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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

Solving small linear systems with Gaussian elimination

In this section, we will learn how to solve an n-by-n linear system of equations Ax = b, if possible, through a method called Gaussian elimination, which we will do by hand for a small problem. In the next section, we implement it with Python.

We will explain through an example of a 3-by-3 system, which should make the idea clear for larger systems, which we will formalize at the end of the section, and which we will prefer to solve with code.

First, notice that there are several manipulations we may do to the equation in the system without changing the solutions:

  • We can switch the order of the equations, which corresponds to swapping the rows of the matrix [A|b].
  • We can multiply both sides of an equation by a constant, which corresponds to multiplying a row of [A|b] by a constant.
  • We can add a multiple of one equation to another equation, which corresponds to adding a multiple of one row of [A|b] to another...
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