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

Chapter 2: Formal Logic and Constructing Mathematical Proofs

This chapter is an introduction to formal logic and mathematical proofs. We'll first introduce some primary results of formal logic and prove logical statements with the use of truth tables. In the remainder of the chapter, we'll consider the most common methods of mathematical proofs (direct proof, proof by contradiction, and proof by mathematical induction) to build skills that you will need for more complex problems to come later.

In this chapter, we will cover the following topics:

  • Formal logic and proofs by truth tables
  • Direct mathematical proofs
  • Proof by contradiction
  • Proof by mathematical induction

By the end of the chapter, you will have a grasp of how formal logic provides a grounding for deductive thought, you will have learned how to model logical problems with truth tables, you will have proved claims with truth tables, and you will have learned how to construct mathematical...