Discrete Mathematical Algorithm, and Data Structure
Discrete Mathematical Algorithm, and Data Structure
Major Components of Mathematics, and Computer Science Explained with the help of C, C++, PHP, Java, C#, Python, and Dart
About the Book
Readers will learn discrete mathematical abstracts as well as its implementation in algorithm and data structures.
I have shown examples using various programming languages.
I have used as C, C++, PHP, Java, C#, Python and Dart. This book combines two major components of Mathematics and Computer Science under one roof.
Firstly, without the core conceptions and tools derived from discrete mathematics, one cannot understand the abstract or the general idea involving algorithm and data structures in Computer Science.
Secondly, the objects of data structures are basically objects of discrete mathematics.
As a result, this book tries to bridge the gap between two major components of Mathematics and Computer Science.
Finally, in any computer science course, studying discrete mathematics is essential, although they are taught separately.
Certainly, there is exception and that proves the rule. Yet, a comprehensive book, combining these two major components, is hard to find out.
Not only that, it is almost impossible to understand one without the help of other.
Consequently, I hope, this book will fill the gap.
Therefore, readers will learn discrete mathematical abstracts as well as its implementation in algorithm and data structures.
Since readers use different programming languages, I try to show examples in different programming languages.
I have used C, C++, PHP, Java, C#, Python and Dart. However, another very basic concept of programing language has motivated me to use such disparate languages.
After all, basic concepts are same in every language. Especially the algorithm and data structure concepts. Although the syntax is different.
As this book combines two major components of Computer Science under one roof, I hope students of Computer Science may find some food for thought.
The book covers the following chapters, you see below, although it’s quite tentative, as it might change a little bit while writing the book.
Bundles that include this book
Table of Contents
-
1. Introduction to the Discourse
- Is Discrete Mathematics enough to study Computer Science?
- A short Introduction to Discrete Mathematics
- What is Discrete Mathematics
- What is the relationship between Discrete Mathematics and Computer Science
- Introducing necessary conceptions
- QUIZZ and Challenge on Chapter One
-
2. Introduction to Programming Language and Boolean Algebra
- Logic, Mathematics, and Programming Language
- Introduction to Boolean Algebra
- QUIZZ and Challenge on on Chapter Two
-
3. De Morgan’s Laws on Boolean Algebra, Logical Expression, and Algorithm
- Logical Expression
- Short Circuit Evaluation
- Syntax, Semantics and Conditional Execution
- Why we need Control Constructs
- Discrete Mathematical Notations and Algorithm
- QUIZZ and Challenge on Chapter Three
-
4. Data Structures in different Programming languages
- Mean, Median and Mode
- Array, the First Step to Data Structure
- Let us understand some Array features
- Set Theory, Probability and Array
- Skewed Mean, Maximized Median
- Complex Array Algorithm
- QUIZZ and Challenge on Chapter Four
- printing result
-
5. Data Structures: Abstractions and Implementation
- How objects work with each other
- More Algorithm and Time Complexity
- Introducing Data Structures
- How Calculus and Linear Algebra are Related to this Discourse
- QUIZZ and Challenge on Chapter Five
-
6. Data Structures in Detail
- Frequently Asked Questions about Data Structures
- Abstract Data Type (ADT)
- Linear Data Structures
- Modeling of a Structure
- ArrayList to overcome limitations of Array
- ArrayList or LinkedList, which is faster?
- Collection Framework in programming languages
- Stack and Queue in Java
- Deque, a high-performance Abstract Data Type
- QUIZZ and Challenge on Chapter Six
- Challenge 1 : Can we test in a program whether the Stack has been overflowed or not?
- Challenge 2 : Can you convert an array to a queue and use all the queue methods to manipulate that array?
- Challenge 3 : Why LinkedList consumes less memory than ArrayList. Write a program and explain why it happens.
- Challenge 4 : Can you give examples of hybrid linear data structure that provides all the capabilities of stacks and queues under one roof?
-
7. Algorithm, Data Structure, Collection Framework and Standard Template Library (STL)
- Introducing Algorithm Library
- Different types of Algorithms
- Binary Tree and Data Structure
- Collection Framework in Java
- Discrete Mathematical Abstractions and Implementation through Java Collection
- Comparator, Comparable and Iterator
- Standard Template Library in C++
- QUIZZ on Chapter Seven
- Challenge 1 : Standard Template Library (STL) provides many generic versions of standard algorithms that replace our low-level plumbing. Can you show the difference by writing code.
