Everybody can count 1, 2, 3. But solving competition counting problems is not easy. Counting related problems appear in various contents at all levels from AMC8 to IMO. For example, 2015 AIME I has 3 such questions of 15 in total. That is 20% of the total score!
Counting does not involve lots of complex formulas. With that said, to be good at counting will require systematic training. Knowing how to analyze and approach a problem is far more important than just remembering some formulas.
This course can be divided into two parts: the basics and the techniques.
The basic part covers the following topics:
- Three fundamental Counting principles
- the addition principle
- the multiplication principle
- the inclusion-exclusion principle (Venn's diagram)
- The permutation and combination formulas
- Elementary probability
In addition to basic knowledge and formulas, pitfalls and cautions when working on competition problems are also emphasized. Collectively, these should provide students with solid foundation for further study.
The techniques part focuses on those patterns and solutions that can be directly employed to solve actual problems in an effective way. The vast majority of competition problems are based on well-known patterns. Therefore a strong contender should be familiar with them in order to avoiding spending time on inventing individualized solution during the contest.
If knowing basic knowledge and formulas is similar to knowing how a chess piece can move, mastering patterns is similar to mastering all these opening, tactics and so on. While many courses and books on the market stop at teaching formulas, this course will provide you with unique opportunity to learn and help improve competition performance in a meaningful way.
As an increasingly popular topic in recent competitions, geometric probability is also covered at the end of the course. Upon completing, students should be able to immediately recognize and effectively solve such problems. An example of geometric probability question is 2015 AMC10A #25 / AMC12A #23.
The online course is organized into several sections. Each section contains a series of lessons. Each lesson comes with a video lecture, instant questions, and homework assignment. A video lecture may also embed interactive quizzes to ensure leaner's engagement. All homework will be reviewed and commented in time. The instructor will be happy to answer questions and provide suggestions. (firstname.lastname@example.org)
Reference book can be found here.
Grade 6 or above.
To enroll into this course, please register and login using your own account.