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Discrete Mathematical structure Notes VSSUT – DMS Notes VSSUT of Total Complete Notes

#### 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,

#### 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,

#### 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.

#### 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,

#### 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, 2nd edition, TMH 2000.

Chapter 11(11.1 – 11.10 except 11.7), Chapter 12(12.1 – 12.8)

3.B.Kalman: Discrete Mathematical Structure, 3rd 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 Mathematics”: Semyour Lipschutz, Varsha Patil IInd Edition Schaum’s Series, TMH

4. “Discrete M a t h ema ti c a l Structures”: Kolman, Busby and Ross, 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. S.