John Carroll
Skip Abstract Section
Abstract
We consider some key issues in the use of computer software in Numerical Analysis teaching. By first examining the role of the computer in education, we consider how the teaching of numerical analysis is enhanced through the introduction of computer software. Practical issues such as programming language requirements and sources of numerical software are reviewed. We also consider the different ways in which textbooks and software have been combined to provide a single teaching tool. The potential for interaction between symbolic and numerical computation is also considered and one particular symbolic algebra package is briefly reviewed. Another mode of software usage within the teaching framework is that of interactive environments and, here, we concentrate on two well-known packages, MATLAB [50] and CLAM [34]. Finally we present the experiences of some Numerical Analysis teachers as they outline individual approaches to efficient use of software in their respective syllabi.
- O. Aberth, Precise Numerical Analysis, Wm. C. Brown Publishers, 1988. Google Scholar
Digital Library
- Ada Programming Language, Department of Defense, Washington, D.C., ANSI/MILSTD 1815A-1983.Google Scholar
- O. B. Arushanian et al, The TOEPLITZ Package Users' Guide, Argonne National Laboratory, ANL-83-16, (1983).Google Scholar
- K. E. Atkinson, An Introduction to Numerical Analysis, 1st edition, John Wiley & Sons, Inc. 1985.Google Scholar
- E. B. Becker, G. F. Carey, J. T. Oden, Finite Elements --- An Introduction, Prentice-Hall Inc. 1981.Google Scholar
- M. Beilby, A. Bowman, P. Bishop, MATHS & STATS Guide to Software for Teaching, 2nd ed., CTI Centre for Mathematics and Statistics, University of Birmingham, 1991.Google Scholar
- P. Bjóórstad, Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles, SIAM J. Numer. Anal., 20 (1983), pp. 59--71.Google ScholarCross Ref
- G. Booch, Software Engineering with Ada, The Benjamin/Cummings Publishing Co., Inc. 1983. Google ScholarDigital Library
- C. de Boor, A Practical Guide to Splines, Applied Mathematical Science, Vol. 27, Springer-Verlag, New York, 1978.Google Scholar
- L. Boutzev, C. Boutzev, Educational software for electrical engineering: a methodology and some results, Computers Educ., 15 (1990), pp. 271--276.Google ScholarCross Ref
- A. Boyle, B. F. Caviness, (eds.), Future Directions for Research in Symbolic Computation, Report of a Workshop on Symbolic and Algebraic Computation, April 29-30, 1988; Society for Industrial and Applied Mathematics, Philadelphia, 1990.Google Scholar
- W. S. Brainerd, C. H. Goldberg, J. C. Adams, Programmer's Guide to Fortran 90, McGraw-Hill, New York, 1990 Google ScholarDigital Library
- B. W. Char et al, MAPLE User's Guide, 4th ed., WATCOM Publications Ltd., Waterloo, Ontario 1985.Google Scholar
- W. Cheney, D. Kincaid, Numerical Mathematics and Computing, 2nd edition, Brooks / Cole Publishing Company 1985. Google ScholarDigital Library
- W. J. Cody, The Construction of Numerical Subroutine Libraries, SIAM Review, 16 (1974), pp. 36--46.Google ScholarCross Ref
- W. J. Cody, Observations on the Mathematical Software Effort, in Sources and Development of Mathematical Software, ed. W. Cowell, Prentice-Hall, Englewood Cliffs, N.J., 1983.Google Scholar
- J. E. Dennis, D. M. Gay, R. E. Welch, An Adaptive Nonlinear Least Squares Algorithm, ACM Trans. Math. Software, 7 (1981) pp. 348--368 and pp. 369--383. Google ScholarDigital Library
- DERIVE User Manual, 3rd ed., Soft Warehouse, Inc., Honolulu 1989.Google Scholar
- J. J. Dongarra, J. R. Bunch, C. B. Moler, G. W. Stewart, LINPACK Users' Guide, SIAM Publications, Philadelphia, 1979.Google Scholar
- J. J. Dongarra, E. Grosse, Distribution of mathematical software via electronic mail, Communications of the ACM, 30 (1987), pp. 403--414. Google ScholarDigital Library
- H. Fong, Models for the integration of computing into mathematics curricula, Computers Educ., 13 (1989), pp. 157--166. Google ScholarDigital Library
- G. E. Forsythe, M. A. Malcolm, C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, N.J., 1977. Google ScholarDigital Library
- Fortran-66, ANSI X3.9-1966: Programming Language Fortran, American National Standards Institute, New York 1966.Google Scholar
