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Veer Surendra Sai University Of Technology VSSUT
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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)

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.

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.

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.

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## Ankita Srivastava

22 days ago00