[DCS] CS201 DISCRETE COMPUTATIONAL STRUCTURES KTU NOTES FOR SECOND YEAR [S3] STUDENTS


 DISCRETE COMPUTATIONAL STRUCTURES KTU NOTES FOR SECOND YEAR

[DCS] CS201 DISCRETE COMPUTATIONAL STRUCTURES KTU NOTES FOR SECOND YEAR [S3] STUDENTS,DCS ktu notes,DCS notes ktu,DCS notes,computational structure notes,computational structure notes ktu,ktu computational structure notes,discrete computational structure notes,discrete computational structure notes ktu,ktu discrete computational structure notes,ktu CS notes,Cs notes,Computer Science Notes
MODULE - 1

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 - 2

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

MODULE - 3

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 - 4

Lattices and Boolean algebra :-

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

MODULE - 5

Propositional Logic:-

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

MODULE - 6

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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