Meet the Stirling Numbers of the Second Kind

This 40-minute mathematics video introduces Stirling numbers of the second kind, a lesser-known but fascinating combinatorial concept. Explore these numbers from basic identities to complex formulas, learning how to establish a recurrence relation, construct a Stirling triangle, and discover surprising connections to sums of products. The comprehensive tutorial progresses through multiple examples and proofs, including a demonstration of the general formula using strong induction and the application of the Sieve Theorem. Perfect for mathematics enthusiasts looking to expand their combinatorial knowledge beyond the more familiar binomial coefficients found in Pascal's triangle. The presentation includes detailed explanations with timestamps covering introductory concepts, basic identities, recurrence relations, counting surjections, and culminates with the complete formula derivation.