Discrete Mathematical Algorithm, and Data Structure
This book is 60% complete
Last updated on 20200403
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.
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?
 Different types of Data Structures used in C, C++, PHP, Java, Python, Dart and C
 What is Big Data
 Time Complexity
 Bg O Notation
 Different type of Sorting Algorithm
 Set, Symmetric Difference and Propositional Logic
 What is Set in Discrete Mathematics and how it is implemented in Java Data Structures
 How we can find symmetric difference in Java
 How to implement propositional logic in Java
 Combinatorial Objects, Permutation and Combination, Combination with Repetition, and Pascal’s Triangle
 What is Combinatorial object, permutation and combination and how we can implement that concepts with the help of Java
 What is combinations with repetition and how it can be implemented
 How we can implement Pascal’s Triangle in Java

7. Rule of Sum and Products, Truth Tables, Logic Laws
 What are rule of sum and rule of products
 How to implement truth tables and conditionals in Java
 How to implement Logic Laws and Exclusive OR in Java

8. Discrete Mathematical Functions and its Implementation
 What is function in Discrete Mathematics and how we can implement that concept in Java
 How to implement inverse of function and other functions that are present in Discrete Mathematics

9. Modular Arithmetic, Primes and GCD, and Euclidean Algorithm
 What is Modular Arithmetic
 How to find Primes and GCD
 Understanding Euclidean Algorithm and its implementation in Java

10. More on Algorithm and Data Structures in Java and how they are related to Discrete Mathematical conceptions
 More on Algorithm
 How to structure data in an efficient way
 More on Data Structures

Appendix: Further reading and what is Next
 Sequence and Series
 How we can use Sequence and Series to structure our Data
 What could be the next challenges to learn more about the relationship between Discrete Mathematical conceptions and Algorithm as well as Date Structures
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