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

Formal Logic and Proofs by Truth Tables

We will be interested in arguments about mathematical structures and mathematical proofs throughout the book so that we can establish mathematical truths that will be used in practical problems. For this reason, in this section, we wish to establish some familiarity with the strict logic required to establish some mathematical theory that allows us to solve practical mathematical problems.

The foundation of all mathematics is logic, which studies how we can construct logically sound arguments that show that certain assumptions lead to certain conclusions with no doubt. In particular, formal logic abstracts away any specifics of the particular arguments being constructed in order to focus on the structure of the arguments, which can establish some general principles or shortcuts that can be used in specific arguments. Aristotle developed many principles of syllogistic logic, which is logic focusing on arguments that deductively lead from some...