Random Number
Computer-generated random numbers are sometimes called Pseudorandom Numbers, while the term``random'' is reserved for the output of unpredictable physical processes. It is impossible to produce an arbitrarily longstring of random digits and prove it is random. Strangely, it is very difficult for humans to produce a string of randomdigits, and computer programs can be written which, on average, actually predict some of the digits humans will write downbased on previous ones.
The Linear Congruence Method is one algorithm for generating Pseudorandom Numbers. The initial number used as the starting point in a random number generating algorithm is known as theSeed. The goodness of random numbers generated by a given Algorithm can beanalyzed by examining its Noise Sphere.
See also Bays' Shuffle, Cliff Random Number Generator, Quasirandom Sequence,Schrage's Algorithm, Stochastic
References
Bassein, S. ``A Sampler of Randomness.'' Amer. Math. Monthly 103, 483-490, 1996. Bratley, P.; Fox, B. L.; and Schrage, E. L. A Guide to Simulation, 2nd ed. New York: Springer-Verlag, 1996. Dahlquist, G. and Bjorck, A. Ch. 11 in Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall, 1974. Deak, I. Random Number Generators and Simulation. New York: State Mutual Book & Periodical Service, 1990. Forsythe, G. E.; Malcolm, M. A.; and Moler, C. B. Ch. 10 in Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall, 1977. Gardner, M. ``Random Numbers.'' Ch. 13 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, 1977. James, F. ``A Review of Pseudorandom Number Generators.'' Computer Physics Comm. 60, 329-344, 1990. Kac, M. ``What is Random?'' Amer. Sci. 71, 405-406, 1983. Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 200-201 and 205-207, 1962. Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 151-154, 1951. Knuth, D. E. Ch. 3 in The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1981. Marsaglia, G. ``A Current View of Random Number Generators.'' In Computer Science and Statistics: Proceedings of the Symposium on the Interface, 16th, Atlanta, Georgia, March 1984 (Ed. L. Billard). New York: Elsevier, 1985. Park, S. and Miller, K. ``Random Number Generators: Good Ones are Hard to Find.'' Comm. ACM 31, 1192-1201, 1988. Peterson, I. The Jungles of Randomness: A Mathematical Safari. New York: Wiley, 1997. Pickover, C. A. ``Computers, Randomness, Mind, and Infinity.'' Ch. 31 in Keys to Infinity. New York: W. H. Freeman, pp. 233-247, 1995. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Random Numbers.'' Ch. 7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 266-306, 1992. Schrage, L. ``A More Portable Fortran Random Number Generator.'' ACM Trans. Math. Software 5, 132-138, 1979. Schroeder, M. ``Random Number Generators.'' In Number Theory in Science and Communication, with Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity, 3rd ed. New York: Springer-Verlag, pp. 289-295, 1990.
Randomness
- Antisymmetric Tensor
- Antoine's Horned Sphere
- Antoine's Necklace
- Apeirogon
- Apoapsis
- Apocalypse Number
- Apocalyptic Number
- Apodization
- Apodization Function
- Apollonius Circles
- Apollonius Point
- Apollonius' Problem
- Apollonius Pursuit Problem
- Apollonius' Theorem
- Apothem
- Apparatus Function
- Appell Hypergeometric Function
- Appell Polynomial
- Appell Transformation
- Apple
- Approximately Equal
- Approximation Theory
- Apéry's Constant
- Arakelov Theory
- Arbelos