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Practical Discrete Mathematics

Practical Discrete Mathematics

By : Ryan T. White, Ray
4.6 (17)
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Practical Discrete Mathematics

Practical Discrete Mathematics

4.6 (17)
By: Ryan T. White, 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)
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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

Implementing the PageRank algorithm in Python

In this section, we will take the insights we learned about the PageRank algorithm in the previous sections to write an effective Python implementation of the algorithm.

As we saw previously, the idea of the PageRank algorithm is to do some calculations to update the PageRank vectors over and over until they reach a steady-state PageRank vector. But we just ran it 15 times, looked at the numbers, and stopped when the updates become so small as to be insignificant.

However, there are a few obstacles to implementing this on a real, large-scale problem:

  • If the "internet" of web pages is large, such as with the real internet, we could not really look at millions or billions of PageRanks in the updates and find when they have stopped changing.
  • We cannot know in advance how many iterations we need to run for the PageRanks to converge to a steady state.
  • We manually defined the initial state of the PageRank vector...
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Practical Discrete Mathematics
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