05-01-2017, 03:32 PM
SYLLABUS:-
UNIT- I
Formal Logic: Preposition, Symbolic Representation and logical entailment theory of Inferences and tautologies, Predicates, Quantifiers, Theory of inferences for predicate calculus, resolution.
Techniques for theorem proving: Direct Proof, Proof by Contraposition, proof by contradiction.
UNIT- II
Overview of Sets and set operations, permutation and combination, principle of inclusion, exclusion (with proof) and pigeonhole principle (with proof), Relation, operation and representation of a relation, equivalence relation, POSET, Hasse Diagrams, extremal Elements, Lattices, composition of function, inverse, binary and nary operations.
UNIT- III
Principle of mathematical induction, principle of complete induction, solution methods for linear and non-linear first-order recurrence relations with constant coefficients,
Graph Theory: Terminology, isomorphic graphs, Euler’s formula (proof) ,chromatic number of a graph, five color theorem(with proof), Euler &Hamiltonian paths.
UNIT-IV
Groups, Symmetry, subgroups, normal subgroups, cyclic group, permutation group and cayles’s theorem(without proof), cosets lagrange’s theorem(with proof) homomorphism, isomorphism, automorphism, rings, Boolean function, Boolean expression, representation & minimization of Boolean function.
UNIT- I
Formal Logic: Preposition, Symbolic Representation and logical entailment theory of Inferences and tautologies, Predicates, Quantifiers, Theory of inferences for predicate calculus, resolution.
Techniques for theorem proving: Direct Proof, Proof by Contraposition, proof by contradiction.
UNIT- II
Overview of Sets and set operations, permutation and combination, principle of inclusion, exclusion (with proof) and pigeonhole principle (with proof), Relation, operation and representation of a relation, equivalence relation, POSET, Hasse Diagrams, extremal Elements, Lattices, composition of function, inverse, binary and nary operations.
UNIT- III
Principle of mathematical induction, principle of complete induction, solution methods for linear and non-linear first-order recurrence relations with constant coefficients,
Graph Theory: Terminology, isomorphic graphs, Euler’s formula (proof) ,chromatic number of a graph, five color theorem(with proof), Euler &Hamiltonian paths.
UNIT-IV
Groups, Symmetry, subgroups, normal subgroups, cyclic group, permutation group and cayles’s theorem(without proof), cosets lagrange’s theorem(with proof) homomorphism, isomorphism, automorphism, rings, Boolean function, Boolean expression, representation & minimization of Boolean function.