What Is Illustrated Mathematics?

Visual presentations aid in understanding complicated objects. Understanding abstract constructions frequently encountered in mathematics is improved with visual representations and graphics. Such visualizations are also important for students who have difficulty grasping abstract objects.

If visualization had been our only goal, we could have published this collection as a printed book instead of as a CD-ROM. CD-ROMs can store much more information, however. Besides, we can animate sequences of graphics and the computer allows direct interaction with the material. For example, it is feasible to create additional images during class and respond to students' questions. This capability improves the quality of instruction.

Collection of Visualizations

The graphics and animations on the CD-ROM can be used directly for teaching. No additional software is necessary (on Macintosh and under Windows).


Examples from this collection can be projected on a screen during class (for example, with an LCD projection panel connected to your computer).


If no computer-compatible projection equipment is available, the examples can be printed for class notes or to create slides.

Part of Documents

The graphics and animations are part of hierarchically structured documents (Mathematica notebooks). This organization allows fast access to particular examples and enables us to add explanatory text.

For Class Notes

Be it directly on the computer or printed out, the graphics can be included in your documents and used as part of class notes. To help with this use of the graphics, many graphics are stored on the CD-ROM outside of their notebooks, in a graphics standard format.


Because many graphics use color, a color monitor is recommended. However, colors have been chosen in a way that makes presentations with a monochrome monitor possible.

Included: MathReader

The MathReader program included on the CD-ROM allows you to read all documents on this CD-ROM, including animations.

Programs for Your Own Examples

Mathematica Is Necessary

The programs are based on Mathematica. For their use, Mathematica is necessary. In fact, the collection of examples was created with these programs.

Prior Knowledge of Mathematica Is Not Necessary

Some experience with Mathematica is an advantage, but not required for the use of the Illustrated Mathematics programs. Simple adjustment of parameters in the examples allows their modification. Each program (package) is accompanied by a manual and many examples of its use.

Creation of Teaching Material

The programs allow you to create your own teaching material in the form of Mathematica notebooks, the form also used for this collection.

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