Discrete Mathematics in the AI Era with Python
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Description
Book Introduction
Let's learn about the practical applications of discrete mathematics and implement them directly in Python!
All fields of computer science require mathematical logic and thinking to solve real-world problems.
This book carefully selects essential topics in discrete mathematics that computer engineering students must know.
By following the clear and detailed explanations, you can lay the foundation for discrete mathematics theory required for computer engineering students.
This book's rich examples and practice problems will help you understand the concepts accurately, and you can develop logical thinking by implementing each discrete mathematics topic directly with Python code.
Additionally, you can simultaneously develop problem-solving and coding skills, which are essential in the AI era.
Let's experience the harmony between the logic of discrete mathematics and programming through this book!
All fields of computer science require mathematical logic and thinking to solve real-world problems.
This book carefully selects essential topics in discrete mathematics that computer engineering students must know.
By following the clear and detailed explanations, you can lay the foundation for discrete mathematics theory required for computer engineering students.
This book's rich examples and practice problems will help you understand the concepts accurately, and you can develop logical thinking by implementing each discrete mathematics topic directly with Python code.
Additionally, you can simultaneously develop problem-solving and coding skills, which are essential in the AI era.
Let's experience the harmony between the logic of discrete mathematics and programming through this book!
- You can preview some of the book's contents.
Preview
index
CHAPTER 01.
Basic concepts for discrete mathematics
1.1 What is discrete mathematics?
1.2 Discrete Mathematics Curriculum
1.3 A typical problem in discrete mathematics: magic cards
Practice problems
Programming practice
CHAPTER 02.
Natural numbers and matrices
2.1 Number system
2.2 Natural numbers and integers
2.3 Prime numbers and the greatest common divisor
2.4 Matrix concept and determinant
2.5 Systems of linear equations and inverse matrices
Practice problems
Programming practice
CHAPTER 03.
Mathematical models and logic
3.1 Mathematical Model
3.2 Logical reasoning
3.3 Proof and Program Verification
3.4 Application: Knowledge Base System
Practice problems
Programming practice
index
CHAPTER 04.
set
4.1 Concept of set
4.2 Set operations
4.3 Algebraic properties of sets
Practice problems
Programming practice
CHAPTER 05.
relationship
5.1 Product set
5.2 Relationships and Relationship Expressions
5.3 Route
5.4 Nature of Relationships
5.5 Inverse and Composite Relationships
5.6 Connections and Warshall's Algorithm
Practice problems
Programming practice
CHAPTER 06.
function
6.1 Definition of functions
6.2 Injective functions, surjective functions, and bijective functions
6.3 Inverse and composite functions
6.4 Special functions
6.5 Application: Permutations
Practice problems
Programming practice
CHAPTER 07.
Partial order relations and Boolean algebra
7.1 Partial order relations
7.2 Upper and lower limits
7.3 Grid
7.4 Special types of grids
7.5 Boolean Algebra
7.6 Application: Design of a 2-bit adder
Practice problems
Programming practice
CHAPTER 08.
graph
8.1 Basic Concepts of Graphs
8.2 Various graphs
8.3 Graph Search and Shortest Paths
8.4 Planar Graphs and Graph Coloring
CHAPTER 09.
tree
9.1 Basic Tree Concepts
9.2 Labeled Trees and Minimum Spanning Trees
9.3 Binary Trees and Tree Traversal Algorithms
Practice problems
Programming practice
CHAPTER 10.
Counting cases and probability
10.1 Basic Principles of the Century
10.2 Permutations and Combinations
10.3 Binomial and polynomial theorems
10.4 Fundamentals of Probability and Conditional Probability
Practice problems
CHAPTER 11.
Ignition Relationships and Algorithms
11.1 Ignition Relationship
11.2 Algorithms and Pseudocode
11.3 Algorithm Complexity
11.4 Various Algorithms
Practice problems
Programming practice
CHAPTER 12.