- Challenge 2 : Can you prove with an example how the STL makes a difference when we want to sort a list of data.
- Challenge 3 : Using recursion in programing is closer to our discrete mathematical definitions. Can you prove it?
- Challenge 4 : Recursive algorithm should have a base case. Write a program where we can proceed towards the base case and a condition to stop the recursion.
- Challenge 5 : Can you prove that Discrete Mathematics, data structure and algorithm are inter-connected?
- Challenge 6 : Can you create a general template class and method that will allow to pass any data of your choice.
-
8. Time Complexity
- Order of n, or O(n)
- Big O Notation
- QUIZZ on Chapter Eight
- Challenge 1 : Data structures are discrete structures and hence, the algorithms are all about discrete structures. Write a program to establish a relationship between algorithms and discrete mathematics
- Challenge 2 : How we can get the total of a series of positive integers that starts from 0 and ends at 5. Can it be done recursive way?
- Challenge 3 : Detect the main problem in the code below and rewrite it in proper way.
-
9. Set, Symmetric Difference and Propositional Logic
- Why Set is important in Data Structures
- How Symmetric Difference and Propositional Logic combine
- QUIZZ on Chapter Nine
- Challenge 1 : Why the Set implementation ‘HashSet’ is better than the general-purpose Set implementation ‘TreeSet’? Can you compare and prove that?
- Challenge 2 : Can you combine Symmetric Difference and Propositional Logic in one program? You can write it in any programming language.
- Challenge 3 : In discrete mathematical paradigms, Set abstraction is basically chaotic, and unordered. However, no duplicate element is allowed in the world of Set. Can you prove it?
-
10. Combinatorics and Counting, Permutation and Combinations
- Permutation and Combination
- QUIZZ on Chapter ten
- Challenge 1 : How many ways we can rearrange 5 balls.
- Challenge 2 : Suppose you have a string “abcd”. You are aked to rearrange the String. How many ways could you rearrange the String when repetition is allowed? Here repetition means, you can rearrange this way: bacd, cdba, dbac, etc.
- Challenge 3 : Can you show the difference between two types of permutation,where repetition is not allowed and allowed.
- What Next
Causes Supported

Amazon Watch
Supporting Indigenous Peoples. Protecting the Amazon.
http://amazonwatch.orgAmazon Watch is a nonprofit organization founded in 1996 to protect the rainforest and advance the rights of indigenous peoples in the Amazon Basin. We partner with indigenous and environmental organizations in campaigns for human rights, corporate accountability and the preservation of the Amazon's ecological systems.
Other books by this author
The Leanpub 60-day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
See full terms
Do Well. Do Good.
Authors have earned$11,600,486writing, publishing and selling on Leanpub, earning 80% royalties while saving up to 25 million pounds of CO2 and up to 46,000 trees.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers), EPUB (for phones and tablets) and MOBI (for Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
Top Books
C++20 - The Complete Guide
Nicolai M. JosuttisAll new language and library features of C++20 (for those who know previous C++ versions).
The book presents all new language and library features of C++20. Learn how this impacts day-to-day programming, to benefit in practice, to combine new features, and to avoid all new traps.
Buy early, pay less, free updates.
Other books:
Jetpack Compose internals
Jorge CastilloJetpack Compose is the future of Android UI. Master how it works internally and become a more efficient developer with it. You'll also find it valuable if you are not an Android dev. This book provides all the details to understand how the Compose compiler & runtime work, and how to create a client library using them.
Cronache di Domain-Driven Design
Francesco Strazzullo, Matteo Baglini, Gianluca Padovani, Emanuele DelBono, Marco Consolaro, Alessandro Colla, Uberto Barbini, Alberto Acerbis, Julie Camosseto, DDD Open, and Alberto BrandoliniCronache di Domain-Driven Design: un libro corale in italiano fatto di storie indipendenti tra loro, che sono il risultato dell’applicazione di Domain-Driven Design su progetti reali.
Ansible for DevOps
Jeff GeerlingAnsible is a simple, but powerful, server and configuration management tool. Learn to use Ansible effectively, whether you manage one server—or thousands.
