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Practical Discrete Mathematics

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

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Product type Paperback
Published in Feb 2021
Publisher Packt
ISBN-13 9781838983147
Length 330 pages
Edition 1st Edition
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Authors (2):
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Ryan T. White Ryan T. White
Author Profile Icon Ryan T. White
Ryan T. White
Archana Tikayat Ray Archana Tikayat Ray
Author Profile Icon Archana Tikayat Ray
Archana Tikayat Ray
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Table of Contents (17) Chapters Close

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

The Development of Search Engines over time

In this section, we will learn about the development of modern search engines on the internet. This will set the stage to learn about Google's PageRank algorithm. But, before we do that, let's briefly learn how older search engines worked and their shortcomings so that we can see why we need to tap into some deeper mathematics to solve the problem of ranking websites based on searches.

In the early 1990s, search engines were relatively simple. The search engine companies maintained databases of as many websites as they could. Users would search a word, say, chicken, and the search engines would search for websites using the word chicken and rank them based on how many times the word chicken appeared on the website. As you might suspect, this isn't necessarily the best approach.

There are several problems with these simple methods:

  • Web pages where a certain search word occurs frequently are not necessarily what...
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