Course abstract

This course is a basic course offered to UG/PG students of Engineering/Science background. It consists of four main topics : 1.Discrete Mathematics: Symbolic representation of statements, Duality, Tutologies and contradictions, Quantifiers, languages and Grammers, Finite state machines, Lattices as partially ordered sets, Lattices as Algebraic systems, Sublattices, Boolean algebra and Boolean functions, Representations of Boolean functions, Application of Boolean functions to synthesis of circuits, Circuit minimizations, Karnaugh Map. 2.Graph theory: Various types of Graphs, Subgraphs, Walks, Trails, Paths, Cycles, Eularian and Hamiltonian graphs, Travelling salesman problem, Vertex and edge connectivity, Matrix representation of graphs, Incidence and adjacency matrices of graphs, Planar graphs, Kuratowski’s graphs, detection of planarity, Euler’s formula, duals of a Planar graph, Colouring of graphs, Four color theorem. 3.Linear programming problems: Graphical method, simplex method, Big-M method, two phase method, Dual Simplex method and applications. 4.Queuing theory: Basic charecteristics of Queuing modles, Distribution of arrivals and service times, M/M/1:∞/FIFO model, M/M/S:∞/FIFO model, M/M/1:N/FIFO model, M/M/S:N/FIFO model and their applications.