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 surfaces with NumPy and SciPy

An appropriate question to ask in this section would be to ask, "Why do we need to fit surfaces to a dataset?" It is important since 2D plots are not enough to show the relationship between the predictor variables (X1, X2, …., Xn) and the predicted variable Y. In many real-life scenarios, Y is affected by more than one X variable, and hence to capture such a relationship, we would need a surface plot (3D), which can show the relationship between X1, X2, and Y. This relationship between the variables can be represented by the following mathematical formulation:

Y βo + β1 X1 + β2 X2

Our goal is to find the values for βo, β1, and β2.

For this section, we will use the horsepower and weight values of a car as input for X1 and X2 respectively. The output variable will be displacement (Y). We can mathematically write this as follows:

Y βo + (β1 * horsepower) + (β...