Our lives are full of combinations. Combinatorial mathematics is just the science to deal with combinations of discrete items. As an ancient field, the history of combinatorial mathematics can be traced back over 4000 years to the age of the Great Yu in ancient China. Today, combinatorial mathematics is regarded as the basis of computer science since the algorithms in programming heavily rely on the analysis of the discrete elements.
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Our lives are full of combinations. Combinatorial mathematics is just the science to deal with combinations of discrete items. As an ancient field, the history of combinatorial mathematics can be traced back over 4000 years to the age of the Great Yu in ancient China. Today, combinatorial mathematics is regarded as the basis of computer science since the algorithms in programming heavily rely on the analysis of the discrete elements.
Our lives are full of combinations. Combinatorial mathematics is just the science to deal with combinations of discrete items. As an ancient field, the history of combinatorial mathematics can be traced back over 4000 years to the age of the Great Yu in ancient China. Today, combinatorial mathematics is regarded as the basis of computer science since the algorithms in programming heavily rely on the analysis of the discrete elements.
Instead of relying on the traditional mathematical "theorem - proof" format, this course demonstrates various principles in an intuitive manner with ancient stories, the scenes of movies and even a magic show. What you’ll learn:
- The counting principles based on the basic operations “+”, “-”, “*”, “/”;
- Generating functions
- Recurrent number serials such as Fibonacci number, Catalan number, and more
- Pigeon hole principles
- Inclusion and exclusion principles
- Polya counting based on group theory
This course is based on a highly regarded on-campus Tsinghua class called Combinatorics, and is ideal for students who are interested in mathematics or computer science. Enroll today and learn the mathematical theory needed to solve the real-world problems!
Every aspect of our lives is full of combinations, and combinatorics is the study of discrete things. As a subject with a long history, the development of combinatorics can be traced back to the era of Dayu 4,000 years ago. Nowadays, combinatorial mathematics has opened a new chapter with the development of computer science. Since the analysis and implementation of program algorithms are based on the analysis of discrete objects, combinatorial mathematics has developed into a basic theory of computer science.
This course changes the "theorem-proof" model of previous mathematics teaching and leads everyone to gradually explore the source of knowledge from the shallower to the deeper. There are ancient stories, movie clips, and even magic to interpret mathematical concepts. These forms are designed to lead everyone to feel the beauty of mathematics. Specific teaching content includes:
- Counting rules based on four arithmetic operations;
- parent function;
- Recursive sequences, such as Fibonacci numbers, Cattelan numbers, etc.;
- pigeonhole principle;
- Inclusion-exclusion principle;
- Polya's theorem based on group theory.
The content and outline of this course are mainly based on the excellent course "Combinatorics" of Tsinghua University. Through the study of this course, learners can have an in-depth understanding of the abstract theory and specific methods of counting, and thus deeply understand the role of combinatorial mathematics in promoting the development of computer theory. .
FAQ
I don’t speak Chinese, can I learn the course?
All the materials are in English. Though the original video was recorded in Chinese, the course team record the corresponding dubbing in English. All the audio and subtitles are processed to fit the English dubbing as much as possible, so that you can enjoy this wonderful course in English.
What are the textbook and the reference books for this course?
There is no textbook requirement for this course. The handouts distributed every week are critical. The following books are references
- Richard A. Brualdi; Introductory Combinatorics (5th edition), Pearson, 2009
- J.H.van Lint and R.M. Wilson; A course in Combinatorics, Cambridge University Press, 2001
- Lu Kaicheng, "Combinatorics" fourth edition, Tsinghua University Press
What is the grading breakdown?
- 70% quizzes and exercises
- 30% final exam
How can I get the certificate?
If your final score is no less than 60.
Do I need to know how to program to learn this class?
Not necessary. This course is a math course which is based on fundamental theory. But to help the students to have the intuitive feel of the effects of the theory, we also provide a code lib that you can compare different implementations by running different programs.
What's inside
Learning objectives
- Counting principles in our daily lives
- Applying math to computer science and financial analysis
- The science behind combinations of discrete items
- Understand the history of combinatorics in life and mathematics
- In-depth study of abstract theories and concrete methods of counting
- Deeply understand the role of combinatorial mathematics in promoting the development of computer theory
- Counting principles in our daily lives
- Applying math to computer science and financial analysis
- The science behind combinations of discrete items
- Understand the history of combinatorics in life and mathematics
- In-depth study of abstract theories and concrete methods of counting
- Deeply understand the role of combinatorial mathematics in promoting the development of computer theory
Good to know
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Reviews summary
Intuitive combinatorics
Activities
Review 'Introductory Combinatorics' by Richard A. Brualdi
Show steps
Familiarize yourself with the fundamental principles and techniques of combinatorics to provide a solid foundation for the course.
