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

Depth-first search (DFS)

In short, graph searches traverse a graph to map its structure. In this section, we will learn about an algorithm to accomplish such a search. Mapping out the structure of a graph can be important on its own, but it is a sub-problem that algorithms must solve in order to solve larger problems in graphs, as we have discussed. The DFS algorithm is quite possibly the most common approach for graph searches; it is an efficient method, and it is used as a subroutine in many more complex algorithms.

DFS starts at a source vertex, traverses the first available edge to visit another vertex, and repeats this until there are no edges leading to unvisited vertices—that is, until it has gone as deep as possible. At this time, it backtracks to the last vertex that has unvisited neighbors and takes another trip from that vertex through as many unvisited vertices until it reaches another dead end. It then backtracks and travels to unvisited vertices again and again...