MathBrush [pdf] is a pen-based system for interactive mathematics. The system allows users to write mathematical expressions as they would using a pen and paper, and manipulate the expressions using computer algebra system operations that are invoked by pen-based interaction. Users can also edit the input and ouput expressions or parts of them.

Despite the benefits of computer algebra systems (CAS) such as Maple, many users prefer a pen-and-paper approach. This is mainly because a pen-and-paper approach does not involve translating the mathematics into a specific CAS-based representation. This motivated our project to bridge the gap between the intuitiveness of free-form pen-and-paper and the power of a CAS.

The second generation of the MathBrush system contains many innovations that enhance the functionality and usability of our system. Some of them are:

• Real-time semantic-based recognition of hand-drawn mathematical expressions.
• Grammar based parser that provides multiple interpretations of recognized expressions.
• The ability for the user to quickly and easily correct misrecognized expressions or subexpressions by selecting alternate interpretations from a ranked list.
• The user can correct single characters, sub-expressions or complete expressions with just a few strokes.
• The user can correct expressions any time during the input.



• Trainable character recognizer.



• Support for matrices, including short forms of matrices.

Some of the computational functionality of MathBrush is as follows:

• Connects to Maple or Mathematica as a computer algebra system. Users can simple draw the equations they are interested in, and select operations from context menus.
• Through the use of context menus, users can operate on the expressions using the power of a CAS, with out specific knowledge of the CAS.



• Supports 2D and 3D graphing operations, and pen based manipulations of the graphs.
• Multi-platform support.
• Manipulate output expressions either by selecting parts of expressions and operate using CAS or using sub-expressions as part of new input expression

For more information please consult our publications and our demos.

• Build a pen-based math system to allow the user to follow a pen and paper paradigm for input and output while taking advantage of the power of CAS to manipulate the mathematical expression.
• Explore the interaction between the user and the recognition techniques, to support the most productive user experience in a complex recognition environment.
• Study the key issues when combining pen-based interfaces with Computer Algebra Systems (CAS) such as Maple.