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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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...