You're reading from Practical Discrete Mathematics Discover math principles that fuel algorithms for computer science and machine learning with Python

Product type Paperback

Published in Feb 2021

Publisher Packt

ISBN-13 9781838983147

Length 330 pages

Edition 1st Edition

Languages

Python

Tools

NumPy

Concepts

Data Science

Authors (2):

Ryan T. White

Archana Tikayat Ray

View More author details

Table of Contents (17) Chapters

Preface

1. Part I – Basic Concepts of Discrete Math

2. Chapter 1: Key Concepts, Notation, Set Theory, Relations, and Functions FREE CHAPTER

3. Chapter 2: Formal Logic and Constructing Mathematical Proofs

4. Chapter 3: Computing with Base-n Numbers

5. Chapter 4: Combinatorics Using SciPy

6. Chapter 5: Elements of Discrete Probability

7. Part II – Implementing Discrete Mathematics in Data and Computer Science

8. Chapter 6: Computational Algorithms in Linear Algebra

9. Chapter 7: Computational Requirements for Algorithms

10. Chapter 8: Storage and Feature Extraction of Graphs, Trees, and Networks

11. Chapter 9: Searching Data Structures and Finding Shortest Paths

12. Part III – Real-World Applications of Discrete Mathematics

13. Chapter 10: Regression Analysis with NumPy and Scikit-Learn

14. Chapter 11: Web Searches with PageRank

15. Chapter 12: Principal Component Analysis with Scikit-Learn

16. Other Books You May Enjoy

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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...