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

Understanding linear systems of equations

Equations of two variables whose graphs are straight lines, or linear equations, are one of the core parts of any elementary algebra course. They model simple proportional relationships well, but several linear equations taken at once, perhaps involving more than just two variables, allow for the modeling of much more complex situations, as we will see.

In this section, we discuss these familiar equations and then consider the idea of a system of multiple linear equations that we wish to solve all at once. We also define linear equations and systems of linear equations that involve more than just two variables and show how to solve them by hand.

Definition – Linear equations in two variables

A linear equation of the variables x1 and x2 is any equation that can be written in the form a1x1 + a2x2 = b for some real numbers a1, a2, and b. The solutions of the equation are all ordered pairs (x1, x2) R2 that satisfy the equation...