×

zbMATH — the first resource for mathematics

Living with a new mathematical species. (English) Zbl 0592.00045
This paper is written in response to a discussion paper issued by the International Commission on Mathematical Education on the Influence of Computers and Informatics on Mathematics and Mathematics Education. In it the author argues that the ecology of mathematics has been profoundly altered by the impact of computers, as if a new mathematics-speaking species is new sharing our intellectual niche. He discusses the impact of computers on mathematics, emphasizing their role in focusing on finite methods, in providing crucial links in proofs, and in simulating physical processes. Then he covers their impact on the curriculum in both mathematics and in computer science, criticizing computer literacy courses for overemphasis on ephemeral detail. Finally, he recommends for optimal use in mathematics instruction that computers be used primarily as an aid in discovery, quoting George Polya in his dictum ”Let us teach guessing”.
MSC:
00A99 General and miscellaneous specific topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arganbright, Dean E.Mathematical Applications of Electronic Spreadsheets. McGraw-Hill, 1985.
[2] Beckman, Frank S.Mathematical Foundations of Programming. The Systems Programming Series, Addison Wesley, 1984. · Zbl 0443.68021
[3] Birkhoff, Garrett. ”The Impact of Computers on Undergraduate Mathematics Education in 1984.”American Mathematical Monthly 79 (1972) 648–657.
[4] Bolter, J. David.Turing’s Man: Western Culture in the Computer Age. University of North Carolina Press, Chapel Hill, 1984.
[5] Committee on the Undergraduate Program in Mathematics.A General Curriculum in Mathematics for Colleges. Mathematical Association of America, 1965.
[6] Committee on the Undergraduate Program in Mathematics.Recommendations for a General Mathematical Sciences Program. Mathematical Association of America, 1980.
[7] Corbitt, Mary Kay, and Fey, James T. (Eds.). ”The Impact of Computing Technology on School Mathematics: Report of an NCTM Conference.” National Council of Teachers of Mathematics, 1985.
[8] Eckmann, J.-P., Koch, H., and Wittwer, P. ”A Computer-assisted Proof of Universality for Area-preserving Maps.”Memoirs of the American Mathematical Society, Vol 47, No. 289 (Jan. 1984). · Zbl 0528.58033
[9] Fey, James T.,et al. (Eds.).Computing and Mathematics: The Impact on Secondary School Curricula. National Council of Teachers of Mathematics, 1984.
[10] Hayes, Brian. ”Computer Recreations.”Scientific American (October 1983) 22–36.
[11] Hodges, Andrew.Alan Turing: The Enigma. Simon and Schuster, 1983. · Zbl 0541.68001
[12] Jaffe, Arthur. ”Ordering the Universe: The Role of Mathematics.” InRenewing U.S. Mathematics, National Academy Press, Washington, D.C., 1984. · Zbl 0558.01023
[13] Kemeny, John G. ”Finite Mathematics–Then and Now.” In Ralston, Anthony and Young, Gail S.The Future of College Mathematics. Springer-Verlag, 1983, pp. 201–208.
[14] Koerner, James D., (Ed.)The New Liberal Arts: An Exchange of Views. Alfred P. Sloan Foundation, 1981.
[15] Lewis, Harry R. and Papadimitriou, Christos H.Elements of the Theory of Computation. Prentice-Hall, 1981. · Zbl 0464.68001
[16] Pölya, George. ”Let Us Teach Guessing.”Etudes de Philosophie des Sciences. Neuchatel: Griffon, 1950, pp. 147-154; reprinted inGeorge Polya: Collected Papers. Vol IV, MIT Press, 1984, pp. 504–511.
[17] Ralston, Anthony. ”Computer Science, Mathematics, and the Undergraduate Curricula in Both.”American Mathematical Monthly 88 (1981) 472–485.
[18] Ralston, Anthony and Shaw, Mary. ”Curriculum ’78: Is Computer Science Really that Unmathematical?”Communications of the ACM 23 (Feb. 1980) 67–70.
[19] Ralston, Anthony and Young, Gail S.The Future of College Mathematics. Springer-Verlag, 1983.
[20] Rand, Richard H.Computer Algebra in Applied Mathematics: An Introduction to MACSYMA. Research Notes in Mathematics No. 94, Pitman Publ., 1984. · Zbl 0583.68012
[21] Rosser, J. Barkley. ”Mathematics Courses in 1984.”American Mathematical Monthly 79 (1972) 635–648.
[22] Saxon, David S. ”Liberal Education in a Technological Age.”Science 218 (26 Nov 1982) 845.
[23] Shaw, Mary (Ed.)The Carnegie-Mellon Curriculum for Undergraduate Computer Science. Springer-Verlag, 1984.
[24] Steen, Lynn Arthur. 1 + 1=0: New Math for a New Age.Science 225 (7 Sept. 1984) 981.
[25] Travers, Kenneth,et. al. Second Study of Mathematics: United States Summary Report. University of Illinois, September 1984.
[26] Turing, Alan M. ”On Computable Numbers, with an Application to the Entscheidungsproblem.”Proc. London Math. Soc. 2nd Ser., 42 (1936) 230–265. · Zbl 0016.09701
[27] Tymoczko, Thomas. ”The Four Color Problem and its Philosophical Significance.”Journal of Philosophy 76:2 (1979) 57–85.
[28] Wilf, Herbert. ”The Disk with the College Education.”American Mathematical Monthly 89 (1982) 4–8.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.