Difference between revisions of "Combinatorics/Introduction"

 
(13 intermediate revisions by the same user not shown)
Line 1: Line 1:
== Introductory topics in 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.
The following topics provide a good study in introductory combinatorics.
 
  
* Counting
+
== Topics ==
 +
=== Counting ===
 +
* Counting [[functions]]
 
** [[Factorial]]
 
** [[Factorial]]
 
** [[Permutation]]
 
** [[Permutation]]
 
** [[Combination]]
 
** [[Combination]]
** Common Stragegies
+
* [[Casework]]
*** [[Casework]]
+
* [[Complementary counting]]
*** [[Complementary counting]]
+
* [[Constructive counting]]
*** [[Constructive counting]]
+
* [[Overcounting]]
*** [[Overcounting]]
+
* [[Committee forming]]
** [[Committee forming]]
+
* [[Distinguishability]]
** [[Distinguishability]]
+
=== Probability ===
* Probability
+
* Counting techniques in probability
** Basic Probability Techniques
+
* [[Geometric probability]]
** [[Geometric Probability]]
+
* [[Expected value]]
** [[Expected Value]]
+
=== Miscellaneous ===
* Miscellaneous
+
* [[Combinatorial identities]]
** [[Pascal's triangle]] and [[Block walking]]
+
** [[Pascal's triangle]]
** [[Combinatorial identities]]
+
** [[Block walking]]
** [[Binomial theorem]]
+
* [[Binomial theorem]]
  
== Introductory combinatorics resources ==
+
== Resources ==
  
 
=== Books ===
 
=== Books ===
* ''the Art of Problem Solving: Introduction to Counting and Probability'' by David Patrick ([https://artofproblemsolving.com/store/item/intro-counting details])
+
* [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]] ([https://artofproblemsolving.com/school/course/catalog/intro-counting information page])
+
* [[AoPS Online School/Introduction to Counting & Probability Course |AoPS Introduction to Counting & Probability Course]]
  
 
=== Videos ===
 
=== Videos ===
* [https://www.youtube.com/watch?v=t6a4uHEwQnM&list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT AMC8 Math Competition Preperation Playlist by Sohil Rathi]
 
 
* [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 ==
* [[Combinatorics/Intermediate | Intermediate topics in combinatorics]]
+
* [[Combinatorics/Intermediate | Intermediate combinatorics]]
* [[Combinatorics/Olympiad | Olympiad topics in combinatorics]]
+
* [[Combinatorics/Olympiad | Olympiad combinatorics]]
  
 +
[[Category:Combinatorics]]
 
[[Category:Introductory Mathematics Topics]]
 
[[Category:Introductory Mathematics Topics]]
[[Category:Combinatorics]]
 

Latest revision as of 21:59, 26 May 2021

Invalid username
Login to AoPS