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

Using graphs, trees, and networks

Graphs and the other similar structures we introduced in the previous section are versatile modeling tools. This section will be an overview of some of the most common areas where these structures are used in discrete mathematics. Note that some of these topics will be explored much more deeply in some forthcoming chapters.

In Chapter 9, Searching Data Structures and Finding Shortest Paths, we will learn how to search graphs (especially trees) to find certain features or characteristics. One application of these searches is in scheduling problems. For example, consider a directed graph where each vertex represents a task that needs to be done to complete a large project where a directed edge between task A and task B means task A must be completed before task B. In other words, the directed edge represents a dependency.

Clearly, there should be no cycles since that would lead to an infinite loop of tasks to complete! This means the directed graph...