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DMS Syllabus.

UNIT – I
 Mathematical Logic: Propositional Calculus: Statements and Notations, Connectives, Truth Tables, Tautologies, Equivalence of Formulas, Duality law, Tautological Implications, Normal Forms, Theory ofInference for Statement Calculus, Consistency of Premises, Indirect Method of Proof. Predicate calculus: Predicative Logic, Statement Functions, Variables and Quantifiers, Free & Bound Variables, Inference theory for predicate calculus.

UNIT – II
Set Theory: Introduction, Operations on Binary Sets. Relations: Properties of Binary Relations, Relation Matrix and Digraph, Operations on Relations, Partition and Covering, Transitive Closure, Equivalence, Compatibility and Partial Ordering Relations, Hasse Diagrams. Functions:Bijective Functions, Composition of Functions, Inverse Functions, Permutation Functions,Recursive Functions.

 UNIT - III
Graph Theory I: Basic Concepts of Graphs, Sub graphs, Matrix Representation of Graphs: AdjacencyMatrices, Incidence Matrices, Isomorphic Graphs, Eulerian and Hamiltonian Graphs, Multigraphs. Graph Theory II: Planar Graphs, Euler‘s Formula, Graph Coloring, ChromaticNumber, Trees, Spanning Trees: Properties, Algorithms for Spanning trees and MinimumSpanning Trees.

UNIT –IV 
Algebraic Structures: Algebraic Systems with one Binary Operation, Properties of Binaryoperations, Semi groups and Monoids: Homomorphism of Semi groups and Monoids,Groups: Abelian group, Cosets, Subgroups (Definitions and Examples of all Structures
Combinatorics: Basic of Counting, Permutations, Permutations with Repetition of Objects,Restricted Permutations, Combinations, Restricted Combinations, Pigeonhole Principle andits Application, Binomial Theorem, Binomial and Multinomial Coefficients.

UNIT – V
Recurrence Relation: Generating Function of Sequences, Calculating Coefficient ofGenerating Functions, Recurrence Relations, Formulation as Recurrence Relations, Solvinglinear homogeneous recurrence Relations by substitution, generating functions and TheMethod of Characteristic Roots. Solving Inhomogeneous Recurrence Relations.

TEXT BOOK :
Tremblay, Manohar, Discrete Mathematical Structures with Applications to ComputerScience, TMH Publications.

 REFERENCES 
1. S.Santha, Discrete Mathematics, Cengage
2. Thomas Koshy, Discrete Mathematics with Applications, Elsevier
 3. JK Sharma, Macmillan Discrete Mathematics, 2nd edition,
4. Chandrasekaran, Umaparvathi, Discrete Mathematics, PHI, 2010
 5. Ralph. P.Grimaldi, Ramana, Discrete and Combinational Mathematics, Pearson, 5thedition.
 6. Mott, Kandel, Baker, Discrete Mathematics for Computer Scientists &Mathematicians, PHI, 2/e

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