Difference between revisions of "Combinatorics/Introduction"
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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. |
| − | == | + | == Topics == |
| − | + | === Counting === | |
| − | + | * Counting [[functions]] | |
| − | * [[ | + | ** [[Factorial]] |
| − | * [[ | + | ** [[Permutation]] |
| − | * [[ | + | ** [[Combination]] |
| − | * [[ | + | * [[Casework]] |
| − | * [[ | ||
* [[Complementary counting]] | * [[Complementary counting]] | ||
| − | |||
* [[Constructive counting]] | * [[Constructive counting]] | ||
| + | * [[Overcounting]] | ||
* [[Committee forming]] | * [[Committee forming]] | ||
| − | |||
| − | |||
* [[Distinguishability]] | * [[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 === | ||
| + | * [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.
Contents
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.
