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Informationen zum Autor S.K. Chakraborty is currently Reader at the Department of Mathematics, BIT, Mesra, Ranchi. He holds a PhD in Applied Mathematics from Uppsala University, Sweden, and has over 15 years of academic experience. He has published several research papers in various journals of national and international repute. He is also a member of Indian Society for Theoretical and Applied Mechanics, and Indian National Science Congress Association. B.K. Sarkar is currently a Senior Lecturer at the Department of Information Technology and MCA, BIT, Mesra, Ranchi. He has around 9 years of teaching experience and is a life member of Indian Society for Technical Education. Klappentext Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of computer applications. The book would also prove useful to post graduate students of mathematics. It seeks to provide a thorough understanding of the subject and present its practical applications tol computer science. Zusammenfassung Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of computer applications. The book would also prove useful to post graduate students of mathematics. It seeks to provide a thorough understanding of the subject and present its practical applications tol computer science. Inhaltsverzeichnis CHAPTER 1: SET RELATION FUNCTION 1.1: INTRODUCTION 1.2: SETS 1.2.1: Representation of a Set 1.2.2: Sets of Special Status 1.2.3: Universal Set and Empty Set 1.2.4: Subsets 1.2.5: Power set 1.2.6: Cardinality of a Set 1.3: ORDERED PAIRS 1.3.1: Cartesian Product of Sets 1.3.2: Properties of Cartesian Product 1.4: VENN DIAGRAMS 1.5: OPERATIONS ON SETS 1.5.1: Union of Sets 1.5.2: Intersections of Set 1.5.3: Complements 1.5.4: Symmetric Difference 1.6: COUNTABLE AND UNCOUNTABLE SETS 1.7: ALGEBRA OF SETS 1.8: MULTISET 1.8.1: Operations on Multisets 1.9: FUZZY SET 1.9.1: Operations on Fuzzy Set 1.10: GROWTH OF FUNCTION 1.11: COMPUTER REPRESENTATION OF SETS 1.12: INTRODUCTION 1.13: BINARY RELATION 1.14: CLASSIFICATION OF RELATIONS 1.14.1: Reflexive Relation 1.14.2: Symmetric Relation 1.14.3: Antisymmetric Relation 1.14.4: Transitive Relation 1.14.5: Equivalence Relation 1.14.6: Associative Relation 1.15: COMPOSITION OF RELATIONS 1.16: INVERSE OF A RELATION 1.17: REPRESENTATION OF RELATIONS ON A SET 1.18: CLOSURE OPERATION ON RELATIONS 1.18.1: Reflexive Closure 1.18.2: Symmetric Closure 1.19: MATRIX REPRESENTATION OF RELATION 1.20: DIGRAPHS 1.20.1: Transitive Closure 1.20.2: Warshall's Algorithm 1.21: PARTIAL ORDERING RELATION 1.22: n-ARY RELATIONS AND THEIR APPLICATIONS 1.23: RELATIONAL MODEL FOR DATABASES 1.24: INTRODUCTION 1.25: ADDITION AND MULTIPLICATION OF FUNCTIONS 1.26: CLASSIFICATION OF FUNCTIONS 1.26.1: One-to-one (Injective) Function 1.26.2: Onto (Surjective) Functions 1.26.3: One-to-one, Onto (Bijective) Function 1.26.4: Identity Function 1.26.5: Constant Function 1.27: COMPOSITION OF FUNCTION 1.27.1: Associativity of Composition of Functions 1.28: INVERSE FUNCTION 1.28.1: Invertible Function 1.28.2: Image of a Subset 1.29: HASH FUNCTION 1.30: RECURSIVELY DEFINED FUNCTIONS 1.31: SOME SPECIAL FUNCTIONS 1.31.1: Floor and Ceiling Functions 1.31.2: Integer and Absolute Value Functions 1.31.3: Remainder Function 1.32: FUNCTIONS OF COMPUTER SCIENCE 1.32.1: Partial and Total Functions 1.32.2: Primitive Recursive Function 1.32.3: Ackermann Function 1.33: THE INCLUSION-EXCLUSION PRINCIPLE 1.33.1: Applications of Inclusion - Exclusion Principle 1.34: SEQUENCE AND SUMMATION 1...
