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

Applications to memory allocation

One area where combinatorics can come into play is in determining how much memory an algorithm needs to complete a certain task. It is frequently useful to know this before we run some code. In most programming languages, when arrays are created, they are given a static size that cannot be changed. Therefore, it is faster or more convenient to change an existing value in an array than to change the size of an array.

So, developers often pre-allocate the memory by creating an array of the maximum size we will need for the whole course of the algorithm, either filled with 0s or empty, depending on the language. This is not a problem with small amounts of data, but when the program needs to process exponentially large amounts of data, this can be very wasteful. Understanding memory usage is also important to avoid certain negative consequences: we may use up so many resources on the device that it cannot complete its other tasks, it may crash, or...