CO2 What does a solution to a counting problem look like?

#combinatorics What kinds of solutions to a counting problem are possible? Sometimes we can get a nice closed formula, but it is also possible to "solve" a counting problem by finding a recurrence relation or by using generating functions. Subscribe @Shahriari for math videos at the college level. 00:00 Introduction 00:51 Example 1: Number of Subsets of a Finite Set (https://youtu.be/T6Vbr0fAzm0) 04:00 Example 2: Hat Check Problem (https://youtu.be/EVLPBzkHBzk) 08:30 Example 3: Number of sets with no consecutive integers 10:57 Recurrence Relation for Example 3 (https://youtu.be/gHy2B8TMn9g https://youtu.be/hYXWiuoP7s0) 15:15 Example 4: Using Generating Functions (https://youtu.be/QtNHo_9mpW0) 21:34 Take Away Message A series of lectures on introductory Combinatorics. This full course is based on my book Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022. DOI: https://doi.org/10.1017/9781108568708 For an annotated list of available videos see https://pomona.box.com/s/by2ay2872avxaf2lzv20i2mqurlpvfpr YouTube Playlist: https://youtube.com/playlist?list=PLpcU2wNhmPYcUS3Mt3y8O2fwduWzco4xV Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.