Practical Discrete Mathematics

Discover math principles that fuel algorithms for computer science and machine learning with Python

Ryan T. White , Archana Tikayat Ray 지음

Packt(GCO Science) 2021년 02월 22일 출간

작품소개

책소개

A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science

▶Book Description
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.

▶What You Will Learn
-Understand the terminology and methods in discrete math and their usage in algorithms and data problems
-Use Boolean algebra in formal logic and elementary control structures
-Implement combinatorics to measure computational complexity and manage memory allocation
-Use random variables, calculate descriptive statistics, and find average-case computational complexity
-Solve graph problems involved in routing, pathfinding, and graph searches, such as depth-first search
-Perform ML tasks such as data visualization, regression, and dimensionality

목차

▶TABLE of CONTENTS
▷Part I ？ Basic Concepts of Discrete Math
-Chapter 1: Key Concepts, Notation, Set Theory, Relations, and Functions
-Chapter 2: Formal Logic and Constructing Mathematical Proofs
-Chapter 3: Computing with Base-n Numbers
-Chapter 4: Combinatorics Using SciPy
-Chapter 5: Elements of Discrete Probability

▷Part II ？ Implementing Discrete Mathematics in Data and Computer Science
-Chapter 6: Computational Algorithms in Linear Algebra
-Chapter 7: Computational Requirements for Algorithms
-Chapter 8: Storage and Feature Extraction of Graphs, Trees, and Networks
-Chapter 9: Searching Data Structures and Finding Shortest Paths

▷Part III ？ Real-World Applications of Discrete Mathematics
-Chapter 10: Regression Analysis with NumPy and Scikit-Learn
-Chapter 11: Web Searches with PageRank
-Chapter 12: Principal Component Analysis with Scikit-Learn

책 속으로

▶What this book covers
▷Part I ？ Basic Concepts of Discrete Math
- Chapter 1, Key Concepts, Notation, Set Theory, Relations, and Functions, is an introduction to the basic vocabulary, concepts, and notation of discrete mathematics.

- Chapter 2, Formal Logic and Constructing Mathematical Proofs, covers formal logic and binary and explains how to prove mathematical results.

- Chapter 3, Computing with Base-n Numbers, discusses arithmetic in different numbering systems, including hexadecimal and binary.

- Chapter 4, Combinatorics Using SciPy, explains how to count the elements in certain types of discrete structures.

- Chapter 5, Elements of Discrete Probability, covers measuring chance and the basics of Google's PageRank algorithm.

▷Part II ？ Implementing Discrete Mathematics in Data and Computer Science
- Chapter 6, Computational Algorithms in Linear Algebra, explains how to solve algebra problems with Python using NumPy.

- Chapter 7, Computational Requirements for Algorithms, gives you the tools to determine how long algorithms take to run and how much space they require.

- Chapter 8, Storage and Feature Extraction of Graphs, Trees, and Networks, covers storing graph structures and finding information about them with code.

- Chapter 9, Searching Data Structures and Finding Shortest Paths, explains how to traverse graphs and figure out efficient paths between vertices.

▷Part III ？ Real-World Applications of Discrete Mathematics
- Chapter 10, Regression Analysis with NumPy, is a discussion on the prediction of variables in datasets containing multiple variables.

- Chapter 11, Web Searches with PageRank, shows you how to rank the results of web searches to find the most relevant web pages.

- Chapter 12, Principal Component Analysis with Scikit-Learn, explains how to reduce the dimensionality of high-dimensional datasets to save space and speed up machine learning.

출판사 서평

▶ Preface
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 another level. You'll learn the language of discrete mathematics and methods crucial to studying and describing objects and algorithms from computer science and machine learning. Complete with real-world examples, this book covers the internal workings of memory and CPUs, analyzes data for useful patterns, and shows you how to solve problems in network routing, web searching, and data science.

작가정보

저자(글) Ryan T. White

Ryan T. White, Ph.D. is a mathematician, researcher, and consultant with expertise in machine learning and probability theory along with private-sector experience in algorithm development and data science. Dr. White is an assistant professor of mathematics at Florida Institute of Technology, where he leads an active academic research program centered on stochastic analysis and related algorithms, heads private-sector projects in machine learning, participates in numerous scientific and engineering research projects, and teaches courses in machine learning, neural networks, probability, and statistics at the undergraduate and graduate levels.

저자(글) Archana Tikayat Ray

Archana Tikayat Ray is a Ph.D. student at Georgia Institute of Technology, Atlanta, where her research work is focused on machine learning and Natural Language Processing (NLP) applications. She has a master's degree from Georgia Tech as well, and a bachelor's degree in aerospace engineering from Florida Institute of Technology.