Difference between revisions of "Combinatorics"
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'''Combinatorics''' is the study of counting. Different kinds of counting problems can be approached by a variety of techniques. | '''Combinatorics''' is the study of counting. Different kinds of counting problems can be approached by a variety of techniques. | ||
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== Introductory Topics == | == Introductory Topics == | ||
The following topics help shape an introduction to counting techniques: | The following topics help shape an introduction to counting techniques: | ||
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* [[Ramsey numbers]] | * [[Ramsey numbers]] | ||
* [[Catalan Numbers]] | * [[Catalan Numbers]] | ||
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| + | == Resources == | ||
| + | Listed below are various combinatorics resources including books, classes and websites. | ||
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| + | === Books === | ||
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| + | * Introductory | ||
| + | ** ''the Art of Problem Solving Introduction to Counting and Probability'' by David Patrick [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 (details)] | ||
== See also == | == See also == | ||
* [[Probability]] | * [[Probability]] | ||
Revision as of 12:28, 1 July 2006
Combinatorics is the study of counting. Different kinds of counting problems can be approached by a variety of techniques.
Contents
Introductory Topics
The following topics help shape an introduction to counting techniques:
- Correspondence
- Venn diagram
- Combinations
- Permutations
- Overcounting
- Complementary counting
- Casework
- Constructive counting
- Committee forming
- Pascal's Triangle
- Combinatorial identities
- Binomial Theorem
Intermediate Topics
- Principle of Inclusion-Exclusion
- Conditional Probability
- Recursion
- Correspondence
- Generating functions
- Partitions
- Geometric probability
Olympiad Topics
Resources
Listed below are various combinatorics resources including books, classes and websites.
Books
- Introductory
- the Art of Problem Solving Introduction to Counting and Probability by David Patrick (details)
