Difference between revisions of "Combinatorics/Introduction"

(Introductory topics in combinatorics)
 
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[[Combinatorics]] is the study of counting [[discrete quantity | discrete quantities]].
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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.
  
== Introductory topics in combinatorics ==
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== Topics ==
The following topics provide a good study in introductory combinatorics.
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=== Counting ===
 
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* Counting [[functions]]
* [[Correspondence]]
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** [[Factorial]]
* [[Venn diagram]]
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** [[Permutation]]
* [[Permutations]]
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** [[Combination]]
* [[Combinations]]
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* [[Casework]]
* [[Overcounting]]
 
 
* [[Complementary counting]]
 
* [[Complementary counting]]
* [[Casework]]
 
 
* [[Constructive counting]]
 
* [[Constructive counting]]
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* [[Overcounting]]
 
* [[Committee forming]]
 
* [[Committee forming]]
* [[Pascal's Triangle]]
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* [[Distinguishability]]
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=== Probability ===
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* Counting techniques in probability
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* [[Geometric probability]]
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* [[Expected value]]
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=== Miscellaneous ===
 
* [[Combinatorial identities]]
 
* [[Combinatorial identities]]
* [[Distinguishability]]
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** [[Pascal's triangle]]
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** [[Block walking]]
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* [[Binomial theorem]]
  
== Introductory combinatorics resources ==
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== Resources ==
  
 
=== Books ===
 
=== Books ===
* ''the Art of Problem Solving Introduction to Counting and Probability'' by David Patrick [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 (details)]
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* [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]] ([http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesS.php#begcount information page])
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* [[AoPS Online School/Introduction to Counting & Probability Course |AoPS Introduction to Counting & Probability Course]]
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=== Videos ===
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* [https://artofproblemsolving.com/videos/counting AoPS Counting & Probability Videos]
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* [https://www.youtube.com/watch?v=t6a4uHEwQnM&list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT Sohil Rathi AMC8 Math Competition Preperation Playlist]
  
 
== See also ==
 
== See also ==
* [[Combinatorics/Intermediate | Intermediate topics in combinatorics]]
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* [[Combinatorics/Intermediate | Intermediate combinatorics]]
* [[Combinatorics/Olympiad | Olympiad topics in combinatorics]]
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* [[Combinatorics/Olympiad | Olympiad combinatorics]]
  
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[[Category:Combinatorics]]
 
[[Category:Introductory Mathematics Topics]]
 
[[Category:Introductory Mathematics Topics]]
[[Category:Combinatorics]]
 

Latest revision as of 21:59, 26 May 2021

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