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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
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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

Matrices and matrix representations of linear systems

Solving systems of more than two equations in more than two variables is very cumbersome under the algebraic notation we used previously for the small notations, so we need an alternate notation. We will take the coefficients of a system of n linear equations with n unknowns denoted aij above and arrange them in a special sort of array called a matrix. What makes matrices distinct from arrays you may be accustomed to using in code is that matrices have a special multiplication operation that simplifies many calculations and, especially, makes solving larger linear systems much easier.

We will also represent the xj and the bi terms as matrices to make a single matrix equation instead of n separate equations. Once we do that, we will be ready to solve these larger systems efficiently by hand and then with Python.

Definition – Matrices and vectors

An m-by-n matrix A is a rectangular array of numbers with m rows and...

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