Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Chapter 11: Web Searches with PageRank

Searching the web is one of the first things we learn to do on the internet. The purpose, simply, is to find information of a topic of interest, but how does Google, or other search engines, take the words we search and effectively return what we want? This is the question we aim to answer in this chapter.

More specifically, this chapter discusses web searches from both a mathematical and practical perspective. We will first build the mathematical setting for common methods for web searches. We'll then look more deeply at Google's PageRank method and the linear algebra required. We'll then construct an implementation of PageRank that combines this linear algebra with the probabilistic aspects of PageRank we discussed in Chapter 5, Elements of Discrete Probability.

In this chapter, we will cover the following topics:

  • The development of search engines over time
  • How Google's PageRank algorithm works
  • Implementing...