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

Solving large linear systems with NumPy

The last example should make it clear that Gaussian elimination will work for any linear system to reduce it to RREF form, but this 3-equation, 3-variable system required a significant amount of effort to solve, and things will only become more complex for larger systems, so the more practical way to do it is to use existing algorithms. In this section, we will learn how to use some methods with NumPy to accomplish this task.

A Python function for solving systems of linear equations Ax = b is available in NumPy named numpy.linalg.solve, which works for square, consistent systems. That is, it finds solutions for all linear systems that have unique solutions.

Typically, the function uses a version of Gaussian elimination just as we have done by hand, but it is a very smart function. First, the function chooses the order of calculations carefully to optimize its speed. Second, if the function detects that A has a special structure (such as...