Fundamental Approach to Discrete Mathematics

Description

Salient Features Mathematical logic, fundamental concepts, proofs and mathematical induction (Chapter 1) Set theory, fundamental concepts, theorems, proofs, Venn diagrams, product of sets, application of set theory and fundamental products (Chapter 2) An introduction to binary relations and concepts, graphs, arrow diagrams, relation matrix, composition of relations, types of relation, partial order relations, total order relation, closure of relations, poset, equivalence classes and partitions. (Chapter 3) An introduction to functions and basic concepts, graphs, composition of functions, floor and ceiling function, characteristic function, remainder function, signum function and introduction to hash function. (Chapter 4) The algebraic structure includes group theory and ring theory. Group theory includes group, subgroups, cyclic group, cosets, homomorphism, introduction to codes and group codes and error correction for block code. The ring theory includes general definition, fundamental concepts, integral domain, division ring, subring, homomorphism, an isomorphism and pigeon hole principle (chapters 5, 6 and 7) A treatment of Boolean algebras that emphasizes the relation of Boolean algebras to combinatorial circuits. (Chapter 8) An introduction to lattices and basic concepts (Chapter 9) A brief introduction to graph theory is discussed. Elements of graph theory are indispensable in almost all computer science areas. Examples are given of its use in such areas as minimum spanning tree, shortest path problems (Dijkastra's algorithm and Floyd-Warshall algorithm) and traveling salesman problem. The computer representation and manipulation of graphs are also discussed so that certain important algorithms can be included (chapters 10 and 11) A strong emphasis is given on understanding the theorems and its applications Numbers of illustrations are used throughout the book for explaining the concepts and its applications. Figures and tables are used to illustrate concepts, to elucidate proofs and to motivate the material. The captions of these figures provide additional explanation. Besides this, a number of exercises are given for practice

About the Author:
D.P. Acharjya is currently working as Assistant Professor of Computer Applications, Vellore Institute of Technology (Deemed University), Vellore. Formerly he was head of the department of Computer Science at Rourkela Institute of Management Studies, Rourkela. He obtained his M.Tech. (Comp. Sc.) from Utkal University, India, M.Phil. (Math.) from Berhampur University, India and M.Sc. (Applied Math.) from National Institute of Technology, Rourkela, India. He has been awarded with Gold Medal in M.Sc. He is also working as guest lecturer in Computer Science for various institutes. He is an academic guide for ICFAI University. He is a life member of Orissa Information Technology Society (OITS). He was holding the post of secretary of OITS, Rourkela chapter. He is doing research work in the field of Neural Network, Digital Image Processing and Fuzzy Logic.


Sreekumar is currently working as Assistant Professor of Computer Science, Rourkela Institute of Management Studies, Rourkela. He obtained his M.Tech. (Comp. Sc.) from Utkal University, India, and M.Sc. (Applied Math.) from National Institute of Technology, Rourkela, India. He is also working as guest lecturer in Computer Science for various institutes. He is a life member of Orissa Information Technology Society (OITS) and Computer Society of India (CSI). He is doing research work in the field of Data Envelopment Analysis and Fuzzy Logic.


Content:

Contents:
Mathematical Logic
Set Theory
Binary Relation
Function
Group Theory
Ring Theory
Boolean Algebra
Introduction to Lattices
Graph Theory
Tree

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