Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Understanding graphs, trees, and networks

We will start by defining graphs mathematically, along with any other related definitions, before moving on to consider common ideas about trees, networks, and directed graphs.

Definition: graph

A graph G has two parts. First, V = {v1, v2, …, vk} is a set of vertices, also known as nodes. Second, E is a set of edges, each of which connects some pairs of nodes. We represent a graph as G = (V, E).

An edge is represented mathematically as a set made up of the two vertices it connects. If there is an edge connecting nodes vi and vj, we will call this edge eij = {vi, vj} and we say it is incident to vertices vi and vj.

An example of a graph follows with vertices V = {v1, v2, v3, v4, v5, v6} and edges E = {e12, e13, e15, e23, e24, e26, e34, e35, e45}:

Figure 8.1 – A graph with six vertices, and nine edges connecting them

We can see, for example, the edge connecting vertex 3 (v3) to vertex 4 (v4...