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 fundamental counting rule

This section is devoted to counting the number of possible ways to select several objects, each from a set of distinct elements. We will first focus on the case of just two sets before extending it to an arbitrary number of sets.

Definition – the Cartesian product

The set of ordered pairs A × B = {(a, b) : a A, b B}, with component a as an element from set A and the second component b from set B, is called the Cartesian product of sets A and B:

Figure 4.1 – If A = {a1, a2} and B = {b1, b2}, then A × B consists of the ordered pairs in this table

This chapter is all about counting the number of elements in sets. Recall from Chapter 1, Key Concepts, Notation, Set Theory, Relations, and Functions that the cardinality of a set is the number of elements in the set. Cartesian products are interesting things to count because we can count the number of ways of choosing one element from set A and another element...