- Fortran-77, ANSI X3.9-1978: Programming Language Fortran, American National Standards Institute, New York 1979.Google Scholar
- Fortran-90, ISO/IEC 1539: Information Technology - Programming Languages - Fortran, 2nd Edition, The International Standards Organisation, Case Postale 56, CH-1211 Genève 20, Switzerland, 1991.Google Scholar
- D. E. Foulser, W. D. Gropp, CLAM and CLAM Shell: An Interactive Environment for Supercomputing and Visualization, Yale University and Scientific Computing Associates, Inc., 1990.Google Scholar
- P. A. Fox, A. D. Hall, N. L. Schryer, The PORT Mathematical Subroutine Library, ACM Trans. Math. Software, 4 (1978) pp. 104--126 and pp. 177--188. Google ScholarDigital Library
- W. Fullerton, FNLIB User's Manual, AT&T Bell Laboratories, 1981.Google Scholar
- B. S. Garbow, J. M. Boyle, J. J. Dongarra, C. B. Moler, Matrix Eigensystem Routines --- EISPACK Guide Extension, Lecture Notes in Computer Science, Vol. 51, Springer-Verlag, Berlin, 1977.Google Scholar
- C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis, Addison-Wesley Publishing Company 1984.Google Scholar
- G. H. Golub, J. H. Welsch, Calculation of Gauss Quadrature Rules, Math. Comp., 23 (1969) pp. 221--230.Google ScholarCross Ref
- T. A. Grandine, The Numerical Methods Programming Projects Book, Oxford University Press 1990. Google ScholarDigital Library
- U. Grenander, Mathematical Experiments on the Computer, Academic Press 1982.Google Scholar
- W. D. Gropp. D. E. Foulser, S. Chang, CLAM User's Guide: The Computational Linear Algebra Machine, Scientific Computing Associates, Inc., New Haven, Connecticut, USA, 1989.Google Scholar
- E. Grosse, Netlib News, SIGNUM Newsletter (see "Greetings" in October 1990, "Contributions" in January 1991 and "Bigfiles" to appear in April 1992).Google Scholar
- R. Harding, D. Quinney, Computer illustrated texts (CITs) for teaching numerical analysis, Computers Educ., 15 (1990), pp. 205--211.Google ScholarCross Ref
- A. C. Hearn, The REDUCE Package, The RAND Corporation, 1700 Main Street, P.O. Box 2138, Santa Monica, CA 90406-2138, USA.Google Scholar
- N. J. Higham, MATLAB: A Tool for Teaching and Research, Mathematics and Statistics Newsletter of Computers in Teaching Initiative, 1 (1990), pp. 4--8.Google Scholar
- N. J. Higham, Algorithm 694: A collection of test matrices in MATLAB, ACM Trans. Math. Soft., 17 (1991), pp. 289--305. Google ScholarDigital Library
- N. J. Higham, Optimization by direct search in matrix computations, Numerical Analysis Report No. 197, University of Manchester, England, 1991; to appear in SIAM J. Matrix Anal. Appl.Google Scholar
- T. Hopkins, C. Phillips, Numerical Methods in Practice: Using the NAG Library, Addison-Wesley Publishers Ltd. 1988.Google Scholar
- E. N. Houstis, J. R. Rice, C. C. Christara, E. A. Vavalis, Performance of scientific software, in {65}.Google Scholar
- K. R. Jackson, T. E. Hull, Using the IMSL MATH/LIBRARY in numerical methods courses, to appear.Google Scholar
- R. D. Jenks, R. S. Sutor, S. M. Watt, Scratchpad II: an abstract datatype system for mathematical computation, in {65}.Google Scholar
- R. L. Johnston, Numerical Methods: A Software Approach, John Wiley & Sons, New York, 1982. Google ScholarDigital Library
- R. L. Johnston, TEAPACK User's Manual - Mathematical Subroutines for Numerical Methods, John Wiley & Sons, New York, 1982. Google ScholarDigital Library
- D. Kahaner, C. Moler, S. Nash, Numerical Methods and Software, Prentice-Hall Inc., 1989. Google ScholarDigital Library
- D. R. Kincaid, J. R. Respess, D. M. Young, ITPACK 2C: A Fortran package for solving large sparse linear systems by adaptive accelerated iterative methods, ACM Trans. Math. Software, 8 (1982), pp. 302--322. Google ScholarDigital Library
- L. Kiser, Using the microcomputer as a tool to improve learning mathematics, Education Technology, September 1989. Google ScholarDigital Library
- PC/MATLAB, Mathworks, 24 Prime Park Way, Natick, MA 01760.Google Scholar
- M. Metcalf, J. Reid, Fortran 90 Explained, Oxford University Press, Oxford, New York and Tokyo, 1990. Google ScholarDigital Library
- M. Metcalf, A first encounter with Fortran 90, to appear in ACM Fortran Forum 10 (1991), No.4.Google Scholar
- J. Moré, D. Sorensen, B. Garbow, K. Hillstrom, The MINPACK Project, in Sources and Development of Mathematical Software, ed. W. Cowell, Prentice Hall, pp. 88--111, 1984.Google Scholar
