Matemática discreta en Haskell

Abstract

Discrete mathematics is characterized as the branch of mathematics dealing with finite and numerable sets. Concepts and notations from discrete mathematics are useful in studying and describing objects and real-life problems. In particular the graph theory has numerous applications in logistics. Throughout this project some of the knowlegde adquired from the course “Matemática Discreta” will be given a computational implementation. The code will be written in Haskell language and a free version of it will be available in GitHub under the name: MDenHaskell. The work will focus on the graph theory and will provide some examples and algorithms in order to give an introduction of it and how it can be implemented in Haskell. At first, two chapters will be presented as a gentle reminder of basic concepts related to the set theory and the relations that can be established among them. The third chapter will introduce the main topic, graph theory, with different representations, definitions and examples on graphs. It will go through aspects such as morphism, connectivity and paths in graphs. Finally some properties and advantages of working with adjacency matrices will be presented in the fourth chapter. This project leaves the door open for the community of programmers to continue and improve it. It can be used as a self-learning tool as well as to make calculations that by hand would be tedious.