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# KTU B.Tech S3 Syllabus Information Technology

## KTU B.Tech S3 Syllabus Information Technology

##### 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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