Recognizing patterns
(how can
a robot tell an orange from a banana).
Computers
in Statistics and Exploratory Data-Analysis:
Graphs and networks.
The minimal spanning
tree and
its application to cluster analysis.
Unsupervised
learning.
Robust estimation of
location
(onion peeling).
Computer
Vision:
The Hough transform.
Detecting lines in a
digital image
with the Hough transform.
Image segmentation
in
document
analysis.
Text-line
orientation
inference
in document analysis (another application of the minimal spanning tree).
Computer
Networks
Electronic mail,
passwords and
privacy.
Coding theory and
cryptography.
Transposition and
substitution
ciphers.
Cryptanalysis
(breaking
secret
codes).
The Knapsack problem.
Public-key
cryptosystems
(the
Hellman-Merkle-Diffie cryptosystem)
Computer
Graphics and Visualization:
Turtle geometry.
Fractals.
Hidden surface
removal.
The painter's
algorithm.
Virtual reality.
Philosophical,
Ethical and Social Implications of Computers:
Can a computer
think?
Turing's
test.
Computer art
(competition with
Mondrian?).
Law.
Medicine.
Computer
psychotherapy.
References
Course
Level
Material
A. K. Dewdney, The
Tinkertoy
Computer and Other Machinations, W. H. Freeman & Co., New York,
1993.
G. T. Toussaint, "A
new
look at
Euclid's second proposition," The Mathematical Intelligencer,
vol.
15, No. 3, 1993, pp. 12-23.
J. Weizenbaum, Computer
Power
and Human Reason, W. H. Freeman & Co., San Francisco, 1976.
R. M. Baer, The
Digital Villain,
Addison-Wesley, Reading, Mass., 1972. (Good
for history of computing, Turing machines, numerical analysis and
artificial
intelligence).
A. K. Dewdney, The
Turing Omnibus:
61 Excursions in Computer Science, Computer Science Press,
Rockville,
U.S.A., 1989.
R. Rucker, Mind
Tools,
Houghton Mifflin Co., Boston, 1987. (Good
for
elementary introduction to Turing machines).
D. M. Davis, The
Nature and
Power of Mathematics, Princeton University Press, Princeton, N.J.,
1993. (Good for basic
number theory
related
to cryptography and fractals).
J. G. Brookshear, Computer
Science: An Overview, The Benjamin/Cummings Publishing Company,
Inc.,
1994.