Rajiv Gandhi Technological University, Bhopal (MP)
Computer Tech. & Applications (UTD, RGTU, Bpl)
Software Systems SATI (Vidisha)
ME/M.Tech. 1st FIRST SEMESTER SYLLABUS

MCTA 101 MATHEMATICAL FOUNDATIONS OF COMPUTER APPLICATION SYLLABUS

Unit 1

Sets: Relationship between sets, Operations on sets, set identity, principle of inclusion and exclusion, Min-sets, Cut-sets. Relations, properties of binary relations, equivalence relations and partitions, partial ordering relations, functions, inverse functions, composition of functions and lattices, chains and anti-chains, complemented & distributive lattices, Boolean algebra, canonical forms

Unit 2

Prepositional logic, conjunction, disjunction and negation, interpretation of formulas in prepositional logic, Validity and consistency, normal form in prepositional logic and logic consequences, first order predicate logic

Unit 3

Introduction to finite state machine, finite state machine as models of physical system, equivalence machines, finite state machine as language recognizers.

Unit 4

Introduction to discrete numeric functions and generating functions
, introduction to combinaric problems, introduction to recurrence relational and recursive algorithms, linear recurrence, relations with constant coefficients, Homogeneous solutions, particular solutions, total solutions.

Unit 5

Graph: Finite graphs, incidence and degree, isomorphism, sub graphs and union of graphs, connectedness, reachability, paths, and circuits, Eulerian graphs, tree: properties of trees, pendant vertices in tree, center of tree ,spanning trees and cut vertices, binary tree ,matrix representation of graph, incidence and adjacency matrix and their propertices, applications of graphs in computer science.
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Reference Readings:
1. Discrete structure, Schaum series
2. C.L. Liu, Elements of Discrete mathematics
3. Sahni S., Concepts in Discrete Mathematics
4. Levy L.S., Discrete Structure of Computer Science
  5. Kanneth H. Rosen, Discrete Mathematics & Its Applications, Mcgraw Hill