Mathematical rigor—a prerequisite for numerical analysis?
Pages 209 - 211
Abstract
Frequently mathematical errors can be attributed to applying a theorem or using a formula in a situation which does not meet all the initial requirements. An obvious example would be the use of the Pythagorean theorem to compute the length of the longest side of a scalene triangle. Such trivial mistakes are rarely made. However, when considering mathematical theory together with the physical universe, this is essentially what some mathematicians have done. Instead of determining theoretical relationships to describe the universe, they idealize the universe to conform to a mathematical model. In doing this some errors slip by under the guise of extrapolation and simplification. To avoid these sources of error and to obtain significant results relevant to the physical universe, it has become necessary for numerical analysis to transcend the bounds of mathematical rigor.
References
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A A ALBERT F BROWDEN IN HERSTEIN IKAPLANSKY S MACLANE Letters to the editor Science 149:3681 16 July 1965 p 243-244
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GEORGE FORSYTHE Contemporary states of numerical analysis Surveys in Applied Mathematics vol 5 John Wiley and Sons Inc New York 1958 p 6
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BERNI J ADLER Few particle experiments in statistical mechanics Proceedings of the symposia in applied mathematics vol 15 American Mathematical Society Providence Rhode Island p 337
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JEROME ROTHSTEIN Numerical analysis: Pure or applied mathematics Science 149:3688 3 September 1965 p 1049-1050
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J O HIRSCHFELDER Applied mathematics as used in theoretical chemistry Proceedings of Symposia in Applied Mathematics vol 15 American Mathematical Society Providence Rhode Island p 371
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WERNER HEISENBERG The uncertainty principle The World of Mathematics ed by James R Newman vol 2 Simon and Schuster New York 1957 p 1051-1055
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ARNOLD NORDSIECH Automatic numerical integration of ordinary differential equations Proceedings of Symposia in Applied Mathematics vol 15 American Mathematical Society Providence Rhode Island p 249-50
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RICHARD W HAMMING State of the art in scientific computing SFIPA Conference Proceedings 1963 Spring Joint Computer Conference Spartan Books Inc Washington D C p 166
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HARVEY COHN Purposeful and unpurposeful computing Proceedings of Symposia in Applied Mathematics vol 15 American Mathematical Society Providence Rhode Island p2 p6
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RALPH G STANTON Numerical methods for science and engineering Prentice Hall Inc Englewood Cliffs New Jersey 1961 p vii
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RICHARD W HAMMING Letters to the editor Science 149:3681 16 July 1965 p 245
[12]
JOHN TODD Survey of numerical analysis McGraw-Hill Book Co Inc San Francisco 1962
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BERNI J ADLER Few particle experiments in statistical mechanics p336
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RICHARD W HAMMING Numerical analysis vs mathematics Science 148:3669 23 April 1965 p 475
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RICHARD W HAMMING Impact of computers American Mathematical Monthly 72: 2 February 1965 Part 2 p 6
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JOHN TODD Survey of numerical analysis p vi
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RALPH G STANTON Numerical methods for science and engineering p vii
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GEORGE FORSYTHE Contemporary states of numerical analysis p6
Index Terms
- Mathematical rigor—a prerequisite for numerical analysis?
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Published In
January 1966
545 pages
Copyright © 1966 ACM.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 01 January 1966
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