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Math-Literate Computers

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Intelligent Computer Mathematics (CICM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5625))

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Abstract

Math notation is a familiar, everyday tool widely used in society. Computers need math literacy – the ability to read and write math notation – in order to assist people with accessing mathematical documents and carrying out mathematical investigations. In this paper, we discuss issues in making computers math-literate. Software for generating math notation is widely used. Software for recognition of math notation is not as widely used: to avoid the intrusiveness and unpredictability of recognition errors, people often prefer to enter and edit math expressions using a computer-oriented representation, such as LaTeX or a structure-based editor. However, computer recognition of math notation is essential in large-scale recognition of mathematical documents; as well, it offers the ability to create people-centric user interfaces focused on math notation rather than computer-centric user interfaces focused on computer-oriented representations. Issues that arise in computer math literacy include the diversity of math notation, the challenges in designing effective user interfaces, and the difficulty of defining and assessing performance.

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References

  1. Blostein, D.: Structural Analysis of Music Notation. In: Proc. IAPR Workshop on Syntactic and Structural Pattern Recognition, Murray Hill, NJ, p. 481 (1990)

    Google Scholar 

  2. Blostein, D., Haken, L.: Justification of Printed Music. Communications of the ACM 34(3), 88–99 (1991)

    Article  Google Scholar 

  3. Blostein, D., Haken, L.: The Lime Music Editor: A Diagram Editor Involving Complex Translations. Software – Practice and Experience 24(3), 289–306 (1994)

    Article  Google Scholar 

  4. Blostein, D.: General Diagram-Recognition Methodologies. In: Kasturi, R., Tombre, K. (eds.) Graphics Recognition 1995. LNCS, vol. 1072, pp. 106–122. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  5. Blostein, D., Grbavec, A.: Recognition of Mathematical Notation. In: Bunke, H., Wang, P. (eds.) Handbook of Character Recognition and Document Image Analysis, pp. 557–582. World Scientific, Singapore (1997)

    Chapter  Google Scholar 

  6. Blostein, D., Haken, L.: Using Diagram Generation Software to Improve Diagram Recognition: A Case Study of Music Notation. IEEE Trans. Pattern Analysis and Machine Intelligence 21(11), 1121–1136 (1999)

    Article  Google Scholar 

  7. Blostein, D., Cordy, J., Zanibbi, R.: Applying Compiler Techniques to Diagram Recognition. In: Proc. 16th Intl. Conf. on Pattern Recognition, Quebec City, Canada, August 2002, vol. III, pp. 123–126 (2002)

    Google Scholar 

  8. Blostein, D., Lank, E., Rose, A., Zanibbi, R.: User Interfaces for Online Diagram Recognition. In: Blostein, D., Kwon, Y.-B. (eds.) GREC 2001. LNCS, vol. 2390, pp. 92–103. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Blostein, D., Zanibbi, R., Nagy, G., Harrap, H.: Document Representations. In: Proc. Fifth IAPR Int’l Workshop on Graphics Recognition (GREC 2003), Barcelona, Spain, July 2003, pp. 3–12 (2003)

    Google Scholar 

  10. Blostein, D.: Graph Transformation in Document Image Analysis: Approaches and Challenges. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 23–34. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Chan, K., Yeung, D.: Mathematics Expression Recognition: a Survey. Int’l Journal on Document Analysis and Recognition 3(1), 3–15 (2000)

    Article  MathSciNet  Google Scholar 

  12. Chaundy, T., Barrett, P., Batey, C.: The Printing of Mathematics. Oxford University Press, Oxford (1957)

    MATH  Google Scholar 

  13. Chhabra, A.: Graphic Symbol Recognition: An Overview. In: Chhabra, A.K., Tombre, K. (eds.) GREC 1997. LNCS, vol. 1389, pp. 68–79. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Cushman, W., Ojha, P., Daniels, C.: Usable OCR: What are the Minimum Performance Requirements? In: Proc. ACM SIGCHI 1990 Conference on Human Factors in Computing Systems, Seattle, Washington, April 1990, pp. 145–151 (1990)

    Google Scholar 

  15. Document Recognition Contests, www.icdar2007.org/competition.html

  16. Gross, M., Do, E.: Ambiguous Intentions: a Paper-like Interface for Creative Design. In: Proc. Ninth Annual Symposium on User Interface Software and Technology (UIST 1996), Seattle, Washington, November 1996, pp. 183–192 (1996)

    Google Scholar 

  17. Haken, L., Blostein, D.: A New Algorithm for Horizontal Spacing of Printed Music. In: International Computer Music Conference, Banff, September 1995, pp. 118–119 (1995)

