dharm
d:\N-com\TITLE.pm5 vi
FEATURE OF THE BOOK
The interesting feature of this book is its organization and structure. That consists of
systematizing of the definitions, methods, and results that something resembling a theory.
Simplicity, clarity, and precision of mathematical language makes theoretical topics more
appealing to the readers who are of mathematical or non-mathematical background. For quick
references and immediate attentions—concepts and definitions, methods and theorems, and
key notes are presented through highlighted points from beginning to end. Whenever, necessary
and probable a visual approach of presentation is used. The amalgamation of text and figures
make mathematical rigors easier to understand. Each chapter begins with the detailed contents
which are discussed inside the chapter and conclude with a summary of the material covered in
the chapter. Summary provides a brief overview of all the topics covered in the chapter. To
demonstrate the principles better, the applicability of the concepts discussed in each topic are
illustrated by several examples followed by the practice sets or exercises.
The material of this book is divided into 5 Units that are distributed among 12 chapters.
Unit I gives general overview of discrete objects theory its relations and functions, enu-
meration, recurrence relations and algebraic structures. It contains four chapters.
Chapter 1 is a discussion of discrete objects theory its relations and functions. We start
our discussion from the theory of discrete objects which is commonly known as algebra of sets.
The concepts of relations and functions are presented after a discussion of algebra of sets. This
chapter is concluded with the study of natural numbers, Peano axioms and mathematical in-
duction.
Chapter 2 discusses enumeration that includes discrete numeric functions and generat-
ing functions. This chapter covers a class of functions whose domain is the set of natural num-
bers and the range is the set of real numbers—better known as discrete numeric functions that
are widely used in digital computations. An alternative way to represent the numeric functions
efficiently and conveniently the reader will also find a discussion over generating function in
the chapter.
Chapter 3 is concerned with recurrence relation and the methods of finding the solution
of the recurrence relation (difference equation). A variety of common recurrences obtained from
the algorithms like divide & conquer and chip & conquer is given. The chapter concludes the
methods to obtain the solution of the recursive procedure codes.
Chapter 4 Latter in this unit we emphasized the algebraic structures where a thorough
discussion of group theory and brief discussion of other algebraic structures like rings and
fields are presented. This discussion is in fact very important in formal language theory and
automata. This chapter concludes with the discussion of class of group mappings like
homomorphism, isomorphism, and automorphism.
Unit II is devoted to the discussion of propositional logic and lattices that are presented
in two chapters.
Oaf! After a successful study of mathematical–rigors, readers find an interesting and
detail overview of logic in Chapter 5. An elementary introduction to logic not only enlightens