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You're probably looking for the tedious information at the bottom. But here is my testament, as it was recorded for PBS 1998 "Life by the Numbers". And here is my publication list through 2013. A more formal description of what I do is elsewhere. A very kind article appeared recently on the Beckman Institue website. There's more on my neglected NCSA homepage. But you should definitely visit the IGL Lab, formerly the REU lab, formerly the grafiXlab, formerly the Apple Lab, where I do much of my work. Here are some pictures of Illinois mathematicians and their students.

2011 For some time now, I have worked on the pedagogical problem of how to teach higher geometry online. Here are two projects I am currently engaged in: netGeometry and my IOUMath blog .

The 2009 mathematics department calendar on altgeld models collections

The ams special session on mathematical visualization, urbana, 27-29 march 2009.


In the fall semester I usually teach MA198, "Hypergraphics" in the Illinois Geometry Lab , formerly the REU Lab of the Mathematics Department.

My second course is often MA402 , "Post-Euclidean Geometery" or MA403 "Modern Euclidean Geometry". In the spring, I sometimes teach MA595 and MA348. The former is a graduate minicourse in geometry called Computer Graphics & Geometrical Visualizaton. This is an updated and streamlined lectures-only version of my MA 428 from the 90's. The project half of that course is now done as an individual study course.

The latter Math 348 is the only course we teach in Mathematics that satisfies both the Compoition II and the Quantitative Reasoning II undergraduate requirements. You'd think it was popular. But it's not an easy course. In the fall semesters I sometimes teach Math 403, aka Math 303 Advanced Topics in Euclidean Geometry. I treat five fascinating threads of useful geometrical applications throughout the history of technology, art and pedagogy.

I also teach the ADVANCED COMPOSITION section of our majors gateway into mathematics Math 348 . The chief feature of this course is that the students learn TeX and write proofs in TeX, just like grown-up mathematicians.

Fall '05 I taught both sections of Post-Euclidean Geometry with UIUC alumnus Mike Hvidsten's fabulous new textbook and software.

Spring '06 I taught Math 198 Hypergraphics for the Campus Honors Program (CHP) in the grafiXlab and the the ISL-CUBE fully immersive virtual environment at the Beckman Institute.

In recent years I also taught:

Fall 2002, Differential Geometry, which is an excellent introduction to the field, but restricted to curves and surfaces in 3-space.

In the Spring of 2002 I taught Math 302 Post-Euclidean Geometry. . My version of this course is a bit more eclectic, hence the provocative title. There is even a questionnaire about what the students thought of it.

Fall 2000, I taught Math 306, History of the Calculus. There are interesting student projects and websites on that page.

For a score of years I taught Math 428 Geometrical Computer Graphics in the UIMATH.grafiXlab of the Mathematics Department, and in the Renaissance Experimental Laboratory (REL) and the CAVE of the National Center for Supercomputing Applications (NCSA) of the Beckman Institute (BI) of the of the University of Illinois (UIUC) in Champaign-Urbana.

At times I also teach a secton of Math 280 Advanced Calculus. Spring'98 it was a 9am adventure in Engineering Math insofar as we used H.M.Schey's cheeky ``Div, grad, curl and all that'' to complement Kaplan's ancient classic used in the other sections of Math 280. Spring'99 it was back to that hoary old classic by Wilfred Kaplan. Someday I may find an appropriate textbook for that course. Any suggestions?

At times I also teach a section of Math 285 Differential Equations, using an interesting text by Edwards and Penney. Theirs is one of the few diff-eq texts with relevant computer generated pictures and instructions for creating them. It also has a good chapter on chaotic dynamical systems.


I'm still a senior researcher with the NCSA, in good standing I hope. When the NCSA moved from the Beckman into their own building, and all the immersive virtual environments came to be administrated by the Illinois Simulator Laboratory (formerly the Integrated Systems Lab). I joined the ISL also in curating new ventures of art and math centered on the CANVAS traveling virtual environment. The original exhibit Calcula*rt at the Krannert Museum at Illinois, has a grander successor at the Dennos Museum in Traverse City.

Participation in the Mathmatics REU Site summer program continues with illiMath06 and illiMath08 Summer 2004 Peter Brinkmann and I directed an REU program, illiMath04, where we developed PyCube. For two summers we had an NSF-VIGRE sponsored REU program, illiMath2001 and illiMath2002.

Fall of 2000 I gave three Buckingham Lectures at Miami University of Ohio and here are the details But you'll find more and better links to this in the grafiXlab.
Summer 1999 and 2000 four talented alumni from Math 198 built the beginnings of the Audible Sketchpad for the CAVE. You'll need to visit their webpage to appreciate the effort.
There's an illiGallery at the NSF in Washington.

Fall 1998 the illiView team split across the wires between Orlando and Urbana to present Superball at Supercomputing98. Summer 1998 saw the world premiere of The Optiverse at Siggraph98 in Orlando and VideoMath'98 during the International Congress of Mathematics in Berlin. My talented RAs and I continued to work on projects from the previous year. We had our usual summer seminar.

Some alumni from these courses, colleagues and friends are helping me put together the grafiXlab. This will eventually be a Linux based successor to the fabled UIMATH.APPLE.LAB, which, since 1983, is the oldest functioning computer lab in the Math Department. In the meantime, however, we remain a Silicon Graphics Lab, with several hand-me-down Indigo Elans from the NCSA, a Mac G3, some fast WiNTels, and a small, but growling pack of Linuxes down the hall. Our first project is the studioCAVE. Once this project is adequately funded we'll really be in business.

You can find some of my more colorful research in the page on the Post-Euclidean Walkabout, which was part of the Virtual Reality Room at SIGGRAPH'94. This all began with the Etruscan Venus , who visited SIGGRAPH , with her NCSA friends , and her brother Apollo , and their their love child, Lotus , who are all living at Ellen Sandor's Art^N Gallery. There are research papers I should tell you about and the Topological Picturebook, but that has to wait for another time. The paper Interactive Methods for Visualizable Geometry, with Andy Hanson and Tamara Munzner pretty much summarizes my ideas on mathematics and graphics. But go to this IEEE panel for a real argument. At the The Geometry Center you can still see what experimental geometry is all about.

  • Office

  • You can learn my vital statistics and other important numbers from the letterhead. But please email me only with gfrancis at

    This is my Fall 2013 weekly schedule of fixed events,

    |Monday     |Tuesday    |Wednesday  |Thursday   |Friday     |
    T=10 E=11 N=noon G=geometry class S=seminar o=off campus . = free 
    Please e-mail me to make an appointment to meet in 101 Altgeld or some place more convenient for both of us.