Discrete Mathematical Algorithm, and Data Structure
This book is 60% complete
Last updated on 2020-04-03
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
Table of Contents
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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
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2. Introduction to Programming Language and Boolean Algebra
- Logic, Mathematics, and Programming Language
- Introduction to Boolean Algebra
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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
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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
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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
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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
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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
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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
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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
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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
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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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