Y.N. Singh, "Mathematical Foundation of Computer Science "
New Age International | 2005 | ISBN: 8122422942, 818412047X | 393 pages | PDF | 2,3 MB
New Age International | 2005 | ISBN: 8122422942, 818412047X | 393 pages | PDF | 2,3 MB
Preface :
To understand the fundamentals of computer science it is essential for us to begin with study of
the related mathematical topics ranging from discrete mathematics, concepts of automata theory
and formal languages. It is high time to recognize the importance of discrete mathematics as it
finds various applications in the field of computer science. However, it requires a full fledged
study and its potential with respect to computer sciences and natural sciences have long been
well recognized. To understand the principles of computer science that is evenly acknowledged
as mathematical foundation of computer science, this book present a selection of topics both
from discrete mathematics and from automata theory and formal languages. The objective of
selection of topics was due to my aspiration to commence with most of the fundamental terminology
employed in higher courses in computer science as plausible. As per the requirements of
the study, the formal appearance of the discrete mathematics includes set theory, algebraic
systems, combinatorics, Boolean algebra, propositional logic, and other relevant issues. Likewise,
abstract models of computations, models of computability, language theory concepts, and
the application of language theory ideas are the subject matter of the concepts of automata and
formal languages. These topics will also assist to understand the concepts and philosophies
used in advanced stages of computer learning such as computation theory and computability,
artificial intelligence, switching theory and logic design, design of softwares like high speed
compilers, sophisticated text processors and programming languages, assembly and rescue of
information.
the related mathematical topics ranging from discrete mathematics, concepts of automata theory
and formal languages. It is high time to recognize the importance of discrete mathematics as it
finds various applications in the field of computer science. However, it requires a full fledged
study and its potential with respect to computer sciences and natural sciences have long been
well recognized. To understand the principles of computer science that is evenly acknowledged
as mathematical foundation of computer science, this book present a selection of topics both
from discrete mathematics and from automata theory and formal languages. The objective of
selection of topics was due to my aspiration to commence with most of the fundamental terminology
employed in higher courses in computer science as plausible. As per the requirements of
the study, the formal appearance of the discrete mathematics includes set theory, algebraic
systems, combinatorics, Boolean algebra, propositional logic, and other relevant issues. Likewise,
abstract models of computations, models of computability, language theory concepts, and
the application of language theory ideas are the subject matter of the concepts of automata and
formal languages. These topics will also assist to understand the concepts and philosophies
used in advanced stages of computer learning such as computation theory and computability,
artificial intelligence, switching theory and logic design, design of softwares like high speed
compilers, sophisticated text processors and programming languages, assembly and rescue of
information.
The texts of this book are intended primarily for use in graduate as well as post graduate
courses in ‘Mathematical Foundation of Computer Science’, ‘Discrete Mathematics’ and
‘Automata Theory and Formal Languages’. Although, the topics discussed in the book primarily
focuses on the mathematical aspects of engineering in context of computer science, however it
is also suited to the technical professionals.
courses in ‘Mathematical Foundation of Computer Science’, ‘Discrete Mathematics’ and
‘Automata Theory and Formal Languages’. Although, the topics discussed in the book primarily
focuses on the mathematical aspects of engineering in context of computer science, however it
is also suited to the technical professionals.
Motivation:
The manuscript presented in this book is an outcome of the experience gained in the teaching
the courses like discrete mathematics, automata theory, and mathematical foundation of computer
science at Department of Computer Science & Engineering at I E T, UP Technical University,
Lucknow and elsewhere for last ten years. I am hopeful that presentation of this text
imitates the planning of the lectures. I always tried to avoid the mathematical-rigors, complicated
concepts and formalisms and presented them in a more precise and interesting manner.
Moreover, I hope during my teaching students not only learned the courses as a powerful mathematical
tool but also widened their ability and understanding to perceive, devise, and attempt
the mathematical problems with the application of the theory to computer science. The prolific
and valuable feedback from my students motivates me to prepare this manuscript. Ultimately,
I expect that this text would extend the understanding of mathematical theory of computer
science with the explosion of computer science, computer application, engineering, and information
technology.
The manuscript presented in this book is an outcome of the experience gained in the teaching
the courses like discrete mathematics, automata theory, and mathematical foundation of computer
science at Department of Computer Science & Engineering at I E T, UP Technical University,
Lucknow and elsewhere for last ten years. I am hopeful that presentation of this text
imitates the planning of the lectures. I always tried to avoid the mathematical-rigors, complicated
concepts and formalisms and presented them in a more precise and interesting manner.
Moreover, I hope during my teaching students not only learned the courses as a powerful mathematical
tool but also widened their ability and understanding to perceive, devise, and attempt
the mathematical problems with the application of the theory to computer science. The prolific
and valuable feedback from my students motivates me to prepare this manuscript. Ultimately,
I expect that this text would extend the understanding of mathematical theory of computer
science with the explosion of computer science, computer application, engineering, and information
technology.
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