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For an idea of what may happen this coming summer, have a look what we did the last time, in illiMath 2006.
Sample LaTeX files, and related materials accumulate here.
Webpage introducing REU students Summer 2008.
Repository of possbly useful files for illiMath projects.

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illiMath2008: an REU of
Geometrical Visualization in Virtual Environments

9 June - 1 August
Program Director: George Francis

Visualization of mathematical phenomena and their transmutations is a maturing field of geometical computer graphics. Though opportunities to learn and practice this discipline are now plentiful, few universities have as long a tradition and as broad a base of application as Illinois.

Students in this program work with current researchers in diverse areas of mathematics, science and technology, who use a common programming platform, Syzygy. This distributed graphics system supports cluster based immersive virtual environments (IVE) such as the CAVE, the Beckman Cube, the Krannert CANVAS at UIUC, the DiVE at Duke, and the PORTAL at the Technical University of Berlin, and the Traveling CANVAS at the Dennos Museum in Traverse City, Michigan.

In this program students with strong interest and some experience in mathematical graphics participate in research programs of their associated mentor (AM). The program provides the facilities (and any necessary training in their use) for the student to assist their AM in creating visual materials illustrating research in a variety of media, including the production of custom software, webpages, animations, print quality images, etc.

Common to all projects is Syzygy, Python, and OpenGL. Syzygy is the distributed graphics system, developed by the Integrated Systems Lab (ISL), for cluster based virtual environments The program also provides the student with tutorials in the mathematical background and lectures by specialists in the subjects of their projects.

Similar REU programs, Audible Sketchpad for the CAVE, illiMath2001, illiMath2002, illiMath2004 and illiMath2006 and were conducted in recent years. Here is a report on a typical summer.

Projects:

Projects of illiMath2008 Research Experience for Undegraduates, Mathematics Department, University of Illinois at Urbana (UIUC), directed by Prof. George Francis, are the original work of the student principal investigator (SPI) and their associated mentor(s) (AM) and corresponding mentor(s) (CM). Other student investigators (SI) assist.