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

The shortest path problem and variations of the problem

In this section, we shift our focus to a different graph-related problem: finding the shortest paths between vertices in a network. As we will discuss, this is a problem that is important for routing problems, such as finding the shortest route to travel in a car to a destination or finding the fastest way to deliver a message over a computer network. Shortest path problems have even been used to determine how to use the thrusters on small fleets of deep-space research satellites to move them into very precise positions in relation to one another with minimal fuel usage so that they could work in unison to capture images of stars.

For graphs with unweighted edges, we have previously solved this problem. Let's review this simpler problem and its solution briefly before continuing to the more general problem on networks (that is, weighted graphs). In Chapter 8, Storage and Feature Extraction of Graphs, Trees, and Networks...