• This Course assumes the knowledge of the course MCS-013, ―Discrete Mathematics‖. In the two blocks of this Course, we discuss recursion and graph theory, respectively. The first Block is aimed at developing the understanding of a very important tool for analyzing recursive programmes, namely, recurrence relations. In the second Block we aim to develop a basic understanding of graph theory, which is a very useful modeling tool for computer programming.
The Fibonacci Sequences, The Tower of Hanoi, Catalan Numbers Related Definitions Divide and Conquer Methods
Unit 2 : Generating FunctionsDefinitions and Constructions Applications for Finding the Number of Integers Solutions of Linear Equations Exponential Generating Functions Solving Recurrence Relations using Generating Functions Applying Generating Functions for Combinatorial Identities and Partitions
Unit 3 : Solving RecurrencesLinear Homogeneous Recurrences Linear Non- Homogeneous Recurrences Methods of Inspection, Telescoping SumsIteration, Substitution
What Graphs are Degree, Regularity and Isomorphism SubGraphs
Unit 2 : ConnectednessConnected Graphs Paths, Circuits and Cycles Components o Connectivity Bipartite Graphs
Unit 3 : Eulerian and Hamiltonian GraphsEulerian Graphs Hamiltonian Graphs Travelling Salesperson Problem
Unit 4 : Graph ColouringsVertex Colouring Edge Colouring Planar Graphs Map Colouring Problem
The Fibonacci Sequences, The Tower of Hanoi, Catalan Numbers Related Definitions Divide and Conquer Methods
Unit 2 : Generating FunctionsDefinitions and Constructions Applications for Finding the Number of Integers Solutions of Linear Equations Exponential Generating Functions Solving Recurrence Relations using Generating Functions Applying Generating Functions for Combinatorial Identities and Partitions
Unit 3 : Solving RecurrencesLinear Homogeneous Recurrences Linear Non- Homogeneous Recurrences Methods of Inspection, Telescoping Sums, Iteration, Substitution
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