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

Least-squares lines with NumPy

In this section, we will learn how to fit a line to a dataset by using the normal equation as well as by using Python libraries. We will also find the parameter values (β) and use these values to predict the Y values for some X value of our choice.

The relationship between the variables (horsepower and weight) can be represented by the following mathematical formulation:

Y βo + β1 X

Our goal is to find the values for βo and β1. Here, horsepower is the dependent variable (Y) and weight is the independent variable (X).

Before beginning the coding part, make sure that the Python file that you are editing and auto_dataset.csv are in the same folder. If not, make sure to include the path for the .csv file location in the Python file so that it can be read and used for computations. Also, the packages used in the coding exercises (numpy, pandas, seaborn, matplotlib.pyplot, and sklearn) should be installed to avoid...