The illiMath Collective consists of students, colleagues, collaborators and contributors to the illiMath Project begun by George Francis in the UIMATH.AppleLab in 1983.

illiMUG Presentation at Wolfram Research, Inc. (WRI), 24jul08.

GeoProj: Geometric projections from the sphere to the plane

John Pacey, UIUC math grad

In the pedagogy of an undergraduate course in non-Euclidean geometry constructions in all, pairwise linked, models of hyperbolic, elliptic, and Euclidean geometry are desirable. Extant plane geometry drawing packages, open source and proprietary, rarely use more than two equivalent models, and almost none link the constructions between pairs of models. This projects seeks to remedy this, using a variety of platforms, including Java, Mathematica, and Syzygy.

subNil.nb: Sub-Riemannian geometry on upper triangular 3x3 matrices

Lisa Hickok, UIUC math grad

One of Thurston's eight 3D geometries, the Nilpotent Lie Group, can also be given a sub-Riemannian geometry. This is easier to imagine and visualize. This Mathematica Notebook contributes to the grand project "ALICE on the eight-fold Way" to visualize Thurston's eight possible 3D geometries.

Cocycles in Finite Fields

Adam Hughes, JohnMark Lau and Eric Peterson, UIUC under graduates

A complete, elementary classification of symmetric 2-cocycles over fields of positive characteristic was obtained with the help of extensive experimentation with Mathematica6. This 10 month long effort contributes materially to the algebraic classification of topological spaces up to homeomorphism, which is, afterall, the raison-d'etre of Algebraic Topology.

baREUcuda: Mathematica and CUDA graphics processing units.

Abdul Dakkak (U. Toledo), Katie Poon (Wellesley), and Chase Boren (UIUC)

Eight innovative and promising experiments involving the NVIDIA GPUs, which are programmable by the C-like CUDA language, will be presented. The CUDA-chip is, in effect, a small but powerful single-instruction multiple-data (SIMD) parallel supercomputer that fits into chassis of a desktop and the limits of a student's budget. In the early 90s, the Connection Machine (CM2) was the SIMD mainline supercomputer of the NCSA. It is celebrated in Richard Power's novel "Galatea 2.0". It also was the platform on which Stephen Wolfram et al performed their lattice gas cellular automata experiments on the Navier Stokes Equation.

NVIDIA provides a library of provocative example, including "fluidsGL" and "Mandelbrot". Extending Jared Schaber's Math 198 project of splitting fluidsGL into a CUDA based data server, and a remote (socketed) OpenGL visualizng client, the baREUcuda team achieved the following variants:

  1. CUDA MathLink Mathematica for both fluidsGL and Mandelbrot

  2. CUDA MathLink caveMathematica for fluidsGL

  3. CUDA MathLink Mathematica for FFTs and other matrix operations.

CaveMathematica is a Syzygy application that functions as a Mathematica front end in cluster based immersive virtual entironments (VEs) such as the Beckman Cube, CAVE, CANVAS, DiVE (Duke), Portal (Technical U Berlin). It started as a illiMath2006 REU project by (later) WRI intern Mimi Tsuruga (now Berlin Mathematical School), mentored by Ulises Cervantes-Pimentel of WRI, and Stuart Levy of the NCSA.