Combinatorics/Introduction: Difference between revisions
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An introduction to [[combinatorics]] primarily involves [[counting]] and [[probability]]. As problem-solving ability improves, the scope of combinatorics grows, leading students to the intermediate level. | |||
* | == Topics == | ||
=== Counting === | |||
* Counting functions | |||
** [[Factorial]] | ** [[Factorial]] | ||
** [[Permutation]] | ** [[Permutation]] | ||
** [[Combination]] | ** [[Combination]] | ||
* Common stragegies | |||
** [[Casework]] | |||
** [[Complementary counting]] | |||
** [[Constructive counting]] | |||
** [[Overcounting]] | |||
* [[Committee forming]] | |||
* [[Distinguishability]] | |||
* | === Probability === | ||
** | * Probability techniques | ||
** [[Geometric probability]] | ** Addition and product rules | ||
** Complementary probability | |||
* | * [[Geometric probability]] | ||
** [[Pascal's triangle | * [[Expected value]] | ||
** [[ | === Miscellaneous === | ||
* [[Combinatorial identities]] | |||
** [[Pascal's triangle]] | |||
** [[Block walking]] | |||
* [[Binomial theorem]] | |||
== Introductory combinatorics resources == | == Introductory combinatorics resources == | ||
Revision as of 18:34, 17 May 2021
An introduction to combinatorics primarily involves counting and probability. As problem-solving ability improves, the scope of combinatorics grows, leading students to the intermediate level.
Topics
Counting
- Counting functions
- Common stragegies
- Committee forming
- Distinguishability
Probability
- Probability techniques
- Addition and product rules
- Complementary probability
- Geometric probability
- Expected value
Miscellaneous
Introductory combinatorics resources
Books
- the Art of Problem Solving: Introduction to Counting and Probability by David Patrick (details)
