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 theory % 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 classroom.
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.
Financial: 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 firstname.lastname@example.org
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
Ethnicity (circle one): Black Asian Hispanic White
Native American Other
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 every 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.