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

Dijkstra's Algorithm for Finding Shortest Paths

In this section, we will learn about Dijkstra's algorithm for finding the shortest paths, consider the process in simple terms, and apply the algorithm by hand to a small network.

The most common algorithm for finding the shortest paths on a network is Dijkstra's algorithm. It was named after the Dutch computer scientist Edsger W. Dijkstra, who constructed it in 1956, but since computing was such a new field at the time, there were so few academic journals dedicated to computing that he did not publish his findings until 1959.

We will first learn about the method in intuitive terms using the small network from Figure 9.5 so that we can understand the ideas behind the approach. This understanding is important because there are many variations of the algorithm and we hope you will learn to adapt it to solve your own problems!

Just like the previous section, we will seek the shortest path from v1 to v2. Since it is...