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 4: Combinatorics Using SciPy

This chapter is about counting (or combinatorics), which seems simple, but rapidly gains complexity when counting the number of ways to combine, order, or select various finite sets. This includes the study of permutations and combinations, which can be applied to determining the memory required to store various types of data.

We will apply these ideas to measure the efficacy of brute-force algorithms applied to cryptography and the traveling salesman problem.

In this chapter, we will cover the following topics:

  • The fundamental counting rule
  • Counting permutations and combinations of objects
  • Applications to memory allocation
  • Efficacy of brute-force algorithms

By the end of the chapter, you will be able to count various mathematical structures, distinguish between combinations and permutations, and be able to count them. You will also be able to apply these ideas to practical problems in memory allocation and measure...