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

Binary numbers and their applications

In this section, we will learn about the binary number system in detail along with its applications and importance in computer science. In particular, we will consider a brief history of binary, provide an explanation as to why they are so foundational to how computers work, and examine the link between binary numbers and Boolean algebra and its use in databases.

The modern binary number system, which is the basis for binary code, was invented by Gottfried Leibniz in 1689, which he described in his article Explication de l'Arithmétique Binaire (translated as "explanation of binary arithmetic").

Binary numbers are represented in a base-2 system. The only digits used to represent a binary number are "0" and "1." Each digit is called a bit. A binary string of eight bits can represent any of 256 (28) possible values.

A bit string is not the only kind of binary code; other systems that allow only two...