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

Understanding base-n numbers

In this section, we will discuss how to write numbers in different bases with the help of some examples.

A base-n system uses n different symbols for writing numbers, as in 0, 1, 2, …, n – 1. This n is called the radix of the numbering system. Of course, the customary base-10, or decimal, numbers use the digits 0 through 9.

All base-n numbers make use of the positional system, like the one used by decimal numbers, which we will discuss in the next example.

Example – Decimal numbers

Let's think about what it means to write the decimal number 3214 with the usual positional system. It seems trivial, but it is important to realize what exactly a digit in each position in this number represents in order to understand the commonality between the base-10 system we all know and this new idea of a base-n system. The number is made up of a sum of three thousands (103), two hundreds (102), one ten (101), and four ones (100)...