MTH 401:DISCRETE MATHEMATICS Syllabus,Units,Mid Term,End Term Details

MTH401:DISCRETE MATHEMATICS Syllabus

Course Outcomes:
• develop the concept of difference equations and different method for their solutions.

• compute the solution of linear congruence equation and use it in cryptography.

Course Outcomes: • develop the concept of difference equations and different method for their solutions. • visualize the different types of relations and apply the Poset in daily lives that involves order. • examine the complex mathematical problem using Graphs and Trees. Unit I Difference equations with constant coefficients : difference equations, linearly dependent and independent solutions, homogeneous linear difference equation with constant coefficients, solution of difference equations Unit II Non-homogeneous difference equation and equations with variable coefficients : method of undetermined coefficient,special operator and variation of parameters., method of reduction of order, method of generating functions, linear difference equations with variable coefficients, nonlinear difference equations Unit III Relations and counting principal : relations and their properties, equivalence relations, partial ordering relations, lattice, sublattice, bounded lattice, Hasse diagram, pigeonhole principle, the generalized pigeonhole principle Unit IV Graphs : graph terminologies and special types of graphs, representing graphs and graph isomorphism, path and connectivity, Euler and Hamilton paths, shortest path, planner graphs and results, colouring of a graph and chromatic number Unit V Trees : tree and it's properties, rooted tree, spanning and minimum spanning tree Applications of trees : binary search tree,, decision tree, game trees Tree traversal : infix, prefix, and postfix notation, preorder traversal, inorder traversal, and postorder traversal Unit VI Number theory and its application in cryptography : divisibility and modular arithmetic, primes and greatest common divisors, congruences, applications of congruence, cryptography