NYMC Talk by Dr. Po-Shen Loh on Catalan Numbers (Part 1)

In this High School D (HSD) level workshop, Dr. Po-Shen Loh describes the Catalan Numbers and develops the necessary methods to compute an explicit formula using generating functions. This talk is self-contained and appropriate for sophisticated high school-aged math enthusiasts.
Dr. Po-Shen Loh is a math professor at Carnegie Mellon University, the national coach of the USA International Math Olympiad team, and the co-founder of expii.com.
See also NYMC Talk by Dr. Po-Shen Loh on Catalan Numbers (Part 2)
• NYMC Talk by Dr. Po-Sh...

[@planetpeter917]

holy shit, po-shen loh is so amazing

[@beanhwak]

A comment on C(zero) =1. Example. We actually have C(4) = C(3)+C(1)C(2)+C(2)C(1)+C(3) then we wish to make the series symmetrical, so we attached C(0) to C(3) to get
C(4) = C(0)C(3)+C(1)C(2)+C(2)C(1)+C(3)C(0) which then make C(0) = 1.That is 1x C(3) becomes C(0)C(3). This is not the same as saying no parenthesis so C(0) = 1.
One can also do this in the triangulation of polygon. C(n+1) = C(n)+C(1)C(n-1)+... just add C(0) to get C(n+1)= C(0)C(n)+C(1)C(n-1)+... to make every term to have two factors so that C(n) is not alone but C(n) = C(0)C(n) so this makes C(0) = 1 by choice and not because no triangulation is a triangulation is rather confusing.

[@sarmadsultan7981]

Cool maths teacher

[@dawon7750]

Its very hard to see in a cellphone. I hope you will do something to move your camera closer to the board!

[@prasanthnaidukaraka6327]

really nice explanation!

[@namannarang4208]

Amazing

[@dannykim1516]

dynamic programming in a high school math circle lol