A first course in computational science: (why a math book isn't enough)

ABSTRACT

There is a change underway in the CS curriculum that reflects a renewed emphasis upon solving applications. Computational science applies solution methods to various scientific models. However, following a computational science approach means more than just using formulas out of a math book. It means having a scientific mindset, understanding and using a scientific approach, thoroughly testing both the theoretical models and the specific implementation of these models, knowing when to use analytic methods instead of numerical ones, using graphics to improve understanding, and knowing how to explain the results of these models to others. This paper addresses what has been learned in designing and teaching a first course in computational science at the undergraduate level.

REFERENCES

• 1: Steven C. Chapra , Raymond P. Canale, Numerical Methods for Engineers: With Programming and Software Applications, McGraw-Hill, Inc., New York, NY, 1997
• 2: Council for Mathematics and its Applications (COMAP), Principles and Practice of Mathematics, Springer, New York, NY, 1997.
• 3: Edwards, Dilwyn and Hamson, Mike, Guide to Mathematical Modeling, CRC Press, Boca Raton, FL, 1989.
• 4: Forsythe, G. E., "Pitfalls in Computation, or Why a Math Book Isn't Enough," The American Mathematical Monthly, Vol. 77, No. 9, (Nov. 1970), Mathematical Association of America, 931-956.
• 5: Giordano, Frank R., Weir, Maurice D., and Fox, William, A First Course in Mathematical Modeling, 2nd Edition, Brooks/Cole, Pacific Grove, CA, 1997.
• 6: Johnson, George, "All Science is Computer Science," New York Times supplement, (March 25, 2001), 1,5.
• 7: Losse, John, A Historical Introduction to the Philosophy of Science, 3rd Edition, Oxford University Press, New York, NY, 1993.
• 8: Michael L. Overton, Numerical computing with IEEE floating point arithmetic, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2001
• 9: S. K. Park , K. W. Miller, Random number generators: good ones are hard to find, Communications of the ACM, v.31 n.10, p.1192-1201, Oct. 1988 [doi>10.1145/63039.63042]
• 10: Polya, G., How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, Princeton, NJ, 1945.
• 11: Heikki Ruskeepaa, Mathematica Navigator: Graphics and Methods of Applied Mathematics, Academic Press, Inc., Orlando, FL, 1999
• 12: G. Michael Schneider, Computational science as an interdisciplinary bridge, ACM SIGCSE Bulletin, v.31 n.1, p.141-145, March 1999
• 13: Joseph L. Zachary , Christopher R. Johnson , Eric N. Eide , Kenneth W. Parker, An entry-level course in computational engineering and science, ACM SIGCSE Bulletin, v.27 n.1, p.209-213, March 1995