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# Fundamental Approach to Discrete Mathematics

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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 pigeonhole 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
New Age International Pvt. Ltd., Publishers; April 2005
279 pages;