Preface
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 Opera-
tions 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 mathe-
matics 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 du-
ality 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 con-
cise 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 pro-