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Topic: Geometry Center Summer Institute for Students
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Gene Klotz

Posts: 30
Registered: 12/3/04
Geometry Center Summer Institute for Students
Posted: Jan 23, 1993 4:24 PM
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Program Description:
The Geometry Center has a unique summer program for
undergraduate students. The10 week program will be held June 14-
August 20, with extensions possible by special arrangement. The
Center is looking for students who have a strong and demonstrated
interest in mathematics and computing and would enjoy working in
an intense environment with other students and researchers. The
enclosed brochure provides some general information about the
Center. The program will be organized as follows.

Week 1:
Orientation and project selection. Students will learn about The
Geometry Center computing environment and decide on a project in
an area of mathematics or computer graphics. Computationally,
many past projects involved Mathematica and/or interactive
graphics programs on the Silicon Graphics Iris workstations. Past
project domains include:
% hyperbolic, Euclidean and spherical
geometry; fractals, chaos, and dynamical
systems; differential geometry; group
% mathematical exposition via visualization
% pure computer graphics

Weeks 2-3:
Students may attend lectures of the course RComputation,
Visualization and GraphicsS taught by Professors David Dobkin and
Patrick Hanrahan of Princeton University, Vibeke Sorenson of the
California Institute of Art, and Diane Souvaine of Rutgers University.

Course Content: Computer generated images are created by
combining algorithms for doing a variety of geometric tasks. These
algorithms give the computer the ability to do geometry as a human
would. We will develop the ideas behind a few geometric algorithms.
Ideas will be Rvertically integrated.S That is, we will consider the
geometry necessary to model the problem, the data structures used
to develop the algorithm, the programs written to implement the
algorithm and the images produced by the algorithm. The ideas we
develop will build from basic principles, starting from the geometry
and computer representation of points, lines and polygons. We will
assume that students are conversant with the details of courses in
high school geometry and are not averse to computers.
Problems involving creating and decomposing complex objects
will be presented. The Voronoi diagram data structure, an important
modelling structure, will be presented. Ray tracing, the method used
to create the images you see on television, will be developed from
basic geometric primitives. Artistic considerations that arise in
creating satisfying images will be described. All of these ideas will
be developed from concepts used in the high school geometry

Weeks 4 - 10:
Students will continue work on their projects. Before leaving,
they will be required to write a report on their accomplishments.
These student reports will be assembled and published as an official
Center research report. Students will also be involved in making a
video illustrating their summer's work.

Eligibility and application procedure:
Applications from students currently enrolled in college with a
strong and demonstrated interest in mathematics and computing are
welcomed. Exceptionally strong applications from graduating high
school seniors, graduating college seniors or foreign nationals may be
considered for acceptance into the Institute. An application form is
enclosed. Please note that a transcipt and a letter of
recommendation are required. In evaluating your application,
special attention will be paid to the letter of recommendation. This
letter should be from a teacher or employer familiar with your work.
There is no single requirement which is essential for involvement;
instead, it is your interest in mathematics and computing and your
drive to succeed that are the most important attributes for a
successful experience. For this reason, seriously consider your
responses to the two questions on the application. If you will bring
the above attributes, the Center will supply Unix workstations, a
gifted and dedicated summer staff to work with you, and a work
environment in which some of the best mathematics research and
software development in the world is being carried out. The summer
program can accommodate up to 20 participants. Women and
underrepresented minorities are especially encouraged to apply.

The total salary paid will be $2000-2500 depending on
background, experience and year in college.
Air conditioned double dorm rooms with full board will be
provided for each participant during the 10 weeks (June 14-August
23) of the Institute. (No additional funding is available for those who
do not live in the dorms.)
No funds are available for travel costs to Minneapolis.

Head Coach:
Professor Tony Phillips of SUNY - Stony Brook will be in overall
charge of the program. He is a topologist, one of the original sphere
everters, who works on topological problems in quantum field
theory. He has taught two math/ art courses and is interested in
discovering visual and musical manifestations of mathematics.

The Geometry Center
1300 South Second Street
Minneapolis, MN 55454
Phone: (612) 626-0888
Fax: (612) 626-7131

Complete applications must be submitted by February 1, 1993.

Return application for the Summer Institute to:
The Geometry Center
Summer Institute '93
1300 South Second Street
Minneapolis, MN 55454


Sex (please circle): M F

Permanent Address:

Home phone:


University address:

University phone:

Ethnicity (circle one): Black Asian Hispanic White

Native American Other

Birth Date:

Year in School:

Expected Date of Graduation:

Yes No I plan to stay in the dorm.
Please reserve a double room for me.

Yes No I require parking at the dorm. I realize this will be
an additional expense for me.

Yes No I would like the dorm to provide me with a bag lunch
weekday so I don't have to walk back to the dorm to eat.

Describe your experience with mathematics and computing in the space
provided below.

What would you like to achieve in a summer research position in geometry,
topology or visualization?

Letter of Recommendation:

Name of writer:

Phone number of writer:

NOTE: Include your transcript.

Incomplete applications, i.e. those without transcripts or letters of
recommendation, will not be considered. It is your responsibility to
see that your letter of recommendation arrives before the deadline date.

This program is open only to U.S. citizens and permanent residents.

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