R Programming for Data Science
Roger D. PengThis book brings the fundamentals of R programming to you, using the same material developed as part of the industry-leading Johns Hopkins Data Science Specialization. The skills taught in this book will lay the foundation for you to begin your journey learning data science. Printed copies of this book are available through Lulu.
OpenIntro Statistics
David Diez, Christopher Barr, Mine Cetinkaya-Rundel, and OpenIntroA complete foundation for Statistics, also serving as a foundation for Data Science.
Leanpub revenue supports OpenIntro (US-based nonprofit) so we can provide free desk copies to teachers interested in using OpenIntro Statistics in the classroom and expand the project to support free textbooks in other subjects.
More resources: openintro.org.
Functional event-driven architecture: Powered by Scala 3
Gabriel VolpeExplore the event-driven architecture (EDA) in a purely functional way, mainly powered by Fs2 streams in Scala 3!
Leverage your functional programming skills by designing and writing stateless microservices that scale, powered by stateful message brokers.
Mastering STM32 - Second Edition
Carmine NovielloWith more than 1200 microcontrollers, STM32 is probably the most complete ARM Cortex-M platform on the market. This book aims to be the first guide around that introduces the reader to this exciting MCU portfolio from ST Microelectronics and its official CubeHAL and STM32CubeIDE development environment.
CCIE Service Provider Version 4 Written and Lab Exam Comprehensive Guide
Nicholas RussoThe service provider landscape has changed rapidly over the past several years. Networking vendors are continuing to propose new standards, techniques, and procedures for overcoming new challenges while concurrently reducing costs and delivering new services. Cisco has recently updated the CCIE Service Provider track to reflect these changes; this book represents the author's personal journey in achieving that certification.
CCIE SP v5.0
Łukasz Bromirski, Piotr Jablonski, and Nicholas RussoAre you striving to prepare to and pass CCIE SP lab exam? Take the opportunity and get this workbook! With the attached initial cfg files you will prepare yourself for the CCIE SP exam as well as learn SP technologies applicable to all kinds of today modern networks! This workbook covers blueprint topics and provides challenging examples.
Top Bundles
- #1
Software Architecture for Developers: Volumes 1 & 2 - Technical leadership and communication
2 Books
"Software Architecture for Developers" is a practical and pragmatic guide to modern, lightweight software architecture, specifically aimed at developers. You'll learn:The essence of software architecture.Why the software architecture role should include coding, coaching and collaboration.The things that you really need to think about before... - #2
Practical FP in Scala + Functional event-driven architecture
2 Books
Practical FP in Scala (A hands-on approach) & Functional event-driven architecture, aka FEDA, (Powered by Scala 3), together as a bundle! The content of PFP in Scala is a requirement to understand FEDA so why not take advantage of this bundle!? - #3
All the Books of The Medical Futurist
6 Books
We put together the most popular books from The Medical Futurist to provide a clear picture about the major trends shaping the future of medicine and healthcare. Digital health technologies, artificial intelligence, the future of 20 medical specialties, big pharma, data privacy, digital health investments and how technology giants such as Amazon... - #4
CCIE Service Provider Ultimate Study Bundle
2 Books
Piotr Jablonski, Lukasz Bromirski, and Nick Russo have joined forces to deliver the only CCIE Service Provider training resource you'll ever need. This bundle contains a detailed and challenging collection of workbook labs, plus an extensively detailed technical reference guide. All of us have earned the CCIE Service Provider certification... - #6
Pattern-Oriented Memory Forensics and Malware Detection
2 Books
This training bundle for security engineers and researchers, malware and memory forensics analysts includes two accelerated training courses for Windows memory dump analysis using WinDbg. It is also useful for technical support and escalation engineers who analyze memory dumps from complex software environments and need to check for possible... - #7
Modern C++ Collection
3 Books
Get All about Modern C++C++ Standard Library, including C++20Concurrency with Modern C++, including C++20C++20Each book has about 200 complete code examples. Updates are included. When I update one of the books, you immediately get the updated bundle. You can expect significant updates to each new C++ standard (C++23, C++26, .. ) and also... - #9
Retromat eBook Bundle for Agile Retrospectives
2 Books
If you facilitate retrospectives this bundle is for you: "Plans for Retrospectives" helps beginners learn the lay of the land with tried-and-true plans. Once you know your way around, "Run great agile retrospectives" contains all 135+ activities in Retromat for you to mix and match.