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

Chapter 6: Computational Algorithms in Linear Algebra

This chapter covers standard methods and algorithms of linear algebra commonly used in computer science and machine learning problems. Linear algebra centers on systems of equations, a problem where we need to find a set of numbers that solve not just one equation, but many equations simultaneously, using special types of arrays called matrices. Matrices can directly model tree, graph, and network structures that are central to so many computer science applications and the math behind Google's PageRank, among others, all ideas to which we will apply these ideas in later chapters. Systems of equations are key in regression analysis and machine learning.

We will delve into solving these systems of equations from both geometric and computational perspectives before scaling the methods up to solve larger problems with algorithms in Python, because the huge amount of work you would have to do to solve large problems by hand would...