Notation Census Manifest

This page describes the purpose and current work methods of the notation census.

Objectives

The notation-census has set itself as mission to collect graphically the mathematical notations used through the world in a graphical form. It should recollect them in groups of semantically equivalent concepts.

The census should report about graphical copies of fragments of mathematical texts that are recognized as being widely used in each culture.

By notations we mean a practice of writing mathematical concepts (such as the representation of decimal numbers or the abbreviations used to denote special functions) in the formula language. Even though the notations we collect are fully instantiated, with chosen variable names or with numbers or elaborate terms in the arguments, we consider the notation as being the rendering process independent of these: any variable name could be used. The real world requirement, however, forces us to insert graphical copies of instantiated formulæ.

Work Methods

The census is created using a wiki, the math-bridge wiki http://wiki.math-bridge.org/display/ntns/, hosted by a project aiming at offering math-courses that propose bridges to enter university's high-level usage of mathematics.

The census encodes one page per semantic containing a short introduction to the topic, pointers to classical references describing the semantic, and a series of observations made from the various texts at hand: each observation has a short description, a bibliographical pointer, and a graphical extract.

One page per semantic currently means we are following the OpenMath content dictionaries naming and grouping methods: one grouping page per content-dictionary, one page per symbol. This may appear arbitrary to many but is an attempt to rely on a classical listing method.

Everyone with an email address is welcome to contribute to this census which is edited as a wiki where everyone with a mail address can register (see on top-right of this page).

Math-Bridge Workflow

Within the math-bridge project, this notation census intends to serve as input to generate the abstract notations, a pair of OpenMath and MathML-presentation with contextual and precedence annotations from which the ActiveMath servers used in Math-Bridge lectures will present their formulæ in web-browsers. A list of the implemented notations thus far can be seen (choose OpenMath-CDs collection for example); see also more about notations in ActiveMath.

The steps to obtain good quality notations for content being encoded are as follows:

• some piece of content, from a visual source, needs to be encoded into ActiveMath
• an attempt is made by an encoder; that encoder realizes that some formulæ, though he can encode them semantically correctly, are not rendered as presented in the source
• (this observation can also be made by content-providers within the content:Review-Workflow)
• an extract is provided, and existing sources of the bibliography are searched to see if this notation is widespread; observations are inserted in the census
• ActiveMath-notations are written, tested, and committed to the ActiveMath CVS (or to the source); a link to the notation experiment (in the symbol-presentation-tool) is made in the observation
• the content encoder or reviewer verifies that the notation is now both semantically and visually correct

Source Selection

Criteria for the choice of a book that contains the notations we are publishing are the following:

• wide usage of the book
• web-accessibility of, at least, a publisher page of the book
• authorization to web-publish extracts (this is generally fair use)
• ability for the contributor of observations to upload picture extracts of the book (scans or PDF screen-shots)

Moreover, we wish but do not request a full access on the web.

Publications

• Paul Libbrecht, Maria Droujkova, Erica Melis, Notations Across Cultures for Teaching, Proceedings of the ICMI Study 21 conference. M. Setati, T. Nkambule & L. Goosen (Eds).
• Paul Libbrecht, Notations Around the World:Census and Exploitation, in Intelligent Computer Mathematics, Serge Autexier, Jacques Calmet, David Delahaye, Patrick D.F. Ion, Laurence Rideau, Renaud Rioboo and Alan P. Sexton (eds), Lecture Notes in Computer Science, Volume 6167/2010, 398-410, DOI: 10.1007/978-3-642-14128-734, 2010.
• Paul Libbrecht Customized and culturally enhanced rendering and search, Deliverable D4.2 of the Math-Bridge project.
• announce of the census on the openmath list or the www-math list
• Math-Bridge D4.1 (to be made public).

Progress and Contributors

Since November 2009, the census is currently being started by Paul Libbrecht and Abdelshafi Bekhit with contributions from Franz Embacher, soon others of Math-Bridge and probably others.

The intent is to cover all mathematical notations needed for early university math educations.

In more details we intend to:

• cover the MathML CD-group until early January 2010
• cover all of the ActiveMath-available content at the end of July 2010 including encoding the notations in ActiveMath
• cover all of the Math-Bridge content for all Math-Bridge languages at the end of October 2010 (see internal content-selection)