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Biyani's Think Tank Concept based notes Discrete Mathematics (MCA I SEM) Alap Mukherjee Revised By: Kalpana BSc (Maths), MCA Lecturer Deptt. of Information Technology Biyani Girls College, Jaipur 2 Published by : Think Tanks Biyani Group of Colleges Concept & Copyright : Biyani Shikshan Samiti Sector-3, Vidhyadhar Nagar, Jaipur-302 023 (Rajasthan) Ph : 0141-2338371, 2338591-95 Fax : 0141-2338007 E-mail : acad@
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    Biyani's Think Tank Concept based notes Discrete Mathematics (MCA I SEM) Alap Mukherjee Revised By: Kalpana BSc (Maths), MCA Lecturer Deptt. of Information Technology Biyani Girls College, Jaipur   2 Published by : Think Tanks Biyani Group of Colleges Concept & Copyright : Biyani Shikshan Samiti Sector-3, Vidhyadhar Nagar,  Jaipur-302 023 (Rajasthan) Ph : 0141-2338371, 2338591-95 Fax : 0141-2338007 E-mail : acad@biyanicolleges.org Website :www.gurukpo.com; www.biyanicolleges.org First Edition : 2011 Leaser Type Setted by : Biyani College Printing Department   While every effort is taken to avoid errors or omissions in this Publication, any mistake or omission that may have crept in is not intentional. It may be taken note of that neither the publisher nor the author will be responsible for any damage or loss of any kind arising to anyone in any manner on account of such errors and omissions.  Discrete Mathematics 3 Preface   I am glad to present this book, especially designed to serve the needs of the stu   dents. The book has been written keeping in mind the general weakness in understanding the fundamental concepts of the topics. The book is self-explanatory and adopts the “Teach Yourself” style. It is based on question -answer pattern. The language of book is quite easy and understandable based on scientific approach. Any further improvement in the contents of the book by making corrections, omission and inclusion is keen to be achieved based on suggestions from the readers for which the author shall be obliged. I acknowledge special thanks to Mr. Rajeev Biyani, Chairman  & Dr. Sanjay Biyani, Director   (  Acad. ) Biyani Group of Colleges, who are the backbones and main concept provider and also have been constant source of motivation throughout this Endeavour. They played an active role in coordinating the various stages of this Endeavour and spearheaded the publishing work. I look forward to receiving valuable suggestions from professors of various educational institutions, other faculty members and students for improvement of the quality of the book. The reader may feel free to send in their comments and suggestions to the under mentioned address. Author   4 Syllabus Introduction to Discrete Mathematical Structures, Formal Methods: Introduction and Analogy, Abstraction. Fundamentals: Sets & Relations- Sets, Types of Sets, Multi Sets, Operations on Sets, Relations and Properties of Relations, Representation of Relations, Equivalence Relation, Closures of Relations, Methods of Proof-Direct Proofs, Indirect Proofs, Mathematical Induction, Method of Contradiction. Combinatorics: Permutations and Combinations, Pigeon Hole Principle, Principle of Inclusion and Exclusion, Generating Functions. Mathematical Logic, Posets and Lattices: Partial Order Set, Bounding Elements, Well Ordered Set, Topological Sorting, Lattices, Principle of Duality, Bounded, Distributed, and Complemented Lattices, Proposition and Propositional Calculus. Graphs and Group Theory: Basic Introduction of Graphs- Types of Graphs, Path and Circuits, Eulerian Path and Circuits, Hamiltonian Path and Circuits, Shortest Path Algorithms, Group, Definitions and Properties, Coset & Subgroup, Normal subgroup, Homomorphism of groups,Cyclic Group, Permutation Group. Finite State Machines and Languages: Grammar and Languages- Phrase structure Grammar, Types of Grammars and Languages, Finite State Machines and Languages, Minimization of Finite State Machines.
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