Formal languages and automata
12.1 Formal Language
12.2 Formal Grammar
12.3 Grammar notation
12.4 Finite Automata
12.5 Application: Missionaries and Cannibals
Practice problems
Programming practice
Appendix: Notation of concepts used in discrete mathematics
Search
Basic concepts for discrete mathematics
1.1 What is discrete mathematics?
1.2 Discrete Mathematics Curriculum
1.3 A typical problem in discrete mathematics: magic cards
Practice problems
Programming practice
CHAPTER 02.
Natural numbers and matrices
2.1 Number system
2.2 Natural numbers and integers
2.3 Prime numbers and the greatest common divisor
2.4 Matrix concept and determinant
2.5 Systems of linear equations and inverse matrices
Practice problems
Programming practice
CHAPTER 03.
Mathematical models and logic
3.1 Mathematical Model
3.2 Logical reasoning
3.3 Proof and Program Verification
3.4 Application: Knowledge Base System
Practice problems
Programming practice
index
CHAPTER 04.
set
4.1 Concept of set
4.2 Set operations
4.3 Algebraic properties of sets
Practice problems
Programming practice
CHAPTER 05.
relationship
5.1 Product set
5.2 Relationships and Relationship Expressions
5.3 Route
5.4 Nature of Relationships
5.5 Inverse and Composite Relationships
5.6 Connections and Warshall's Algorithm
Practice problems
Programming practice
CHAPTER 06.
function
6.1 Definition of functions
6.2 Injective functions, surjective functions, and bijective functions
6.3 Inverse and composite functions
6.4 Special functions
6.5 Application: Permutations
Practice problems
Programming practice
CHAPTER 07.
Partial order relations and Boolean algebra
7.1 Partial order relations
7.2 Upper and lower limits
7.3 Grid
7.4 Special types of grids
7.5 Boolean Algebra
7.6 Application: Design of a 2-bit adder
Practice problems
Programming practice
CHAPTER 08.
graph
8.1 Basic Concepts of Graphs
8.2 Various graphs
8.3 Graph Search and Shortest Paths
8.4 Planar Graphs and Graph Coloring
CHAPTER 09.
tree
9.1 Basic Tree Concepts
9.2 Labeled Trees and Minimum Spanning Trees
9.3 Binary Trees and Tree Traversal Algorithms
Practice problems
Programming practice
CHAPTER 10.
Counting cases and probability
10.1 Basic Principles of the Century
10.2 Permutations and Combinations
10.3 Binomial and polynomial theorems
10.4 Fundamentals of Probability and Conditional Probability
Practice problems
CHAPTER 11.
Ignition Relationships and Algorithms
11.1 Ignition Relationship
11.2 Algorithms and Pseudocode
11.3 Algorithm Complexity
11.4 Various Algorithms
Practice problems
Programming practice
CHAPTER 12.
Formal languages and automata
12.1 Formal Language
12.2 Formal Grammar
12.3 Grammar notation
12.4 Finite Automata
12.5 Application: Missionaries and Cannibals
Practice problems
Programming practice
Appendix: Notation of concepts used in discrete mathematics
Search
Detailed image
Publisher's Review
An Introduction to Discrete Mathematics with Python
This book explains the essential discrete mathematics topics recommended by the ACM and IEEE for the 2023 computer science curriculum, tailored to the domestic classroom environment.
We've included plenty of examples and practice problems to help even students with limited basics understand the concepts, and cover a variety of topics, including magic cards, one-stroke drawing, and the Tower of Hanoi.
[Programming Practice] allows you to develop both problem-solving and coding skills by implementing each discrete mathematics topic in Python.
This book explains the essential discrete mathematics topics recommended by the ACM and IEEE for the 2023 computer science curriculum, tailored to the domestic classroom environment.
We've included plenty of examples and practice problems to help even students with limited basics understand the concepts, and cover a variety of topics, including magic cards, one-stroke drawing, and the Tower of Hanoi.
[Programming Practice] allows you to develop both problem-solving and coding skills by implementing each discrete mathematics topic in Python.
GOODS SPECIFICS
- Date of issue: June 28, 2024
- Page count, weight, size: 544 pages | 1,093g | 188*257*21mm
- ISBN13: 9791156640417
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