Principles of Mathematics in Operations Research

Principles of Mathematics in Operations Research ...

Recent titles in the INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor, S ...

Levent Kandiller Principles of Mathematics in Operations Research 4y Springer ...

Levent Kandiller Middle East Technical University Ankara, Turkey Library of Congress Control Number: ISBN-10: 0-387-37734-4 (HB) ...

To my daughter, Deniz ...

Preface The aim of this book is to provide an overview of mathematical concepts and their relationships not only for graduate st ...

VIII Preface vided within that chapter. Various Operations Research applications from de- terministic (continuous, discrete, sta ...

Contents ...

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1 Introduction 1.1 Mathematics and OR 1.2 Mathematics as a language 1.3 The art of making proofs 1.3.1 Forward-Backward method ...

1 Introduction Operations Research, in a narrow sense, is the application of scientific models, especially mathematical and stat ...

1 Introduction cognitive interest ANALYTIC H pure EMPIRICAL applied logic methodology y O.R. mathematics ' • l " physics chemist ...

1.2 Mathematics as a language 3 If as many numbers as we please beginning from a unit be set out continu- ously in double propor ...

4 1 Introduction Needs proof! There is an angle t such that cos t = t. Proof. Proofs should not contain ambiguity. However, one ...

1.3 The art of making proofs 5 Table 1.1. Operation table for A => B A True True False False B True False True False A=>B ...

6 1 Introduction X y Z x Fig. 1.2. Proposition 1.3. Proof. Backward: B: x = y (a; - y = 0) <=> FXZ = .XTZ (triangle is equ ...

1.3 The art of making proofs 7 of generality, we can fix an object with the property. If we can show that something happens for ...

8 1 Introduction Proof. Base: n = 1 = -j-1- Hypothesis: n = j, ELi * = =L^- Conciusion: n = j + 1, Efc=i-J + l & I. _ (.7 + ...

1.3 Problems 9 Proposition 1.3. p,qeR+3 y/pq^ V-~Y- => P hi- proof. A: y/pq^^ and hence A: ^pq = *f*. Similarly, B: p £ q and ...