- NAGWare f90 Compiler, Report of NAG Ltd, Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, UK, 1991.Google Scholar
- T. A. S. Obaid, S. M. Alak, Application of spreadsheet programs in the learning of numerical methods, Computers Educ., 13 (1989), pp. 25--31. Google ScholarDigital Library
- T. C. O'Haver, Teaching and learning chemometrics with MATLAB, Chemometrics and Intelligent Laboratory Systems, 6 (1989), pp. 95--103.Google ScholarCross Ref
- J. M. Ortega, W. G. Poole Jr., An Introduction to Numerical Methods for Differential Equations, Pitman, Mansfield, MA. 1981.Google Scholar
- J. Phillips, The NAG Library: A Beginner's Guide, Clarendon Press, Oxford 1987. Google ScholarDigital Library
- R. Piessens, E. de Doncker-Kapenga, C. Uberhuber, D. Kahaner, Quadpack: A Subroutine Package for Automatic Integration, Series in Computational Mathematics v. 1, Springer Verlag, 1983.Google Scholar
- T. Plomp, W. J. Pelgrum, A. H. M. Steerneman, Influence of computer use on schools' curriculum: limited integration, Computers Educ., 14 (1990) pp. 159--171. Google ScholarDigital Library
- W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Cambridge University Press 1987. Google ScholarDigital Library
- J. K. Reid, The advantages of Fortran 90, to appear in Computing. Google ScholarDigital Library
- J. R. Rice, Matrix Computations and Mathematical Software, McGraw-Hill Inc. 1981.Google Scholar
- J. R. Rice, Numerical Methods, Software and Analysis: IMSL Reference Edition, McGraw-Hill, New York 1983. Google ScholarDigital Library
- J. R. Rice, ed., Mathematical Aspects of Scientific Software, Springer-Verlag, New York 1988. Google ScholarDigital Library
- D. H. Schultz, N.A. Tutor --- A Computer Based Numerical Analysis Tutorial, Addison-Wesley 1990.Google Scholar
- K. Sigmon, MATLAB Primer, of Mathematics, University of Florida, Gainesville, 1989. Google ScholarDigital Library
- B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, C. B. Moler, Matrix Eigensystem Routines --- EISPACK Guide, Lecture Notes in Computer Science, Vol. 6, 2nd Edition, Springer-Verlag, Berlin, 1976.Google Scholar
- J. G. M. M. Smits, J. J. M. Rijpkema, A linear algebra course with PC-Matlab: some experiences, Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands, 1990.Google Scholar
- P. N. Swarztrauber, R. A. Sweet, Efficient Fortran subroutines for the solution of separable elliptic equations, Algorithm 541, ACM Trans. Math. Software, 5 (1979), pp. 352--364. Google ScholarDigital Library
- L. N. Trefethen, Numerical computation of the Schwarz-Christoffel transformation, SIAM J. Sci. Stat. Comput., 1 (1980), pp. 82--102.Google ScholarDigital Library
- J. J. Uhl, Mathematica and me, Notices of the AMS, 35 (1988), pp. 1345--1347.Google Scholar
- S. Wolfram, Mathematica---A System for Doing Mathematics by Computer, Addison-Wesley Publishing Co., Redwood City, California 1988. Google ScholarDigital Library
- P. Zorn, Mathematica in undergraduate mathematics, Notices of the AMS, 35 (1988), pp. 1347--1349.Google Scholar
Index Terms
- The role of computer software in numerical analysis teaching
Recommendations
Numerical analysis in a Ph.D. computer science program
Numerical Analysis is the study of methods and procedures used to obtain“approximate solutions” to mathematical problems. Much of the emphasis is on scientific calculation. The difficulties of education in such a broad area center around the question of ...
Computer Science Teaching Knowledge: A Framework and Assessment (Abstract Only)
SIGCSE '17: Proceedings of the 2017 ACM SIGCSE Technical Symposium on Computer Science EducationEducators, researchers, politicians, tech companies, and others continue to advocate for the importance of K-12 students learning computer science in our increasingly tech-driven society. One way school districts in the United States address this ...
Teaching computer aided software engineering at the graduate level
ITiCSE '08: Proceedings of the 13th annual conference on Innovation and technology in computer science educationAlthough computer-aided software engineering (CASE) is one of the most current and interesting subjects within software engineering, relatively little has been published on the issue of teaching CASE at the graduate level. This paper reports a case ...
Comments