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# KTU B.Tech S3 Syllabus Computer Science and Engineering

## KTU B.Tech S3 Syllabus Computer Science and Engineering

##### CS201: DISCRETE COMPUTATIONAL STRUCTURES
###### MODULE I

Review of elementary set theory : Algebra of sets – Ordered pairs and Cartesian products – Countable and Uncountable sets

Relations :– Relations on sets –Types of relations and their properties – Relational matrix and the graph of a relation – Partitions – Equivalence relations – Partial ordering- Posets – Hasse diagrams – Meet and Join – Infimum and Supremum Functions :– Injective, Surjective and Bijective functions – Inverse of a function- Composition

###### MODULE II

Review of Permutations and combinations, Principle of inclusion exclusion, Pigeon Hole Principle,

Recurrence Relations: Introduction- Linear recurrence relations with constant coefficients– Homogeneous solutions – Particular solutions – Total solutions Algebraic systems:– Semigroups and monoids – Homomorphism, Subsemigroups and submonoids

FIRST INTERNAL EXAM

###### MODULE III

Algebraic systems (contd…):– Groups, definition and elementary properties, subgroups, Homomorphism and Isomorphism, Generators – Cyclic Groups, Cosets and Lagrange’s Theorem Algebraic systems with two binary operations- rings, fields-sub rings, ring homomorphism

MODULE IV

Lattices and Boolean algebra :– Lattices –Sublattices – Complete lattices – Bounded Lattices – Complemented Lattices – Distributive Lattices – Lattice Homomorphisms. Boolean algebra – sub algebra, direct product and homomorphisms

SECOND INTERNAL EXAM

MODULE V

Propositional Logic:- Propositions – Logical connectives – Truth tables Tautologies and contradictions – Contra positive – Logical equivalences and implications Rules of inference: Validity of arguments.

MODULE VI

Predicate Logic:- Predicates – Variables – Free and bound variables – Universal and Existential Quantifiers – Universe of discourse. Logical equivalences and implications for quantified statements – Theory of inference : Validity of arguments. Proof techniques: Mathematical induction and its variants – Proof by Contradiction – Proof by Counter Example – Proof by Contra positive.

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