UNIVERSITY OF CALICUT
IT14 304 : Discrete Computational Structures (Common with CS14 304)
Teaching scheme Credits: 4 (3 hours lecture and 1 hour tutorial per week)
Objectives • To provide the mathematical foundations required in any stream of study in Computing. • To provide a sound understanding of the various algorithms and methods • To get familiar with the essential proof techniques, logic and useful mathematical objects.
Module I (13 hours) Logic – Logical connectives and Truth tables – Logical equivalence and laws of logic – Logical implication and rules of inference- Quantifiers – Proofs of theorems using rules of universal specification and universal generalization.
Module II (13 hours) Relational Structures – Cartesian products – Relations – Relation matrices – Properties of relations – Composition of relations – Equivalence relations and partitions – Functions – One-to-one, onto functions – Composition of functions and inverse functions – Partial orders – Hasse diagrams.
Module III (13 hours) Group Theory – Definition and elementary properties – Cyclic groups – Homomorphisms and Isomorphisms – Subgroups – Cosets and Lagrange’s theorem – Elements of coding theory- Hamming metric – Generator matrices – Group codes – Hamming matrices.
Module IV (13 hours) Recurrence Relations – Introduction, Linear recurrence relations with constant coefficients – Homogeneous solutions – Particular solutions – Total solutions Generating Function – solutions of recurrence relations by the method of generating functions.
Click here to download complete syllabus
for more details click here or visit http://www.universityofcalicut.info
IT14 304 : Discrete Computational Structures (Common with CS14 304)
Teaching scheme Credits: 4 (3 hours lecture and 1 hour tutorial per week)
Objectives • To provide the mathematical foundations required in any stream of study in Computing. • To provide a sound understanding of the various algorithms and methods • To get familiar with the essential proof techniques, logic and useful mathematical objects.
Module I (13 hours) Logic – Logical connectives and Truth tables – Logical equivalence and laws of logic – Logical implication and rules of inference- Quantifiers – Proofs of theorems using rules of universal specification and universal generalization.
Module II (13 hours) Relational Structures – Cartesian products – Relations – Relation matrices – Properties of relations – Composition of relations – Equivalence relations and partitions – Functions – One-to-one, onto functions – Composition of functions and inverse functions – Partial orders – Hasse diagrams.
Module III (13 hours) Group Theory – Definition and elementary properties – Cyclic groups – Homomorphisms and Isomorphisms – Subgroups – Cosets and Lagrange’s theorem – Elements of coding theory- Hamming metric – Generator matrices – Group codes – Hamming matrices.
Module IV (13 hours) Recurrence Relations – Introduction, Linear recurrence relations with constant coefficients – Homogeneous solutions – Particular solutions – Total solutions Generating Function – solutions of recurrence relations by the method of generating functions.
Click here to download complete syllabus
for more details click here or visit http://www.universityofcalicut.info