Mathematical Systems Accessed on the Web: Preliminary Overview Paul Libbrecht paul@activemath.org July 1, 2002 Keywords: mathematical systems, web-access, mathematical user-interfaces, mathematical learning, math- ematical computations, Internet accessible. 1 Introduction Mathematical Systems offer interesting capabilities to explore the mathematical reality with the help of properly triggered computations and display. As soon as mathematical content is placed on the Web, the capability to share the computation methods with others appears. The first method to share mathematical computations is by distributing so-called worksheets. These files are made of code specifying to the mathematical system the sequence of operations and its data. They require the receiving side to be able to run the same system which may be a problem in many situations: some mathematical systems require specific platforms, some others have a high price, all require a non-trivial installation, etc. A more elaborate method to share mathematical computations is to offer the mathematical system acces- sible through a Web interface. We call a session of mathematical computations accessible through a Web- interface if it is triggered by few mouse-clicks while browsing and reading related documents. We call these systems “web-mathematical-systems-connection”. The sole fact that they are on the Web makes them different from the classical computer-algebra desktop applications as the interactions happening within the session are related, most-probably tightly, to the content the user is browsing. Sessions of such connections can be used for plain exploration purposes as is generally done with computer- algebra-systems. The user is then free to use the computations and their visible results to understand, conjecture, or verify mathematical facts. Within learning environments, however, such connections can be used to have users perform exercises whose solutions are automatically evaluated. For these sessions, interaction is expected to be richer than a normal mathematical system: the user’s actions are to be evaluated and feedback is to be provided. Contents: This preliminary article attempts to introduce the basic building blocks found in most of the available web-mathematical-systems-connection available, technologies associated to them are described followed by a list of characters. We conclude with the start of a list of available systems with a little description of their characters under the lights of the concepts introduced. This article is preliminary in the sense that the set of available solutions is not extensively covered and, as such, the study may appear superficial. It is the intent of the author, however, to enrich a web-based version of this overview which shall be found under http://www.activemath.org/math_sys_through_web. 1