CS 530: Geometric and Probabilistic Methods in Computer Science *
Instructor: Lance Williams
<williams@cs.unm.edu>
Time: MWF 11:00 - 11:50 AM
Location: Woodward 149
Office Hours: Mon. 4:00-5:00, Wed. 4:00-5:00.
Office: FEC 349C
Description
This is a course in applied mathematics for computer scientists, with
an emphasis on information theory and linear systems theory. The goal
of this course is to introduce computer science graduate students to
the practical kind of mathematics useful for simulation and modeling
and by researchers in scientific computation, computer vision and
graphics, image processing, robotics, machine learning, and neural
networks.
Course Syllabus **
- Aug. 23-27
- Aug. 30-Sept. 3
- Sept. 6-10
- Sept. 13-17
- Sept. 20-24
- Sept. 27-Oct. 1
- Oct. 4-8
- Oct. 11-15
- Oct 18-22
- Oct. 25-29
- Nov. 1-5
- Nov. 8-12
- Nov. 15-19
- Nov. 22-26
- Nov. 29-Dec. 3
- Dec. 6-10
Prerequisites
This is not a linear algebra course. Knowledge of basic
linear algebra is a prerequisite! Concepts you should understand are:
vector sum and difference, inner product, matrix product, matrix
transpose, matrix inverse, linear independence, span, basis, rank,
orthogonality, change of basis, eigenvectors, and eigenvalues. There
will be an examination during the second meeting of the class on the
mathematics prerequisites. Students who do poorly on the prerequisite
examination should take Math 321.
Homeworks
There will be approximately six homework assignments. Many of the
homework problems will be similar to those you will find on the
midterms and final exams. Other problems will require experimentation
in MATLAB. All are designed to increase your understanding of the
fundamental ideas. Homeworks are to be turned in during class on the
day they are due. They should not be emailed to the professor.
Additional Resources
- Schaum's Outline of Probability, Random Variables, and Random Processes (Hsu).
- Schaum's Outline of Linear Algebra (Lipschutz-Lipson).
- ven der Lubbe, J.C., Information Theory, Cambridge
Univ. Press, Cambridge, UK, 1997.
- Reza, F.M., Introduction to Information Theory, Dover
Publications, New York, NY, 1994.
- Lay, D.C., Linear Algebra and Its Applications (2nd Ed.),
Addison-Wesley, 2000.
- Strang, G., Linear Algebra and Its Applications (3rd Ed.),
Harcourt Brace Jovanovich, San Diego, CA, 1988.
- Roberts, M.J., Signals and Systems, McGraw Hill, New York, NY, 2004.
- Schaum's Outline of Signals and Systems (Hsu).
- Hubbard, B.B., The World According to Wavelets (2nd Ed.),
A.K. Peters, Wellesley, MA, 1998.
Grading
- Homeworks (approx. 6): 30%
- Midterm I: 18%
- Midterm II: 18%
- Final Exam: 34%
Miscellany
MATLAB
Most programming will be done in MATLAB or GNU Octave. Both have excellent
online documentation. Here are some useful routines:
Images
Calculators
Although experience shows them to be of little actual value, on all
exams (including the prerequisites exam), you are welcome to use a
basic scientific calculator, e.g., a TI-30. You will not
be allowed to use graphing calculators, programmable calculators,
PDA's, or laptops. A good rule of thumb is that if it cost you more
than $20, you probably cannot use it. If you have doubts, see me.
* This page can be found at http://www.cs.unm.edu/~williams/cs530f04.html
** Subject to change.