    Google Scholar 

  18. Higham, N.: Handbook of Writing for the Mathematical Sciences. SIAM, Philadelphia (1993)

    MATH  Google Scholar 

  19. Hsu, R., Mitchell, W.: After 400 Years, Print is Still Superior. CACM 40(10), 27–28 (1997)

    Article  Google Scholar 

  20. Int’l Journal on Document Analysis and Recognition. Springer Verlag (since 1998)

    Google Scholar 

  21. (Int’l Conf.) Computer Vision/ Computer Graphics Collaboration Techniques and Applications, INRIA Rocquencourt, France, May 4-6 (2009)

    Google Scholar 

  22. Knuth, D.: Mathematical Typography. Bulletin of the American Mathematical Society 1(2), 337–372 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  23. Knuth, D., Plass, M.: Breaking Paragraphs into Lines. Software – Practice and Experience 11, 1119–1184 (1981)

    Article  MATH  Google Scholar 

  24. Lapointe, A., Blostein, D.: Issues in Performance Evaluation: A Case Study of Math Recognition. In: Int’l Conf. Document Analysis and Recognition (ICDAR 2009), Barcelona (July 2009) (to appear)

    Google Scholar 

  25. Martin, W.: Computer Input/Output of Mathematical Expressions. In: Proc. 2nd Symposium on Symbolic and Algebraic Manipulations, pp. 78–87. ACM, New York (1971)

    Chapter  Google Scholar 

  26. Nielsen, J.: Usability Engineering. Academic Press, San Diego (1993)

    MATH  Google Scholar 

  27. Nielsen, J., Levy, J.: Measuring Usability: Preference vs. Performance. Communications of the ACM 37(4), 66–75 (1994)

    Article  Google Scholar 

  28. Petre, M.: Why Looking Isn’t Always Seeing: Readership Skills and Graphical Programming. Communications of the ACM 38(6), 33–44 (1995)

    Article  Google Scholar 

  29. Proc. ACM Conference on Human Factors in Computing Systems (CHI). ACM Press, New York (annual since 1982)

    Google Scholar 

  30. Proc. ACM Symposium on User Interface Software and Technology (UIST). ACM Press, New York (annual since 1988)

    Google Scholar 

  31. Proc. IAPR Int’l Workshop on Document Analysis Systems (biennial since 1994)

    Google Scholar 

  32. Proc. IAPR Int’l Workshop on Graphics Recognition (biennial since 1995)

    Google Scholar 

  33. Proc. IEEE Symposium on Visual Languages and Human-Centric Computing (annual since 1988) (earlier name: Proc. IEEE Symposium on Visual Languages)

    Google Scholar 

  34. Proc. Int’l Conf. on Document Analysis and Recognition (biennial since 1991) (sponsored by IAPR and IEEE)

    Google Scholar 

  35. Proc. Int’l Conf. on the Theory and Application of Diagrams (biennial since 2000)

    Google Scholar 

  36. Proc. Int’l Symposium on Graph Drawing (held annually since 1993)

    Google Scholar 

  37. Tombre, K., Tabbone, S., Dosch, P.: Musings on Symbol Recognition. In: Liu, W., Lladós, J. (eds.) GREC 2005. LNCS, vol. 3926, pp. 23–34. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  38. Vaxivière, P., Tombre, K.: Knowledge Organization and Interpretation Process in Engineering Drawing Interpretation. In: Proc. IAPR Workshop on Document Analysis Systems, Kaiserslautern, Germany, October 1994, pp. 313–321 (1994)

    Google Scholar 

  39. Wang, Z., Faure, C.: Structural Analysis of Handwritten Mathematical Expressions. In: Proc. Ninth Int’l Conf. on Pattern Recognition, Rome, Italy, November 1988, pp. 32–34 (1988)

    Google Scholar 

  40. Wick, K.: Rules for Typesetting Mathematics, translated by V. Boublik and M. Hejlova, The Hague, Mouton (1965)

    Google Scholar 

  41. Workshop on Document Layout Interpretation and its Applications (DLIA) (1999 and 2001)

    Google Scholar 

  42. Zanibbi, R., Blostein, D., Cordy, J.: Recognizing Handwritten Mathematical Expressions Using Tree Transformation. IEEE Trans. Pattern Analysis and Machine Intelligence 24(11), 1455–1467 (2002)

    Article  Google Scholar 

  43. Zanibbi, R., Novins, K., Arvo, J., Zanibbi, K.: Aiding Manipulation of Handwritten Mathematical Expressions through Style-Preserving Morphs. In: Proc. Graphics Interface 2001, Ottawa, Ontario, June 2001, pp. 127–134 (2001)

    Google Scholar 

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Blostein, D. (2009). Math-Literate Computers. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-02614-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02613-3

  • Online ISBN: 978-3-642-02614-0

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