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# Note for Discrete Mathematics - DMS by Ashutosh Jaiswal

• Discrete Mathematics - DMS
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#### Note for Discrete Mathematics - DMS by Ashutosh Jaiswal

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LECTURE NOTES ON Discrete Mathematics B.Tech II YEAR , I SEMESTER (JNTUA-R15) CREC, Dept of CSE Page 1

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR B. Tech II - I sem (Common to CSE & IT) T 3 Tu 1 C 3 DISCRETE MATHEMATICS Year B.Tech. I Sem. Course Objectives Understand the methods of discrete mathematics such as proofs, counting principles, number theory, logic and set theory. Understand the concepts of graph theory, binomial theorem, and generating function in analysis of various computer science applications. Course Outcomes Able to apply mathematical concepts and logical reasoning to solve problems in different fields of Computer science and information technology. Able to apply the concepts in courses like Computer Organization, DBMS, Analysis of Algorithms, Theoretical Computer Science, Cryptography, Artificial Intelligence UNIT I: Mathematical Logic: Introduction, Connectives, Normal Forms, The theory of Inference for the Statement Calculus, The Predicate Calculus, Inference Theory of Predicate Calculus. UNIT II: SET Theory: Basic concepts of Set Theory, Representation of Discrete structures, Relations and Ordering, Functions, Recursion. UNIT III: Algebraic Structures: Algebraic Systems: Examples and General Properties, Semi groups and Monoids, Polish expressions and their compilation, Groups: Definitions and Examples, Subgroups and Homomorphism’s, Group Codes. Lattices and Boolean algebra: Lattices and Partially Ordered sets, Boolean algebra. UNIT IV: CREC, Dept of CSE Page 2

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An Introduction to Graph Theory: Definitions and Examples, Sub graphs, complements, Graph Isomorphism, Vertex Degree: Euler Trails and Circuits, Planar Graphs, Hamilton Paths and Cycles, Graph Coloring and Chromatic Polynomials. Trees: Definitions, Properties, Examples, Rooted Trees, Trees and Sorting, Weighted trees and Prefix Codes, Biconnected Components and Articulation Points UNIT V: Fundamental Principles of Counting: The rules of Sum and Product, Permutations, Combinations: The Binomial Theorem, Combinations with Repetition The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion, Generalizations of Principle, Derangements: Nothing is in Its Right Place, Rook Polynomials, Arrangements with Forbidden Positions Generating Functions: Introductory Examples, Definitions and Examples: Calculation Techniques, Partitions of Integers, The Exponential Generating Functions, The Summation Operator. TEXT BOOKS: “Discrete Mathematical Structures with Applications to Computer Science”, J.P. Tremblay and R. Manohar, Mc Graw Hill Education,2015. “Discrete and Combinatorial Mathematics, an Applied Introduction”, Ralph P. Grimaldi and B.V.Ramana, Pearson, 5th Edition, 2016. REFERENCE BOOKS: Graph Theory with Applications to Engineering by NARSINGH DEO, PHI. Discrete Mathematics by R.K.Bishtand H.S. Dhami, Oxford Higher Education. Discrete Mathematics theory and Applications by D.S.Malik and M.K.Sen, Cenegage Learning. Elements of Discrete Mathematics, A computer Oriented approach by C L Liu and D P Mohapatra, MC GRAW HILL Education. Discrete Mathematics for Computer scientists and Mathematicians by JOE L.Mott, Abraham Kandel and Theodore P.Baker, Pearson ,2nd Edition CREC, Dept of CSE Page 3

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UNIT -1 Mathematical Logic CREC, Dept of CSE Page 4