Oct 13th 2016

Combinatorial Mathematics 组合数学 (edX)

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Discover how to apply counting principles and combinatorics to solve problems in computer science, financial analysis, and your daily life.

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 could be traced back over 4000 years to the age of the Great Yu in ancient China. Nowadays, it is regarded as the fundamental knowledge 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, we show various principles in an intuitive manner with ancient stories, the scenes of movies and even the magic show. Specific topics covered include:

- The counting principles based on the basic operations “+”, “-”, “*”, “/”;

- Generating functions;

- Recurrent number serials such as Fibonacci number, Catalan number etc;

- Pigeon hole principles;

- Inclusion and exclusion principles;

- Polya counting based on group theory.

The contents of this course are mainly based on the corresponding Tsinghua Class (Combinatorics) -- a course that has been awarded as the quality curriculum in Tsinghua. It is ideal for students who are interested in mathematics or computer science. It will lead you to gasp the mathematical theory essentially needed to solve the real-world applications.