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

The basics of discrete probability

As we have said, making predictions or finding probabilities requires careful analysis, so we need a mathematical framework for probability. It will all center around the idea of a random experiment.

Definition – random experiment

A random experiment is any process that has an uncertain outcome.

Simple examples of random experiments are tossing a coin or rolling a die, each of which has an uncertain outcome. These are easy to analyze, but some random experiments are much more difficult, such as predicting tomorrow's weather. Despite the complexity, experts can estimate the chance of each possible result of the random experiment using complex meteorological models, taking into account temperatures, humidity, and other atmospheric data.

Something each example has in common is that there is a random result for each experiment. A coin toss may result in heads or tails. We may roll a 1, 2, 3, 4, 5, or 6 on the die. The weather may...