September 21, 2011 10:16 AM Subscribe
posted by kmz (38 comments total)
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Counting is one of the first and simplest concepts most people are taught. But when you get beyond simple 123s, counting can become an advanced subject
all its own. Essentially the science of counting, combinatorics
is a key component of everything from abstract algebra
Basic combinatorics (such as the number of ways can you choose a 3-person committee from 5 potential candidates) can be accessible
to those with basic mathematical knowledge. Advanced topics such as Ramsey Theory
can give rise to things like Graham's Number
, so large that even stacked exponential notation cannot be used to describe it. Combinatorics was also one of Erdös's favorite subjects
(PDF, combinatorics article starts on page 5).
Want to dive in yourself?
- Carl Wagner offers an introductory text (PDF) covering probability and statistics as well.
- Similarly, a George Tech course intro (PDF) on combinatorics.
- MathReference has a basic tutorial, thought the site layout and navigation are a bit cumbersome.
- OpenCourseWare has an undergrad level combinatorics course here.
(Advanced counting can also lead to infinity, covered previously