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.
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
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