Difference between revisions of "Combinatorics/Introduction"
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| − | An introduction to [[combinatorics]] | + | 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 == | == Topics == | ||
| Line 14: | Line 14: | ||
* [[Distinguishability]] | * [[Distinguishability]] | ||
=== Probability === | === Probability === | ||
| − | + | * Counting techniques in probability | |
| − | |||
* [[Geometric probability]] | * [[Geometric probability]] | ||
* [[Expected value]] | * [[Expected value]] | ||
| Line 28: | Line 27: | ||
=== Books === | === Books === | ||
* [https://artofproblemsolving.com/store/item/intro-counting AoPS Introduction to Counting & Probability Book] | * [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 === | ||
| Line 37: | Line 37: | ||
== 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 20:39, 6 October 2023
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.
