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Practical Discrete Mathematics

Practical Discrete Mathematics

By : Ryan T. White, Ray
4.6 (17)
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Practical Discrete Mathematics

Practical Discrete Mathematics

4.6 (17)
By: Ryan T. White, 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)
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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 have primarily discussed the core ideas of probability theory, and in particular discrete probability. These allow us to calculate the probability that an event will occur, or, in other words, the chance that it will occur. We then applied these ideas to some popular modern innovations.

First, we constructed a probability space, made up of a sample space, a set of events, and a probability measure. The definition of these topics led directly to many elementary properties of probabilities and formulas to compute probabilities of events, such as those made up of unions of events and certain intersections of events. This led to an important class of probability spaces: the Laplacian space, where each outcome is equally likely. This reduces many probability calculations to counting problems, which we learned to solve in Chapter 4, Combinatorics Using SciPy.

Then, we considered conditional probability, which is essentially the idea that gaining new knowledge...

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