Finite mathematics

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In mathematics education, Finite Mathematics is a syllabus in college and university mathematics that is independent of calculus. A course in precalculus may be a prerequisite for Finite Mathematics.

Contents

Contents of the course include an eclectic selection of topics often applied in social science and business, such as finite probability spaces, matrix multiplication, Markov processes, finite graphs, or mathematical models. These topics were used in Finite Mathematics courses at Dartmouth College as developed by John G. Kemeny, Gerald L. Thompson, and J. Laurie Snell and published by Prentice-Hall. Other publishers followed with their own topics. With the arrival of software to facilitate computations, teaching and usage shifted from a broad-spectrum Finite Mathematics with paper and pen, into development and usage of software.

Textbooks

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References

  1. Duncan Luce (1957) American Mathematical Monthly 64:688
  2. Mathematics Magazine 30(5):272
  3. H.E. Chrestenson (1964) American Mathematical Monthly 71(7): 813
  4. H.J. Ricardo (1975) American Mathematical Monthly 82(6): 681–4
  5. G.M. Kaufman (1963) American Mathematical Monthly 70(10): 1116
  6. 1 2 3 4 G. C. Dorner (1971) Mathematics Magazine 44(4): 223–6
  7. J.D. Emerson & K. Larson (1981) American Mathematical Monthly 88(5): 357