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

Summary

In this chapter, we have discussed the meaning of discrete mathematics and discrete objects. Furthermore, we provided an overview of some of the many applications of discrete mathematics in the real world, especially in the computer and data sciences, which we will discuss in depth in later chapters.

In addition, we have established some common language and notation of importance for discrete mathematics in the form of set notation, which will allow us to refer to mathematical objects with ease, count the size of sets, represent them as Venn diagrams, and much more. Beyond this, we learned about a number of operations that allow us to manipulate sets by combining them, intersecting them, and finding complements. These give rise to some of the foundational results in set theory in De Morgan's laws, which we will make use of in later chapters.

Lastly, we took a look at the ideas of functions and relations, which map mathematical objects such as numbers to one another. While certain types of functions may be familiar to the reader from high school or secondary school, these familiar functions are typically defined on continuous domains. Since we focus on discrete, rather than continuous, sets in discrete mathematics, we drew the distinction between the familiar idea and a new one we need in this field. Similarly, we showed the difference between functions in mathematics and functions in Python and saw that some Python "functions" are mathematical functions, but others are not.

In the remaining four chapters of Part I: Core Concepts of Discrete Mathematics, we will fill our discrete mathematics toolbox with more tools, including logic in Chapter 2, Formal Logic and Constructing Mathematical Proofs, numerical systems, such as binary and decimal, in Chapter 3, Computing with Base n Numbers, counting complex sorts of objects, including permutations and combinations, in Chapter 4, Combinatorics Using SciPy, and dealing with uncertainty and randomness in Chapter 5, Elements of Discrete Probability. With this array of tools, we will be able to consider more and more real-world applications of discrete mathematics.