View
Introductory Combinatorics, 5th edition
on Amazon
Show steps
-
Read Chapters 1 and 2 to gain an overview of counting principles and basic combinatorics.
-
Solve the practice problems at the end of each chapter to test your understanding. (Optional)
-
Attend the first few lectures to identify any areas where you may need additional support.
Attend a virtual study session with classmates
Show steps
Engage with peers to discuss course concepts, clarify doubts, and reinforce your learning.
Show steps
-
Organize a virtual study session with 2-3 classmates.
-
Choose a specific topic or problem set to focus on.
-
Discuss the topic, ask questions, and work together to solve problems.
Solve practice problems from 'Combinatorics' by J.H. van Lint and R.M. Wilson
Show steps
Reinforce your understanding of combinatorial techniques by solving a variety of practice problems.
View
A Course in Combinatorics
on Amazon
Show steps
-
Choose a section from the book that aligns with the current course material.
-
Attempt to solve 5-10 problems from that section independently.
-
Review your solutions and identify any areas where you need further clarification.
Three other activities
Expand to see all activities and additional details
Show all six activities
Create a visual representation of a combinatorial problem
Show steps
Enhance your problem-solving skills by visualizing combinatorial concepts.
Browse courses on
Graph Theory
Show steps
-
Choose a combinatorial problem that interests you.
-
Represent the problem using a diagram, chart, or other visual format.
-
Analyze the visual representation to identify patterns and relationships.
Follow tutorials on Polya's Theorem and its applications
Show steps
Enhance your understanding of Polya's Theorem and its use in counting problems.
Show steps
-
Search for online tutorials or videos that explain Polya's Theorem.
-
Follow along with the tutorial and work through the examples provided.
-
Apply the theorem to solve a few problems on your own.
Attend a workshop on combinatorial game theory
Show steps
Expand your knowledge and explore real-world applications of combinatorial game theory.
Browse courses on
Game Theory
Show steps
-
Identify and register for a workshop on combinatorial game theory.
-
Attend the workshop and engage actively in the discussions and exercises.
-
Reflect on the concepts learned and their potential applications in your own research or career.
Review 'Introductory Combinatorics' by Richard A. Brualdi
Show steps
Familiarize yourself with the fundamental principles and techniques of combinatorics to provide a solid foundation for the course.
View
Introductory Combinatorics, 5th edition
on Amazon
Show steps
- Read Chapters 1 and 2 to gain an overview of counting principles and basic combinatorics.
- Solve the practice problems at the end of each chapter to test your understanding. (Optional)
- Attend the first few lectures to identify any areas where you may need additional support.
Attend a virtual study session with classmates
Show steps
Engage with peers to discuss course concepts, clarify doubts, and reinforce your learning.
Show steps
- Organize a virtual study session with 2-3 classmates.
- Choose a specific topic or problem set to focus on.
- Discuss the topic, ask questions, and work together to solve problems.
Solve practice problems from 'Combinatorics' by J.H. van Lint and R.M. Wilson
Show steps
Reinforce your understanding of combinatorial techniques by solving a variety of practice problems.
View
A Course in Combinatorics
on Amazon
Show steps
- Choose a section from the book that aligns with the current course material.
- Attempt to solve 5-10 problems from that section independently.
- Review your solutions and identify any areas where you need further clarification.
Create a visual representation of a combinatorial problem
Show steps
Enhance your problem-solving skills by visualizing combinatorial concepts.
Browse courses on
Graph Theory
Show steps
- Choose a combinatorial problem that interests you.
- Represent the problem using a diagram, chart, or other visual format.
- Analyze the visual representation to identify patterns and relationships.
Follow tutorials on Polya's Theorem and its applications
Show steps
Enhance your understanding of Polya's Theorem and its use in counting problems.
Show steps
- Search for online tutorials or videos that explain Polya's Theorem.
- Follow along with the tutorial and work through the examples provided.
- Apply the theorem to solve a few problems on your own.
Attend a workshop on combinatorial game theory
Show steps
Expand your knowledge and explore real-world applications of combinatorial game theory.
Browse courses on
Game Theory
Show steps
- Identify and register for a workshop on combinatorial game theory.
- Attend the workshop and engage actively in the discussions and exercises.
- Reflect on the concepts learned and their potential applications in your own research or career.
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