Georgia Tech Undergraduate Mathematics

Upcoming Classes in the School of Mathematics

Honors Classes Information: 1522, 2412, 2414, 3022, 3225

For the Upcoming Semester, From the Official Math Page

Fall 2003, Spring 2003 , Fall 2002 , Spring 2001

Fall 2003

Fall 2003

Putnam Exam Pracice sessions

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.

Mathematical Biology 4755

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, Math 4441, Professor Tomaso Pacini

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 Math 4803, Professor Brody Johnson

This course may be cancelled, as Professor Johnson will be taking a postition at Saint Louis University in the Fall.

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)

Spring 2003

Two Noteworthy classes at the undergraduate level.

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
cryptography, teleportation.
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.

Fall 2002 

At the undergraduate level, there are two noteworthy things. First, the Honors Differential Equations Math 2413, will be running in the ACE Lab. This will be Professor McCuan's second time to teach this course in the Lab. The course will involve a significant amount of project work, in which experiments are performed, and modeled by differential equations. Professor McCuan has archived some of the web pages used in this course in the Fall of 2001.

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.  

At the graduate level, there are some things cooking.  Professor Ciucu will be teaching a special topics course in Algebraic Combinatorics.  Professor Bellisard, in his first semester at Georgia Tech, will be teaching a special topics on Random Matricies.   This is currently a very hot topic in physics, number theory, statistical mechanics, and probability theory. Finally, Professor Mockenhoupt will be teaching harmonic analysis.  While this course is on the books, it hasn't been offered in a couple of years.


Spring 2001

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.

Math 4432  Algebraic Topology, Spring 2001

Professor Mischaikow
Homology is a standard tool used to study the global properties of spaces and continuous functions. Furthermore, as it was developed at the turn of the century, it was a purely combinatorial theory. Therefore, in principle, it is an ideal tool for the computational study of global structures and global nonlinear analysis. Unfortunately, analyzing even simple spaces or maps leads to large combinatorial problems and for this reason much of the mathematical development of the early half of this century focussed on the construction of sophisticated algebraic techniques to circumvent the complicated combinatorial computations. The standard presentations of homology theory reflect this development.

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.

Textbook:Computational Homology by T. Kaczynski, K. Mischaikow, and M. Mrozek.

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).


1-  Introduction
2-  Classic methods of linear filtering
3-  Sketch of wavelet techniques
4-  Edge detection
5-  Segmentation
6-  Optical flow and stereo disparity
7-  Shape recognition
8-  Color and texture processing
9-  Motion planning and tracking
10- Applications:
       a- Robotics
       b- Image-guided surgery
       c- Controlled active vision

    Math 4221, Stochastic Processes

Professor Marchal


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.

MWF       0205-0255pm                              140  Skiles