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 7: Computational Requirements for Algorithms

Algorithms that solve useful problems are at the heart of computer science, but an algorithm must not only be proven to work to be practical. They may take too long to run with our computational resources, or it may require storage of more data than our resources allow. This chapter is dedicated to finding the amount of time and space required to run algorithms; in short, the computational complexity of algorithms when it comes to time and space requirements to run a certain algorithm. We will focus on the complexity of foundational control structures and popular exemplar algorithms of common classes of time and space complexity. Different algorithms will be implemented using Python and the trade-off when it comes to runtime, computational resources, and suchlike will be discussed.

By the end of this chapter, you should have learned about different algorithms, their computational complexities, runtime, and the space required....