Note for Discrete Mathematics - DMS by Vssut Rulers

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B. TECH. 5 SEMESTER DISCRETE MATHEMATICS (I.T & Comp. Science Engg.) Th SYLLABUS B.Tech (CSE/IT, Discrete Mathematical Structures) Unit I Logic: Propositional equivalence, predicates and quantifiers, Methods of proofs, proof strategy, sequences and summation, mathematical induction, recursive definitions and structural induction, program correctness. Counting: The basics of counting, the pigeonhole principle, permutations and combinations, recurrence relations, solving recurrence relations, generating functions, inclusion-exclusion principle, application of inclusion-exclusion. Unit II Relations: Relations and their properties, n-array relations and their applications, representing relations, closure of relations, equivalence of relations, partial orderings. Graph theory: Introduction to graphs, graph terminology, representing graphs and graph isomorphism, connectivity, Euler and Hamilton paths, planar graphs, graph coloring, introduction to trees, application of trees. Unit III Group theory: Groups, subgroups, generators and evaluation of powers, cosets and Lagrange's theorem, permutation groups and Burnside's theorem, isomorphism, automorphisms, homomorphism and normal subgroups, rings, integral domains and fields. Unit IV Lattice theory: Lattices and algebras systems, principles of duality, basic properties of algebraic systems defined by lattices, distributive and complimented lattices, Boolean lattices and Boolean algebras, uniqueness of finite Boolean expressions, prepositional calculus. Coding theory: Coding of binary information and error detection, decoding and error correction. Text Books: 1) K.H. Rosen: Discrete Mathematics and its application, 5th edition, Tata McGraw Hill.Chapter 1(1.1-1.5), Chapter 3(3.1-3.4,3.6), Chapter 4(4.1-4.3,4.5), Chapter 6(6.1,6.2,6.4-6.6) Chapter 7(7.1-7.6), Chapter 8(8.1-8.5,8.7,8.8) 2. C. L. Liu: Elements of Discrete Mathematics, 2 nd edition, TMH 2000. Chapter 11(11.1 – 11.10 except 11.7), Chapter 12(12.1 – 12.8) 3.B.Kalman: Discrete Mathematical Structure, 3 rd edition, Chapter 11(11.1,11.2)

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References: 1. “Discrete Mathematical Structures”: Tremblay and Manohar, Tata McGraw Hill 2. “Discrete Mathematics”: 1st edition by Maggard Thomson 3. “Discrete M a t h e m a t i c s ”: Semyour Lipschutz, Varsha Patil IInd Edition Schaum’s Series, TMH 4. “Discrete M a t h e m a t i c a l Structures”: Kolman, B u s b y a n d R o s s , Prentice Hall India, Edition 3 5. “Discrete Mathematics and its application” – Mott Kendle 6. “Discrete Mathematical Structure” : G. Shankar Rao, New Age Publisher. 7. “Fundamental Approach to Discrete Mathematics” Acharjaya D. P. Sreekumar, New Age Publisher.

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Disclaimer This document does not claim any originality and cannot be used as a substitute of prescribed text books. The information presented here is merely a collection by the committee members for their respective teaching assignments. Various sources as mentioned references at the beginning of the document as well as freely available materials from the internet were constituted for preparing this document. The ownership of the information lies with respective authors or institutions. Further this document is not intended to be used for commercial purposes and the committee members are not accountable for any issues, legal or otherwise, arising out of this document. The committee members make no representations or warranties with respect to the accuracy or completeness of the contents of the document and disclaim any implied warranties of merchantability or fitness for a particular purpose. The committee members shall not be liable for any loss or profit or any other commercial, incidental, consequential or any other damages.

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Acknowledgement The committee members gratefully acknowledge Google, NPTEL and different reference books for getting help for preparation of this lecture note. The committee members also want to express their gratitude to the persons those who thinks knowledge should be free and be accessible and sharable without any restrictions so that every individual on this world has the same opportunity to explore and become enlightened by the collective gift of mankind. This lecture note being first draft so there may be some error. Also detail proofs and some graphs are omitted; however details discussion has been made in the class. Thus apart from this lecture note students/readers are strongly recommended following the mentioned books in the references and above all conferring with the faculty members for thorough knowledge in the subject.       