Advanced Counting: Generating Functions and Recurrence Relations

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Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Explores moment-generating functions, linear combinations, and normality of random variables.

Covers the pentagonal number theorem, Jacobi identity, and modularity of eta and theta functions.

Explores the technical derivation and properties of Multivariate Extreme Value models.

Explores generating functions for moments and cumulants, showcasing their role in distribution analysis.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Covers the thermal partition function using Feynman diagrams and perturbation theory.

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

Covers moment and cumulant generating functions for random variables, enabling calculation of moments and cumulants.