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

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.

[1]  Georges Ifrah,et al.  The Universal History of Numbers , 1998 .

[2]  J. B. S. HALDANE,et al.  Number: the Language of Science , 1941, Nature.

[3]  G. Pólya,et al.  How to Solve It. A New Aspect of Mathematical Method. , 1945 .

[4]  J. Losee.  A historical introduction to the philosophy of science , 1972 .

[5]  Heikki Ruskeepaa,et al.  Mathematica Navigator: Graphics and Methods of Applied Mathematics , 1999 .

[6]  Michael L. Overton,et al.  Numerical Computing with IEEE Floating Point Arithmetic , 2001 .

[7]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[8]  H. R. Pitt.  Divergent Series , 1951, Nature.

[9]  J. O'brien.  A Historical Introduction to the Philosophy of Science , 1974 .

[10]  Dilwyn Edwards,et al.  Guide to Mathematical Modeling , 1990 .

[11]  A. Arcavi,et al.  Farey series and pick’s area theorem , 1995 .

[12]  G. Michael Schneider.  Computational science as an interdisciplinary bridge , 1999, SIGCSE '99.

[13]  Frank R. Giordano,et al.  A first course in mathematical modeling , 1997 .

[14]  G. Forsythe.  Pitfalls in computation, or why a math book isn''t enough , 1970 .

[15]  Eric Eide,et al.  An entry-level course in computational engineering and science , 1995, SIGCSE '95.

[16]  Prouhet-Thue-Morse sequenceJean-Paul Allouche,et al.  The ubiquitous , 1999 .

[17]  Steven C. Chapra,et al.  Numerical Methods for Engineers: With Programming and Software Applications , 1997 .

[18]  Mary Tiles,et al.  Georg Cantor: His Mathematics and Philosophy of the Infinite. , 1982 .

[19]  O NEUGEBAUER,et al.  The exact sciences in antiquity. , 1952, Acta historica scientiarum naturalium et medicinalium.

[20]  T. Holyoke,et al.  Number Words and Number Symbols , 1978 .