Counting with Recurrence Relations: Summary

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Related lectures (27)

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Generating Functions: Advanced Counting

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

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Advanced Counting: Generating Functions and Recurrence Relations

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

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Generating Functions for Correlation Functions

Explores generating functions for correlation functions in the context of the forced harmonic oscillator.

Sequences: Arithmetic and Geometric Progressions

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

Sequences: Relations, Summation, Strings

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

Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Extended Binomial Theorem

Explores the Extended Binomial Theorem and counting problems using generating functions.

Linear Recurrence Relations: Solving Techniques and Examples

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

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Extreme Value Models: Technical Derivation MOOC: Selected Topics on Discrete Choice

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

Linear Recurrence Relations: Solving Techniques

Explores linear homogeneous recurrence relations, solving techniques, characteristic equations, and examples like Fibonacci numbers.

Pentagonal Number Theorem and Jacobi Identity

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

Meromorphic Functions & Differentials

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

Linear Recurrence Sequences MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Explores linear recurrence sequences, discussing convergence, divergence, and Cauchy sequences.

Linear Combinations: Moment-Generating Functions

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

Linear Recurrent Sequences Systems

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

Thermal Partition Function: Feynman Diagrams

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

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