Search icon Close icon
Search icon CANCEL
Subscription
0
Cart icon
Your Cart (0 item)
Close icon
You have no products in your basket yet
Save more on your purchases now! discount-offer-chevron-icon
Savings automatically calculated. No voucher code required.

Change country

Modal Close icon
Country selected Country selected
country flag United States
Country selected
country flag United Kingdom
Country selected
country flag India
Country selected
country flag Germany
Country selected
country flag France
Country selected
country flag Canada
Country selected
country flag Russia
Country selected
country flag Spain
Country selected
country flag Brazil
Country selected
country flag Australia
Country selected
country flag Argentina
Country selected
country flag Austria
Country selected
country flag Belgium
Country selected
country flag Bulgaria
Country selected
country flag Chile
Country selected
country flag Colombia
Country selected
country flag Cyprus
Country selected
country flag Czechia
Country selected
country flag Denmark
Country selected
country flag Ecuador
Country selected
country flag Egypt
Country selected
country flag Estonia
Country selected
country flag Finland
Country selected
country flag Greece
Country selected
country flag Hungary
Country selected
country flag Indonesia
Country selected
country flag Ireland
Country selected
country flag Italy
Country selected
country flag Japan
Country selected
country flag Latvia
Country selected
country flag Lithuania
Country selected
country flag Luxembourg
Country selected
country flag Malaysia
Country selected
country flag Malta
Country selected
country flag Mexico
Country selected
country flag Netherlands
Country selected
country flag New Zealand
Country selected
country flag Norway
Country selected
country flag Philippines
Country selected
country flag Poland
Country selected
country flag Portugal
Country selected
country flag Romania
Country selected
country flag Singapore
Country selected
country flag Slovakia
Country selected
country flag Slovenia
Country selected
country flag South Africa
Country selected
country flag South Korea
Country selected
country flag Sweden
Country selected
country flag Switzerland
Country selected
country flag Taiwan
Country selected
country flag Thailand
Country selected
country flag Turkey
Country selected
country flag Ukraine
Country selected
Arrow left icon
Explore Products
Best Sellers
New Releases
Books
Videos
Audiobooks
Learning Hub
Conferences
Free Learning
Arrow right icon
Arrow up icon
GO TO TOP
Practical Discrete Mathematics

You're reading from   Practical Discrete Mathematics Discover math principles that fuel algorithms for computer science and machine learning with Python

Arrow left icon
Product type Paperback
Published in Feb 2021
Publisher Packt
ISBN-13 9781838983147
Length 330 pages
Edition 1st Edition
Languages
Tools
Concepts
Arrow right icon
Authors (2):
Arrow left icon
Ryan T. White Ryan T. White
Author Profile Icon Ryan T. White
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.
Read more
See other products by Ryan T. White
Archana Tikayat Ray Archana Tikayat Ray
Author Profile Icon Archana Tikayat Ray
Archana Tikayat Ray
LinkedIn
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.
Read more
See other products by Archana Tikayat Ray
Arrow right icon
View More author details
Toc

Table of Contents (17) Chapters Close

Preface 1. Part I – Basic Concepts of Discrete Math
2. Chapter 1: Key Concepts, Notation, Set Theory, Relations, and Functions FREE CHAPTER 3. Chapter 2: Formal Logic and Constructing Mathematical Proofs 4. Chapter 3: Computing with Base-n Numbers 5. Chapter 4: Combinatorics Using SciPy 6. Chapter 5: Elements of Discrete Probability 7. Part II – Implementing Discrete Mathematics in Data and Computer Science
8. Chapter 6: Computational Algorithms in Linear Algebra 9. Chapter 7: Computational Requirements for Algorithms 10. Chapter 8: Storage and Feature Extraction of Graphs, Trees, and Networks 11. Chapter 9: Searching Data Structures and Finding Shortest Paths 12. Part III – Real-World Applications of Discrete Mathematics
13. Chapter 10: Regression Analysis with NumPy and Scikit-Learn 14. Chapter 11: Web Searches with PageRank 15. Chapter 12: Principal Component Analysis with Scikit-Learn 16. Other Books You May Enjoy

Chapter 2: Formal Logic and Constructing Mathematical Proofs

This chapter is an introduction to formal logic and mathematical proofs. We'll first introduce some primary results of formal logic and prove logical statements with the use of truth tables. In the remainder of the chapter, we'll consider the most common methods of mathematical proofs (direct proof, proof by contradiction, and proof by mathematical induction) to build skills that you will need for more complex problems to come later.

In this chapter, we will cover the following topics:

  • Formal logic and proofs by truth tables
  • Direct mathematical proofs
  • Proof by contradiction
  • Proof by mathematical induction

By the end of the chapter, you will have a grasp of how formal logic provides a grounding for deductive thought, you will have learned how to model logical problems with truth tables, you will have proved claims with truth tables, and you will have learned how to construct mathematical...

lock icon The rest of the chapter is locked
arrow left Previous Section
Section 1 of 6
Next Section arrow right
Register for a free Packt account to unlock a world of extra content!
A free Packt account unlocks extra newsletters, articles, discounted offers, and much more. Start advancing your knowledge today.
Sign up now
Unlock this book and the full library FREE for 7 days
Get unlimited access to 7000+ expert-authored eBooks and videos courses covering every tech area you can think of
Start free trial
Renews at R$50/month. Cancel anytime

Authors (2)

Left arrow icon
Profile icon Ryan T. White
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.
Read more
See other products by Ryan T. White
Profile icon Ray
Ray
LinkedIn icon
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.
Read more
See other products by Ray
Right arrow icon

Other recommended products

Related to this chapter
Left arrow icon
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
Beginning Java Data Structures and Algorithms
Beginning Java Data Structures and Algorithms
Read more
Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You'll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Read more
Jul 2018 6h 44m
PHP 7 Data Structures and Algorithms
PHP 7 Data Structures and Algorithms
Read more
PHP has always been the the go-to language for web based application development, but there are materials and resources you can refer to to see how it works. Data structures and algorithms help you to code and execute them effectively, cutting down on processing time significantly. If you want to explore data structures and algorithms in a practical way with real-life projects, then this book is for you.
Read more
May 2017 11h 20m
PHP 7 Data Structures and Algorithms
PHP 7 Data Structures and Algorithms
Read more
PHP has always been the the go-to language for web based application development, but there are materials and resources you can refer to to see how it works. Data structures and algorithms help you to code and execute them effectively, cutting down on processing time significantly. If you want to explore data structures and algorithms in a practical way with real-life projects, then this book is for you.
Read more
May 2017 11h 20m
Right arrow icon

Personalised recommendations for you

Based on your interests and search pattern
Left arrow icon
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Modern Computer Vision with PyTorch
Modern Computer Vision with PyTorch
Read more
This book provides a hands-on approach to solving over 30 prominent real-world computer vision problems using PyTorch 2.x on actual datasets. Here you'll learn to build a neural network from scratch and optimize hyperparameters, perform image classification, multi-object detection, segmentation, and more. You'll also explore facial expression manipulation and combining CV with NLP and RL techniques, build generative AI applications, and take your model to production on AWS. By the end of this book, you'll master modern NN architectures and confidently solve real-world CV problems.
Read more
Jun 2024 24h 52m
Right arrow icon