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I Formal
Logic: Statement, Symbolic Representation and Tautologies,
Quantifiers, Predicator and validity, Normal form. Propositional Logic,
Predicate Logic, Logic Programming and Proof of correctness.
II Proof, Relation and Analysis of Algorithm Techniques for theorem
proving: Direct Proof, Proof by Contra position, Proof by exhausting
cares and proof by contradiction, principle of mathematical induction,
principle of complete induction. Recursive definitions, solution methods
for linear, first-order recurrence relations with constant coefficients.
III Graph Theory: Graphs - Directed and Undirected, Eulerian chains
and cycles Hamilltonian chains and cycles, Trees, chromatic number,
connectivity and other graphical parameters Applications. Polya's Theory
of enumeration and its applications.
IV Sets and Fucntions : Sets, relations, functions, operations,
equivalence relations, relation of partial order, partitions, binary
relations. Transforms: Discrete Fourier and Inverse Fourier Transforms in
one and two dimensions, discrete Cosine transform.
V Monoids
and Groups : Groups, Semigroups and Monoids cyclic semi graphs and sub
monoids, Subgroups and cosets. Congruence relations on semi groups.
Morphism, Normal sub groups. Structure off cyclic groups, permutation
groups, dihedral groups elementary applications in coding theory. |