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Practical Discrete Mathematics

Practical Discrete Mathematics

By : Ryan T. White, Ray
4.6 (17)
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Practical Discrete Mathematics

Practical Discrete Mathematics

4.6 (17)
By: Ryan T. White, 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)
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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

Storage of graphs and networks

In this section, we'll learn about a few ways graph structures are commonly stored in computer memory and their benefits and drawbacks, including adjacency lists, adjacency matrices, and weight matrices.

Definition: adjacency list

For a graph G = (V, E), an adjacency list is an enumeration of the edges in a graph. In computer memory, we would store it as a list of pairs of vertex numbers.

Definition: adjacency matrix

For a graph G = (V, E), an adjacency matrix for a graph is a binary matrix A = (aij). If eij E, then the number in row i and column j is aij = 1. Otherwise, it is 0.

In other words, the value in the ith row and jth column of the adjacency matrix A, aij, is 1 if vertices vi and vj are adjacent. Otherwise, it is 0.

Example: an adjacency list and an adjacency matrix

For the graph G in Figure 8.1, we previously listed the edges as E = {e12, e13, e15, e23, e24, e26, e34, e35, e45}. The adjacency list will simply be a...

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