Discrete Computational Structures CS201 KTU Notes| KTU DCS Notes | KTU Students Note| Textbook | Syllabus | Question Papers

DCS NOTES S3 CS

Discrete Computational Structures CS201 DCS study material,this contains all the six modules notes useful textbook and question papers click on the below option to download all the files.

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DCS NOTES S3 CS

Discrete Computational Structures CS201 DCS study material,this contains all the six modules notes useful textbook and question papers click on the below option to download all the files.

__DCS Syllabus__

__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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