Abstract
It is a commonplace, that the use of mathematical software is in the process of influencing, if not shaping, the working style of the mathematician, physicist and engineer. Considerable effort has been put into the creation of integrated systems by various groups. On the other hand, relatively small progress has been seen in making a telling impact on the larger scientific community with respect to widespread use of such systems. The computer workplace for the scientist has not quite happened yet.
We feel, that this is a question foremost of education. It is imperative that we give the advanced student of the exact sciences and engineering a memorable experience of success with using mathematical software. Obviously the attainment of such an aim depends crucially on a very carefully thought-out collection of representative, well motivated projects originating in physics, pure and applied mathematics, electrical engineering, computer science etc.. And, of course, on the easy access to mathematical software, documentation and expert counselling.
At ETH we have been working for some years to provide and enhance such an environment. We think that we have succeeded with this pilot project. The present report gives an overview of the concept of our mathematical laboratory and provides some details of the projects that are presently provided for our students. Since there are more than a hundred students that take the laboratory course during a given term, we also describe some of the software support for the administration of the lab.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References, Software
John J. Cannon: A Language for Group Theory, Dept. of Pure Mathematics, University of Sydney, Australia.
E. Anderheggen et al.: FLOWERS Users Manual (2nd ed.), Institut für Informatik, ETHZ, 1983.
IMSL, NBC Building, 7500 Bellaire Blvd., Houston, Texas 77036, USA.
Richard P. Brent: A FORTRAN Multiple-Precision Arithmetic Package, ACM Transactions on Mathematical Software 4 (1978), pp 57–81.
D.L. Bowen (ed.): DECsystem-10 PROLOG User's Manual, Dept. of Artificial Intelligence, University of Edinburgh, 1982.
REDUCE2 has been replaced by: REDUCE 3.1 (April 15, 1984): The Rand Corporation, Attn: Dr. A.C. Hearn, 1700 Main Street, Santa Monica, CA 90406, USA.
SAC-2 system documentation in Europe available from: Prof. R. Loos, Universität Karlsruhe, Informatik I, Postfach 6380, D-7500 Karlsruhe, in the U.S. available from: Prof. G.E. Collins, Computer Science Dept., University of Wisconsin, 1210 West Dayton Street, Madison, WI 53706, USA.
R. Loos: The Algorithm Description Language ALDES (Report), SIGSAM Bull. of the ACM, 10 (1976).
A. Vladimirescu et al.: SPICE Version 2G.5 User's Guide, Dept. of Electrical Engineering, University of California, Berkley, Ca. 94720, USA.
Wolfgang W. Küchlin: An Implementation and Investigation of the Knuth-Bendix Completion Procedure, Internal Report 17/82, Universität Karlsruhe, FRG, 1982.
Roman Mäder: NumInt Beschreibung, Vers. 4.1, Mathematisches Seminar, ETHZ, 1982.
Program PLA written by Matthew Morrise, Institut für Informatik, ETHZ.
Program PHI written by Ray Horne, Middlesex Polytechnic, London, GB.
The program TPU is taken from [Chang/Lee].
References, Literature
C.L. Chang, R.C. Lee: Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.
W.F. Clocksin, C.S. Mellish: Programming in Prolog, Springer 1981.
L. Collatz: Differentialgleichungen, B.G. Teubner 1973.
R.W. Gosper: Decision Procedure for Indefinite Hypergeometric Summation, Proc. Natl. Acad. Sci USA, 75 (1978), No 1.
A.C. Hearn: REDUCE 2 User's Manual, University of Utah, Salt Lake City, Utah 84112, USA.
U. Kirchgraber, E. Stiefel: Methoden der analytischen Störungsrechnung und ihre Anwendungen, B.G. Teubner, 1978.
Donald E. Knuth, Peter B. Bendix: Simple Word Problems in Universal Algebras, in: J. Leech (ed.): Computational Problems in Abstract Algebra, Pergamon Press, 1970, pp 263–279.
J.C. Lagarias, A.M. Odlyzko: New algorithms for computing π(x), Proceedings of the 1981–82 New York number-theory seminar, Springer LNM ?? (19??).
Shu Lin: An Introduction to Error-Correcting Codes, Prentice-Hall, 1970.
D.H. Lehmer: On the exact number of primes less than a given limit, Illinois Journal of Mathematics 3 (1959), pp. 381–388.
D.W. Loveland: Automated Theorem Proving, North-Holland, 1978.
K. Magnus: Schwingungen, B.G. Teubner, 1976.
W.Wesley Peterson, E.J. Weldon, Jr.: Error-Correcting Codes, MIT Press, 1972.
W.M. Newman, R.F Sproull: Principles of Interactive Computer Graphics (2nd ed.), McGraw-Hill, 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Engeler, E., Mäder, R. (1985). Scientific computation: The integration of symbolic, numeric and graphic computation. In: Buchberger, B. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15983-5_14
Download citation
DOI: https://doi.org/10.1007/3-540-15983-5_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15983-4
Online ISBN: 978-3-540-39684-0
eBook Packages: Springer Book Archive