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

Conditional probability and Bayes' theorem

In everyday life, our knowledge of the past informs our predictions about the future. For example, if the team with the best record in a basketball league were about to play against the team with the worst record, we would likely estimate the chance of the first team winning the game to be higher than if we did not know that fact.

This same idea in the context of this chapter would be to calculate the probability of an event occurring after learning that another event has occurred. This is a conditional probability and it applies in situations where we learn information over time, which influences our evaluations of probabilities for subsequent events, which is important to machine learning, artificial intelligence, and many other fields.

Definition – conditional probability

For two events A and B where P(B) > 0, the conditional probability of A given B is as follows:

This is the proportion of the time A occurs...