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Practical Discrete Mathematics

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

Concepts

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

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 9: Searching Data Structures and Finding Shortest Paths

This chapter will discuss the searching techniques of graph, tree, and network data structures and practical applications of graph searches. We will introduce and analyze two popular algorithms for related problems: depth-first search (DFS) for graph searches and Dijkstra's algorithm for finding the shortest paths between vertices in networks. Both are introduced on small graphs to build intuitive understanding, and Python implementations are written that can scale up to real-world problems.

In this chapter, we will cover the following topics:

Searching graph and tree data structures
Depth-first search algorithm
The shortest path problem and variations of the problem
Finding shortest paths with brute force
Dijkstra's algorithm for finding shortest paths
Python implementation of Dijkstra's algorithm

By the end of this chapter, you will be able to explain the purpose...

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Authors (2)

Ryan T. White

Ryan T. White, Ph.D. is a mathematician, researcher, and consultant with expertise in machine learning and probability theory along with private-sector experience in algorithm development and data science. Dr. White is an assistant professor of mathematics at Florida Institute of Technology, where he leads an active academic research program centered on stochastic analysis and related algorithms, heads private-sector projects in machine learning, participates in numerous scientific and engineering research projects, and teaches courses in machine learning, neural networks, probability, and statistics at the undergraduate and graduate levels.

See other products by Ryan T. White

Archana Tikayat Ray

Archana Tikayat Ray is a Ph.D. student at Georgia Institute of Technology, Atlanta, where her research work is focused on machine learning and Natural Language Processing (NLP) applications. She has a master's degree from Georgia Tech as well, and a bachelor's degree in aerospace engineering from Florida Institute of Technology.

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