Combinatorics/Introduction: Difference between revisions
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An introduction to [[combinatorics]] concerns mostly [[counting]] and [[probability]]. As problem-solving ability becomes more advanced, the scope of combinatorics grows, leading students to the [[Combinatorics/Intermediate | intermediate]] level. | |||
* Counting | == Topics == | ||
=== Counting === | |||
* Counting [[functions]] | |||
** [[Factorial]] | ** [[Factorial]] | ||
** [[Permutation]] | ** [[Permutation]] | ||
** [[Combination]] | ** [[Combination]] | ||
* [[Casework]] | |||
* [[Complementary counting]] | |||
* [[Constructive counting]] | |||
* [[Overcounting]] | |||
* [[Committee forming]] | |||
* [[Distinguishability]] | |||
=== Probability === | |||
* Counting techniques in probability | |||
* | * [[Geometric probability]] | ||
* [[Expected value]] | |||
== | === Miscellaneous === | ||
* [[Combinatorial identities]] | |||
** [[Pascal's triangle]] | |||
** [[Block walking]] | |||
* [[Binomial theorem]] | |||
== Resources == | |||
=== Books === | === Books === | ||
* | * [https://artofproblemsolving.com/store/item/intro-counting AoPS Introduction to Counting & Probability Book] | ||
* Ritvik Rustagi's [https://www.tmasacademy.com/ace-the-amc10-12-free-book ACE The AMC 10 and AMC 12 book] has a chapter on combinatorics. | |||
=== Classes === | === Classes === | ||
* [[AoPS Online School/Introduction to Counting & Probability Course |Introduction to Counting & Probability]] | * [[AoPS Online School/Introduction to Counting & Probability Course |AoPS Introduction to Counting & Probability Course]] | ||
=== Videos === | === Videos === | ||
* [https://artofproblemsolving.com/videos/counting AoPS Counting & Probability Videos] | * [https://artofproblemsolving.com/videos/counting AoPS Counting & Probability Videos] | ||
* [https://www.youtube.com/watch?v=t6a4uHEwQnM&list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT Sohil Rathi AMC8 Math Competition Preperation Playlist] | |||
== See also == | == See also == | ||
* [[Combinatorics/Intermediate | Intermediate | * [[Combinatorics/Intermediate | Intermediate combinatorics]] | ||
* [[Combinatorics/Olympiad | Olympiad | * [[Combinatorics/Olympiad | Olympiad combinatorics]] | ||
[[Category:Combinatorics]] | |||
[[Category:Introductory Mathematics Topics]] | [[Category:Introductory Mathematics Topics]] | ||
Latest revision as of 21:35, 1 August 2025
An introduction to combinatorics concerns mostly counting and probability. As problem-solving ability becomes more advanced, the scope of combinatorics grows, leading students to the intermediate level.
Topics
Counting
- Counting functions
- Casework
- Complementary counting
- Constructive counting
- Overcounting
- Committee forming
- Distinguishability
Probability
- Counting techniques in probability
- Geometric probability
- Expected value
Miscellaneous
Resources
Books
- AoPS Introduction to Counting & Probability Book
- Ritvik Rustagi's ACE The AMC 10 and AMC 12 book has a chapter on combinatorics.
