Practical Discrete Mathematics: Discover math principles that fuel algorithms for computer science and machine learning with Python
暫譯: 實用離散數學：探索推動計算機科學和機器學習演算法的數學原則，使用 Python

White, Ryan T., Ray, Archana Tikayat

Practical Discrete Mathematics: Discover math principles that fuel algorithms for computer science and machine learning with Python

相關主題

商品描述

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

Key Features

  • Apply the math of countable objects to practical problems in computer science
  • Explore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematics
  • Learn complex statistical and mathematical concepts with the help of hands-on examples and expert guidance

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 reduction

Who this book is for

This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.

商品描述(中文翻譯)

一本實用指南，簡化離散數學，適合好奇的心靈，並展示其在解決與軟體開發、計算機演算法和數據科學相關問題中的應用

主要特點


  • 將可數對象的數學應用於計算機科學中的實際問題

  • 探索現代 Python 函式庫，如 scikit-learn、NumPy 和 SciPy，以進行數學運算

  • 在實作範例和專家指導的幫助下學習複雜的統計和數學概念

書籍描述

離散數學研究可數的、獨特的元素，其原則廣泛應用於計算機科學和數據科學的演算法構建。掌握離散數學概念將幫助您理解數據驅動任務核心的演算法、二進位制和一般數學。

《實用離散數學》是一本全面的入門書，適合對可數對象的數學感到陌生的讀者。本書將幫助您掌握使用離散數學原則，將您的計算機科學技能提升到更高的水平。

在學習離散數學的語言時，您還將涵蓋研究和描述計算機科學及機器學習對象和演算法的關鍵方法。接下來的章節將指導您了解記憶體和 CPU 的運作。此外，您將學會如何分析數據以尋找有用的模式，最後探索如何將數學概念應用於網路路由、網頁搜尋和數據科學。

在本書結束時，您將對離散數學及其在計算機科學中的應用有更深入的理解，並準備好進行實際的演算法開發和機器學習。

您將學到什麼


  • 理解離散數學中的術語和方法及其在演算法和數據問題中的應用

  • 在形式邏輯和基本控制結構中使用布林代數

  • 實施組合數學以衡量計算複雜度並管理記憶體分配

  • 使用隨機變數，計算描述性統計，並找出平均情況下的計算複雜度

  • 解決與路由、尋路和圖形搜尋相關的圖形問題，例如深度優先搜尋

  • 執行機器學習任務，如數據視覺化、回歸和降維

本書適合誰

本書適合希望擴展離散數學知識的計算機科學家，這是他們領域的核心主題。希望實踐計算機科學、數學、統計學、工程或相關學科的大學學生也會發現本書有用。開始閱讀本書需要具備基本的 Python 程式設計技能和初步的實數代數知識。

作者簡介

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.

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.

作者簡介(中文翻譯)

瑞安·T·懷特（Ryan T. White），博士，是一位數學家、研究員和顧問，專長於機器學習和機率論，並在私營部門擁有算法開發和數據科學的經驗。懷特博士是佛羅里達理工學院的數學助理教授，負責一個以隨機分析及相關算法為中心的活躍學術研究計劃，領導私營部門的機器學習項目，參與多個科學和工程研究項目，並在本科和研究生層次教授機器學習、神經網絡、機率和統計等課程。

阿爾查娜·提卡亞特·雷（Archana Tikayat Ray）是喬治亞理工學院（Georgia Institute of Technology）的一名博士生，研究工作專注於機器學習和自然語言處理（Natural Language Processing, NLP）應用。她同樣擁有喬治亞理工學院的碩士學位，以及佛羅里達理工學院的航空航天工程學士學位。

目錄大綱

Table of Contents

  1. Key Concepts, Notation, Set Theory, Relations, and Functions
  2. Formal Logic and Constructing Mathematical Proofs
  3. Computing with Base-n Numbers
  4. Combinatorics Using SciPy
  5. Elements of Discrete Probability
  6. Computational Algorithms in Linear Algebra
  7. Computational Requirements for Algorithms
  8. Storage and Feature Extraction of Graphs, Trees, and Networks
  9. Searching Data Structures and Finding Shortest Paths
  10. Regression Analysis with NumPy and Scikit-Learn
  11. Web Searches with PageRank
  12. Principal Component Analysis with Scikit-Learn

目錄大綱(中文翻譯)

Table of Contents


  1. Key Concepts, Notation, Set Theory, Relations, and Functions

  2. Formal Logic and Constructing Mathematical Proofs

  3. Computing with Base-n Numbers

  4. Combinatorics Using SciPy

  5. Elements of Discrete Probability

  6. Computational Algorithms in Linear Algebra

  7. Computational Requirements for Algorithms

  8. Storage and Feature Extraction of Graphs, Trees, and Networks

  9. Searching Data Structures and Finding Shortest Paths

  10. Regression Analysis with NumPy and Scikit-Learn

  11. Web Searches with PageRank

  12. Principal Component Analysis with Scikit-Learn

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