wise convergence of partial sums for differentiable functions. (3 weeks) 4. Fourier Series II: Sine and cosine series, convolution, and applications. (1 week) 5. Discrete Fourier transform: DFT for R^n and l^2(Z), convolution, relationship to Fourier series and the z-transform, and applications to signal processing. (3 weeks) 6. Subband coding: Burt-Adelson pyramid scheme, perfect reconstruction filter banks, and basic signal compression. (1.5 weeks) 7. Frames: Finite- and infinite-dimensional frames, and the frame algorithm. (1.5 weeks) 8. Wavelets: Examples, multiresolution analysis (MRAs), connection with subband coding, discrete wavelet transform (DWT), the `a trous algorithm. (2 weeks)
Professor Jean Bellisard will teach a course in Quantum Computing at the undergraduate level. The course will be listed as a special topics class.
Title: Quantum Information and Quantum Computation
Level: Senior students in mathematics, physics and computer sciences.
Quantum computing and quantum information might give rise to important
technological developpements in the future. this course will be organized
around the following topics:
Classical information theory. Clues in quantum theory.
Quantum systems used in experiments.
Quantum information: Compression, transmission, noise, entanglement
Quantum Complexity: introduction, algorithm, error correcting codes.
Prerequisite: familiarity with matrix calculus and finite dimensional
vector spaces. That is, Mathematics at the level of M 2403.
I think we will also offer Math 4012, Algebraic Aspects of Coding Theory. I expect that the presentation of the course will be assuming a prerequisite of MATH 4107, Algebra I. I'll confirm details later.
Second, Professor Lefton will be teaching the recommended course 4777---Vector and Parallel Processing. Professors Lefton and Shonkweiler are writing a text for the course. We will aim to get some out of the ordinary things happening for the Spring 2003 Semester.
Math 4880 Information Theory, Spring 2001
Taught by Professor Bunimovich. T Th 12-1:30 pm
The measurement and quantification of information. Entropy,
relative entropy and mutual information, entropy rates of Markov
chains and Hidden Markov Models, optimal codes, data compression
and gambling, Kolmogorov complexity, universal source coding
and large deviation theory.
In this course we return to the origins of the subject and with the use of the computer take a computational approach. Motivated by applications to numerical analysis, dynamical systems, image processing, and efficiency of computation we will develop a theory based on cubical complexes (as opposed to the standard simplicial theory). This will lead to a cubical homology theory which includes homology groups and homology maps. Particular attention will be paid to algorithms for computing these objects.
Time permitting and depending on the interests of the participants, the last few weeks will be spend discussing applications of the theory to computational dynamics and image processing.
Prerequisites: Linear Algebra and Introductory Analysis or Topology,
or permission of the Instructor
Time: Monday Wednesday 1:30 - 3:00
Instructor: Professor Allen Tannenbaum
"Introduction to Computational Computer Vision"
We will introduce the students to the area of computer vision with an
emphasis on computations and problem solving. Applications will be
given to robotics, autonomous vehicles, tracking, and image-guided
Textbook: B. Horn, Robot Vision
I will also hand out extensive class notes.
Grades will be based on
(1) Midterm: 15%
(2) Project: 45%
(3) Final: 40%
The Project is an essential part of the course. The students
will be required to choose a topic in computer vision,
and work out a computer implementation of their idea.
This may involve the implementation of a smoothing filter,
segmentation method, and edge detector. This was allow
the student to have hands-on experience in understanding and
implementing a given computer vision algorithm.
Requirements: Basic course in signal processing.
Knowledge of some programming language (Matlab or C/C++ or FORTRAN).
2- Classic methods of linear filtering
3- Sketch of wavelet techniques
4- Edge detection
6- Optical flow and stereo disparity
7- Shape recognition
8- Color and texture processing
9- Motion planning and tracking
b- Image-guided surgery
c- Controlled active vision
Math 4221, Stochastic Processes
Stochastic processes modelize the evolution in time of a random phenomenon:
one can think of the random motion of a physical particle, of the
fluctuations of the Dow Jones etc. From a mathematical point of view, a
stochastic process is a random function on a given state space. This course
will focus on the simplest setting, when both time and space are discrete.
Still many interesting features of stochastic processes can be introduced
in this framework. The prerequisites are a good knowledge of basic calculus
and an introductory course of probability.