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By D R & Wallenius, K T Shier

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The stress on axioms in these cases is often put in the wrong place. They often come after the really creative activity is done. They get formulated toward the end of a theory when one attempts to refine it into a precise, concise, and compact form. This does have the advantage of allowing one to teach a subject more rapidly so as to get on sooner to newer and more advanced topics. It is also true, on the other hand, that many great applied mathematicians, like John von Neumann, had a solid grounding in pure mathematics and the axiomatic approach was integral to his applied work, too.

If land were measured in hectares rather than in acres and labor in days rather than in hours, all of the x1j and x3j would have to be adjusted (by a cogredient transformation). Thus if, say, x3j is 16 then the adjusted x3j is 2 (assuming an 8-hour day). The important point for now is that summing the components of any xj or yj is dimensionally and hence scientifically unsound, a point that has been overlooked by many modelers in (and editors of) their research papers. Given a data matrix, how do we compare efficiencies of the DMUs?

F. Lucas, “Problem solving and modeling in the first two years,” in The Future of College Mathematics, A. Ralston and G. S. ), Springer-Verlag, New York, 1983, 43–54. [7] W. F. Lucas, “Discrete mathematics courses have constituents besides computer scientists,” College Mathematics Journal 15, 386– 388 (1984). © 1999 by Chapman & Hall/CRC [8] W. F. ” UME Trends 1, 7–8 (1989). [9] H. J. Ricardo, “Modeling as a precursor and beneficiary of mathematics reform,” UMAP Models: Tools for Teaching, COMAP, Lexington, MA, 1994, 25–28.

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