MCA Syllabus : www.manit.ac.in Maulana Azad National Institute of Technology

[mariammal]

MCA - 501 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
UNIT - I :
Prepositional and predicate calculus : Logic Propositions and logical operations truth tables and proposition generated by a set equivalence and implication. The laws of first order predicate logic, mathematical systems. Fuzzy sets, operations on fuzzy sets, Fuzzy Relations, properties and
operations on fuzzy relations.

http://www.manit.ac.in/manitbhopal/i...292&Itemid=220
http://www.manit.ac.in/manitbhopal/d...mca%20syll.pdf

UNIT - II :
Relations : Definitions, graphs of relations, properties of relations, matrices of relations, equivalence relations, Posets, Lattices , Complemented Lattices, Sub lattices. Distributive and Modular lattices. Boolean Algebra.

UNIT - III :
Graph Theory : Notions & terminology, directed and undirected graphs, incidence and degrees, Sub-graphs, Walks paths, cycles, circuits, components, connectedness algorithms, shorter pathalgorithm. Euclidian and Hamiltonian graphs, The traveling Salesman Problem, Trees: Spanning trees, rooted trees and binary trees.

UNIT - IV :
Discrete numeric functions, Generating functions, Recursion and recurrence relation, many faces of recursion, sequences solving a recurrence relation including non-homogeneous finite order linear relations.

UNIT - V :
Coding Theory, Binary symmetric channel, Coding Process, decoding, error detection and correction codes. Vector Spaces : Linear Independence, bases, Subspaces, dimensionality, Linear mapping, linear in-equality, inner products, norms.

TEXT BOOK :
Applied Discrete Structures for Computer Science by A Doerr and K Levasser.
Text & Reference Books :
1) Discrete Mathematical Structures for Computer Science by B Kolman & R.C. Busby.
2) Discrete Mathematical Structures with Application to Computer Science by J.P. Trembley & R.P.Manohar.
3) Graph Theory by F.Harary.
4) Elements of Discrete Mathematics by C.Liu.
5) Graph Theory with Application to Computer Science by N.Deo.