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Posted 2 June 2008

THE LANGUAGES OF MATH

Mathematics in the English-speaking world is communicated using two languages:

¨     Mathematical English is a special form of English.

·       It uses ordinary words with special meanings

·       Some of its structural words (“if”, “or”) have different meanings

·       Mathematicians both speak and write mathematical English.

¨     The symbolic language of math is a distinct, special-purpose language.

·       It has its own symbols and rules.

·       It is not a dialect of English.

·       The symbolic language is largely a written language.  Simple expressions can be pronounced, but complicated expressions may only be pointed to or referred to.

·       The symbolic language is used by all mathematicians, not just those who write math in English.   

¨  Math in writing and in lectures involve both mathematical English and the symbolic language embedded in each other and referring back and forth to each other.

Contents

The languages of math are covered in three chapters, each with several parts.

¨ Mathematical English   Incomplete

· Assertions Incomplete

· Names   Incomplete

· Glossary.  Not all sections are finished   The glossary contains short entries about words, expressions and symbols used in Math English that cause trouble for those new to abstract math.  This is not a general list of technical terms.   Use Wikipedia or MathWorld for that.

¨  The symbolic language of math

·  Variables

·  Substitution

·  Symbols

·  Alphabets

·  Delimiters

·  Other symbols

· More about the symbolic language

¨  More about the languages of math.  This chapter covers topics that involve both math English and the symbolic language.

References

Bagchi, A. and C. Wells (1998, ‘On the communication of mathematical reasoning’.

Bagchi, A. and C. Wells (1998), ‘Varieties of mathematical prose’.

Bullock, J. O. (1994), ‘Literacy in the language of mathematics’. American Mathematical Monthly, volume 101, pages 735743.

de Bruijn, N. G. (1994), ‘The mathematical vernacular, a language for mathematics with typed sets’. In Selected Papers on Automath, Nederpelt, R. P., J. H. Geuvers, and R. C. de Vrijer, editors, volume 133 of Studies in Logic and the Foundations of Mathematics, pages 865  935.  

Epp, S. S. (1999), ‘The language of quantification in mathematics instruction’. In Developing Mathematical Reasoning in Grades K-12. Stiff, L. V., editor (1999),  NCTM Publications.  Pages 188197.

Gillman, L. (1987), Writing Mathematics Well. Mathematical Association of America

Higham, N. J. (1993), Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics.  

Knuth, D. E., T. Larrabee, and P. M. Roberts (1989), Mathematical Writing, volume 14 of MAA Notes. Mathematical Association of America.

Krantz, S. G. (1997), A Primer of Mathematical Writing. American Mathematical Society.

O'Halloran, K. L.  (2005), Mathematical Discourse: Language, Symbolism And Visual Images.  Continuum International Publishing Group.

Schwartzman, S. (1994), The Words of Mathematics. American Mathematical Society.

Schweiger, F. (1994b), ‘Mathematics is a language’. In Selected Lectures from the 7th International Congress on Mathematical Education, Robitaille, D. F., D. H. Wheeler, and C. Kieran, editors. Sainte-Foy: Presses de l’Université Laval.

Steenrod, N. E., P. R. Halmos, M. M. Schiffer, and J. A. Dieudonné (1975), How to Write Mathematics. American Mathematical Society.

Stiff, L. V., editor (1999), Developing Mathematical Reasoning in Grades K-12. NCTM Publications

Wells, C. (2003). The Handbook of Mathematical Discourse.