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

Summary

In this chapter, we began by introducing the ideas of graphs, directed graphs, networks, and directed networks along with some common language used to describe them. Next, we introduced a few ways in which these structures are used for modeling practical problems, many to be investigated more deeply in the forthcoming chapters.

After this, we moved on to consider ways in which graphs and networks can be stored in computer memory with Python. Especially popular are adjacency matrices and adjacency lists for graphs and weight matrices for networks. In the last section, we showed many features of graphs from adjacency matrices, such as degrees of vertices, the number of paths between pairs of vertices, and the length of the minimum-edge paths between the vertices.

Altogether, this chapter has defined graphs, trees, networks, and the directed types of these structures, established some common vocabulary on these topics, familiarized you with some practical applications of...