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.
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!
What you'll learn:
- Counting principles in our daily lives
- Applying math to computer science and financial analysis
- The science behind combinations of discrete items
Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed. In the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers.
MOOCs – Massive Open Online Courses – enable students around the world to take university courses online. This guide, by the instructors of edX’s most successful MOOC in 2013-2014, Principles of Written English (based on both enrollments and rate of completion), advises current and future students how to get the most out of their online study, covering areas such as what types of courses are offered and who offers them, what resources students need, how to register, how to work effectively with other students, how to interact with professors and staff, and how to handle assignments. This second edition offers a new chapter on how to stay motivated. This book is suitable for both native and non-native speakers of English, and is applicable to MOOC classes on any subject (and indeed, for just about any type of online study).