This comprehensive and self-contained text provides a thorough understanding of the concepts and applications of discrete mathematics and graph theory. It is written in such a manner that beginners can develop an interest in the subject. Besides providing the essentials of theory, the book helps develop problem-solving techniques and sharpens the skill of thinking logically. The book is organized in two parts. The first part on discrete mathematics covers a wide range of topics such as predicate logic, recurrences, generating function, combinatorics, partially ordered sets, lattices, Boolean algebra, finite state machines, finite fields, elementary number theory and discrete probability. The second part on graph theory covers planarity, colouring and partitioning, directed and algebraic graphs. In the Second Edition, more exercises with answers have been added in various chapters. Besides, an appendix on languages has also been included at the end of the book. The book is intended to serve as a textbook for undergraduate engineering students of computer science and engineering, information communication technology (ICT), and undergraduate and postgraduate students of mathematics. It will also be useful for undergraduate and postgraduate students of computer applications. KEY FEATURES • Provides algorithms and flow charts to explain several concepts. • Gives a large number of examples to illustrate the concepts discussed. • Includes many worked-out problems to enhance the student’s grasp of the subject. • Provides exercises with answers to strengthen the student’s problem-solving ability. AUDIENCE • Undergraduate Engineering students of Computer Science and Engineering, Information communication technology (ICT) • Undergraduate and Postgraduate students of Mathematics. • Undergraduate and Postgraduate students of Computer Applications.
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About the Author
Satyanarayana, Bhavanari BHAVANARI SATYANARAYANA, Ph.D., is Professor of Mathematics at Acharya Nagarjuna University, Nagarjuna Nagar, Andhra Pradesh. Dr. Satyanarayana has over three decades of teaching experience in mathematics. He has co-authored/edited more than 39 books and published about 66 research papers (in algebra/fuzzy algebra/graph theory) in reputed national and international journals. He is the recipient of AP Scientist Award (2009), Glory of India Award (Thialand, 2011), Rajiv Gandhi Excellence Award (2011) and Bharat Vikas Ratan Award (2011). His research interests include discrete mathematics, fuzzy algebra, graph theory, linear programming and quantitative methods. Prasad, Kuncham Syam KUNCHAM SYAM PRASAD, Ph.D., is Associate Professor of Mathematics at Manipal Institute of Technology, Manipal, Karnataka. Dr. Prasad has over 17 years of teaching experience in mathematics. He has co-authored nine books and published 21 research papers in reputed journals. He is a recipient of the national level Best Research Paper Prize (2000) by the Indian Mathematical Society and also Indian National Science Academy Visiting Fellowship Award (2004). His research interests include discrete mathematics, algebra, linear programming, topology and graph theory.
Table of ContentsPreface Part I: DISCRETE MATHEMATICS 1. Preliminary Notations 2. Fundamentals of Logic 3. Recurrences and Integer Functions 4. Counting Techniques 5. Algebraic Systems 6. Partially-Ordered Sets 7. Lattices 8. Boolean Algebras 9. Finite Machines 10. Finite Fields 11. Elementary Number Theory 12. Discrete Probability Part II: GRAPH THEORY 13. Preliminary Concepts 14. Planarity, Colouring and Partitioning 15. Some Algebraic Aspects of Graphs 16. Directed Graphs Appendix: Languages • Bibliography • Glossary • Index