You're reading from Practical Discrete Mathematics

Product type Book

Published in Feb 2021

Publisher Packt

ISBN-13 9781838983147

Pages 330 pages

Edition 1st Edition

Languages

Python

Concepts

Data Science

Authors (2):

Ryan T. White

Archana Tikayat Ray

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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

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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Summary

In this chapter, we began by introducing the ideas of graphs, directed graphs, networks, and directed networks along with some common language used to describe them. Next, we introduced a few ways in which these structures are used for modeling practical problems, many to be investigated more deeply in the forthcoming chapters.

After this, we moved on to consider ways in which graphs and networks can be stored in computer memory with Python. Especially popular are adjacency matrices and adjacency lists for graphs and weight matrices for networks. In the last section, we showed many features of graphs from adjacency matrices, such as degrees of vertices, the number of paths between pairs of vertices, and the length of the minimum-edge paths between the vertices.

Altogether, this chapter has defined graphs, trees, networks, and the directed types of these structures, established some common vocabulary on these topics, familiarized you with some practical applications of...