Difference between revisions of "Combinatorics/Introduction"
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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. | |
− | |||
− | * Counting | + | == Topics == |
+ | === Counting === | ||
+ | * Counting [[functions]] | ||
** [[Factorial]] | ** [[Factorial]] | ||
** [[Permutation]] | ** [[Permutation]] | ||
** [[Combination]] | ** [[Combination]] | ||
− | + | * [[Casework]] | |
− | + | * [[Complementary counting]] | |
− | + | * [[Constructive counting]] | |
− | + | * [[Overcounting]] | |
− | + | * [[Committee forming]] | |
− | + | * [[Distinguishability]] | |
− | + | === Probability === | |
− | * Probability | + | * Probability techniques |
− | ** | + | ** Complementary probability |
− | + | * [[Geometric probability]] | |
− | + | * [[Expected value]] | |
− | * | + | === Miscellaneous === |
− | ** [[Pascal's triangle | + | * [[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] |
=== 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 == |
Revision as of 21:09, 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.
Contents
Topics
Counting
- Counting functions
- Casework
- Complementary counting
- Constructive counting
- Overcounting
- Committee forming
- Distinguishability
Probability
- Probability techniques
- Complementary probability
- Geometric probability
- Expected value