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

Common classes of computational complexity

In this section, we will learn about some other common classes of computational complexity other than the constant, linear, quadratic, and suchlike complexities that have been discussed in the previous sections.

"Pretty well everybody outside the area of computer science thinks that if your program is running too slowly, what you need is a faster machine."

– Rod Downey and Mike Fellows

However, this is not the case, since some problems might require a brute-force search through a large class of cases that exponentially increases the number of steps required to solve the problem. An important distinction is often made between a tractable and intractable problem:

  • Tractable problems make use of algorithms that take polynomial time (P) for their execution – time complexity is of the order O(nc), where c is any constant that belongs to the natural numbers.

    Feasibly decidable kinds of problems are problems...