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
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. The objects of data structures are basically objects of discrete mathematics. This book tries to bridge the gap between two major components of Mathematics and Computer Science.
In any computer science course, studying discrete mathematics is essential, although they are taught separately, except in a few cases. 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.
Hope, this book will fill the gap. Readers will learn discrete mathematical abstracts as well as its implementation in algorithm and data structures shown in various programming language, such as C++, Java, C#, Python and Dart. This book combines two major components of Computer Science under one roof.
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.
About the Author
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
-
2. Introduction to Programming Language and Boolean Algebra
- Logic, Mathematics, and Programming Language
- Introduction to Boolean Algebra
-
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
-
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
-
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
-
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
-
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++
-
8. Time Complexity
- Order of n, or O(n)
- Big O Notation
-
9. Set, Symmetric Difference and Propositional Logic
- Why Set is important in Data Structures
- How Symmetric Difference and Propositional Logic combine
-
10. Combinatorics and Counting, Permutation and Combinations
- Permutation and Combination
- 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
Authors have earned$9,690,775writing, 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
The Leanpub 45-day 100% Happiness Guarantee
Within 45 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
See full terms
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
- #1
Ansible for Kubernetes
Jeff GeerlingAnsible is a powerful infrastructure automation tool. Kubernetes is a powerful application deployment platform. Learn how to use these tools to automate massively-scalable, highly-available infrastructure.
- #2
Practical FP in Scala: A hands-on approach
Gabriel VolpeA practical book aimed for those familiar with functional programming in Scala who are yet not confident about architecting an application from scratch.
Together, we will develop a purely functional application using the best libraries in the Cats ecosystem, while learning about design patterns and best practices.
- #3
Functional Design and Architecture
Alexander GraninSoftware Design in Functional Programming, Design Patterns and Practices, Methodologies and Application Architectures. How to build real software in Haskell with less efforts and low risks. The first complete source of knowledge.
- #4
Production Haskell
Matt ParsonsAre you excited about Haskell, but don't know where to begin? Are you thrilled by the technical advantages, but worried about the unknown pitfalls? This book has you covered.
- #5
Tame your Work Flow
Steve Tendon and Daniel DoironDo you need a high performance enterprise governance approach improving management, execution and delivery while dealing with multiple projects/products, events, stakeholders and teams? Giving you better bottom line results, faster time to market, less work, better predictability, happier employees, and delighted clients? Then learn about TameFlow!
- #6
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.
- #7
Machine Learning Engineering
Andriy Burkov"If you intend to use machine learning to solve business problems at scale, I'm delighted you got your hands on this book."
—Cassie Kozyrkov, Chief Decision Scientist at Google
"Foundational work about the reality of building machine learning models in production."
—Karolis Urbonas, Head of Machine Learning and Science at Amazon
- #8
C++ Best Practices
Jason TurnerLevel up your C++, get the tools working for you, eliminate common problems, and move on to more exciting things!
- #9
Composing Software
Eric ElliottAll software design is composition: the act of breaking complex problems down into smaller problems and composing those solutions. Most developers have a limited understanding of compositional techniques. It's time for that to change.
- #10
El Manual del Manager
Keyvan Akbary, Félix López, and Álvaro Salazar¿Has deseado alguna vez el haber tenido una buena introducción al rol del Engineering Manager? En este libro aprenderás lo necesario para ejercer el rol de una manera efectiva: Expectativas y Responsabilidades del Rol, 1-1s, Ayudar a Crecer, Objetivos, Planes de Carrera, Cultura, Feedback, Contratación, Cultura de Producto y mucho más.
Top Bundles
- #1
The Tester's Library
8 Books
The Tester's Library consists of eight five-star books that every software tester should read and re-read. As bound books, this collection would cost over $200. Even as e-books, their price would exceed $80, but in this bundle, their cost is only $49.99. Here are the books, and why they should be in your library: Perfect Software and Other... - #2
agile
11 Books
In this bundle, you will find 10 different agile books. They are about different aspects of being agile. - finding a job - doing coding dojo's - Retrospectives - Personal kanban - a non-typical coaching book and even a book that gives you an insight in the lives of some agile people. - #3
WTFlop 6M + HU - Beta Bundle
6 Books
- #4
Marionette.js A to Z
3 Books
Marionette.js has become a popular Backbone-based javascript library, because it helps you avoid boiler-plate code and focus on what makes your app special. But how do you get started?Whether you want to finally get started with dynamic client-side programming (like one reader did), or are an experienced front-end dev who has inherited a... - #5
Build A Better Backbone App
3 Books
The best way to learn new development skills is through experience, but that takes time you don't have.Get the best of both worlds with this bundle: you'll learn how to produce modern web applications by learning from experienced developers like Derick Bailey and David Sulc. BackboneJS is one of the favorite tools on the web today, but it... - #6
General Systems Thinker Bundle
5 Books
The General Systems Thinker Bundle is just that: a bundle of five books to advance the reader one giant step toward improved thinking, based on General Systems principles. Four of the books are the complete General Systems Series. The fifth is fictional piece which shows some general systems thinkers in action. It's a mystery in which a group of... - #7
Experiential Learning Bundle
4 Books
This bundle provides all four volumes of the popular Experiential Learning Series at a savings of $20 over the price if purchased separately. - #8
Ansible Bundle
2 Books
After getting up and running with Ansible in Jeff Geerling's Ansible for DevOps, strengthen your skills managing tens to thousands of instances and services in Amazon's AWS cloud with Yan Kurniawan's Ansible for AWS. - #9
Learn ECMAScript 6 inside and out
2 Books
For any technology, it helps to get multiple points of view on the functionality to get the best possible understanding. For ECMAScript 6/2015, no two resources are recommended more frequently thanExploring ES6by Dr. Axel Rauschmayer andUnderstanding ECMAScript 6by Nicholas C. Zakas. These two points of view, investigating the specification and... - #10
Software architecture, for systems old and new
2 Books
This bundle includes books about hands-on software architecture.
