Notations Around the World: Census and Exploitation
Mathematical notations around the world are diverse. Not as much as requiring computing machines’ makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics.
In order to understand better this diversity, we are building a census of notations: it should allow any content creator or mathematician to grasp which mathematical notation is used in which language and culture. The census is built collaboratively, collected in pages with a given semantic and presenting observations of the widespread notations being used in existing materials by a graphical extract. We contend that our approach should dissipate the fallacies found here and there about the notations in “other cultures” so that a better understanding of the cultures can be realized.
The exploitation of the census in the math-bridge project is also presented: this project aims at taking learners “where they are in their math-knowledge” and bring them to a level ready to start engineering studies. The census serves as definitive reference for the transformation elements that generate the rendering of formulæ in web-browsers.
KeywordsMathematical Notation Cultural Context Imaginary Unit Mathematical Symbol Book Title
Unable to display preview. Download preview PDF.
- [Caj28]Cajori, F.: A History of Mathematical Notations. 2 vols. Open Court (1928), Browsable from http://www.archive.org/stream/historyofmathema031756mbp
- [CIMP01]Carlisle, D., Ion, P., Miner, R., Poppelier, N.: Mathematical markup language, version 2.0 (2001), http://www.w3.org/TR/MathML2/
- [DL08]Davenport, J.H., Libbrecht, P.: The freedom to extend openmath and its utility. Journal of Computer Science and Mathematics 59, 1–19 (2008)Google Scholar
- [Fra09]Bergeron, F.: Re: Fascicule de combinatoire, Private email communication on August 31st at 16:09 GMT+2 (2009)Google Scholar
- [Hof01]Hofstede, G.: Culture’s consequences. Comparing values, behaviors, institutions, and organizations across nations. Sage Publications, Thousand Oaks (2001)Google Scholar
- [KMM07]Kohlhase, M., Müller, C., Müller, N.: Documents with flexible notation contexts as interfaces to mathematical knowledge. In: Proceedings of MathUI 2007, Linz (2007), http://www.activemath.org/workshops/MathUI/07/proceedings/Kolhase-et-al-DocumentNotations.html
- [LAG09]Libbrecht, P., Andrès, É., Gu, Y.: Smart Pasting for ActiveMath Authoring. In: Proceedings of MathUI 2009 (July 2009), http://www.activemath.org/workshops/MathUI/09/
- [LCME+08]Laborde, C., Creus-Mir, A., Egido, S., Dietrich, M., Libbrecht, P.: Curricula categorisation into ontology. Deliverable D2.5, The Intergeo consortium (September 2008)Google Scholar
- [Mar09]Marcus, A.: Global/intercultural user interface design. In: Sears, A., Jacko, J. (eds.) Human-Computer Interaction: Design Issues, Solutions, and Applications, ch. 18, pp. 355–381. CRC Press, Inc., Boca Raton (2009)Google Scholar
- [MGLU09]Melis, E., Goguadze, G., Libbrecht, P., Ullrich, C.: Culturally adapted mathematics education with activemath. Artificial Intelligence and Society, Special Issue on Enculturating HCI 24, 251–265 (2009)Google Scholar
- [SW06]Smirnova, E., Watt, S.: Generating tex from mathematical content with respect to notational settings. In: Proc. International Conference on Digital Typography and Electronic Publishing: Localization and Internationalization (TUG 2006), Marrakech, Morocco, November, pp. 96–105 (2006), http://www.tug.org/TUGboat/Contents/contents27-2.html
- [ULWM04]Ullrich, C., Libbrecht, P., Winterstein, S., Mühlenbrock, M.: A flexible and efficient presentation-architecture for adaptive hypermedia: Description and technical evaluation. In: Kinshuk, C., Looi, E., Sutinen, D., Sampson, I., Aedo, L.U., Kähkönen, E. (eds.) Proceedings of the 4th IEEE International Conference on Advanced Learning Technologies (ICALT 2004), Joensuu, Finland, pp. 21–25 (2004)Google Scholar
- [Weia]Weisstein, E.: Mathworld, the web’s most extensive mathematics resource, http://mathworld.wolfram.com/
- [Weib]Weisstein, E.W.: Natural number, http://mathworld.wolfram.com/NaturalNumber.html