Principles of Mathematics in Operations Research

1 Introduction

cognitive interest

ANALYTIC

H

pure

EMPIRICAL

applied

logic

methodology y O.R.

mathematics ' •

l "

physics

chemistry

biology

psychology

astronomy

/.I

i

/ ' i

social sciences' '

management sciences

medicine '

agriculture

engineering - - - -

instrumental interest

Fig. 1.1. The scientific inquiry.

1.2 Mathematics as a language

The main objective of mathematics is to state certainty. Hence, the main role

of a mathematician is to communicate truths but usually in its own language.

One example is

V* e 5, 3j e T 3 ilj => Vj G T, 3i e S 3 i±j <=> S±T.

That is, if for all i in S there exists an element j of T such that i is orthogonal

to j then for all elements j of T there is an element j of S such that j is

orthogonal to i; if and only if, S is orthogonal to T.

To help the reader appreciate the expressive power of modern mathemat-

ical language, and as a tribute to those who achieved so much without it,

a few samples of (original but translated) formulation of theorems and their

equivalents have been collected below.

(a + bf = a^2 + b^2 + lab

If a straight line be cut at random, the square on the whole is equal to the
squares on the segments and twice the rectangle contained by the segments
(Euclid, Elements, II.4, 300B.C).

1 + 2 + • • • + 2" is prime => 2 n(l + 2 + • • • + 2") is perfect