Lectures related to Stirling numbers of the first kind

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Explores binomial coefficient estimation, Stirling's formula, and properties of the bell curve.

Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.

Explores generating functions, recurrence relations, and advanced counting techniques.

Covers the definition of generating functions and their application in solving recurrence relations.

Explores Stirling's formula, Euler's integral, and the Gaussian integral for estimating n factorial.

Covers arithmetic and geometric progressions, strings, and recurrence relations.

Covers arithmetic and geometric progressions, strings, and recurrence relations in sequences.

Explores the notions of transience and recurrence in Markov chains through various examples and calculations.

Explores Stirling's formula applications, polarization in vectors, and graph embeddings in Euclidean space.

Explores polynomial irreducibility and Vieta's relations in depth.

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Covers the proof of non-vanishing of Quadratic Dirichlet L-function and reviews basic properties of Gamma function.

Explains linear homogeneous recurrence relations and provides solving techniques and examples.

Covers explicating sequences using matrices and their implications, illustrated with examples.