Principles of Mathematics in Operations Research

Operations Research is the application of scientific models, mathematical and statistical ones, to decision making problems, and PRINCIPLES OF MATHEMATICS IN OPERATIONS RESEARCH is a comprehensive survey of the mathematical concepts and principles of industrial mathematics. Its purpose is to provide students and professionals with an understanding of the fundamental mathematical principles used in Industrial Mathematics/OR in modeling problems and application solutions.

Over the past seven years, all the concepts presented in each chapter have undergone the learning scrutiny of the author and his students. The conceptual relationships within the chapter material have been developed in the classroom experience working with the students' level of understanding. The illustrative material throughout the book (i.e., worked-out problems and examples of the mathematical principles) was refined for student comprehension as the manuscript developed through its iterations. The chapter exercises were formulated each year and refined from the previous year's exercises.

The book uses a very broad spectrum of industrial mathematical applications, which include applications from deterministic (continuous, discrete, static, dynamic) modeling, combinatorics, regression, optimization, and graph theory. Also it's important to note that solutions of equation systems, geometric and conceptual visualization of abstract mathematical concepts have been included. In addition to the end-of-the-chapter exercises, active web resources have been provided at the end of each chapter as well. In sum, the author has carefully developed a pedagogically strong survey textbook of OR and Industrial Mathematics.


Written for: Students, industry practitioners, and academic researchers



The aim of this book is to provide an overview of mathematical concepts
and their relationships not only for graduate students in the fields of Operations
Research, Management Science and Industrial Engineering but also for
practitioners and academicians who seek to refresh their mathematical skills.
The contents, which could broadly be divided into two as linear algebra
and real analysis, may also be more specifically categorized as linear algebra,
convex analysis, linear programming, real and functional analysis.

The book has been designed to include fourteen chapters so that it might assist a 14-
week graduate course, one chapter to be covered each week.
The introductory chapter aims to introduce or review the relationship
between Operations Research and mathematics, to offer a view of mathematics
as a language and to expose the reader to the art of proof-making.


The chapters in Part 1, linear algebra, aim to provide input on preliminary
linear algebra, orthogonality, eigen values and vectors, positive definiteness,
condition numbers, convex sets and functions, linear programming and duality
theory. The chapters in Part 2, real analysis, aim to raise awareness of
number systems, basic topology, continuity, differentiation, power series and
special functions, and Laplace and z-transforms.
The book has been written with an approach that aims to create a snowball
effect. To this end, each chapter has been designed so that it adds to what the
reader has gained insight into in previous chapters, and thus leads the reader
to the broader picture while helping establish connections between concepts.


The chapters have been designed in a reference book style to offer a concise
review of related mathematical concepts embedded in small examples.
The remarks in each section aim to set and establish the relationship between
concepts, to highlight the importance of previously discussed ones or those
currently under discussion, and to occasionally help relate the concepts under
scrutiny to Operations Research and engineering applications. The problems
at the end of each chapter have been designed not merely as simple exercises
requiring little time and effort for solving but rather as in-depth problem
solving tasks requiring thorough mastery of almost all of the concepts provided
within that chapter.


Table of contents

Introduction.
- Preliminary linear algebra.
- Orthogonality.
- Eigen values and vectors.
- Positive definiteness.
- Computational aspects.
- Convex sets.
- Linear programming.
- Number systems.
- Basic topology.
- Continuity.
- Differentiation.
- Power series and special functions.
- Special transformations.
- Solutions.
- Index.