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. | |
| − | |||
| − | * | + | == 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 19:34, 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.
Contents
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)
