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Lecture
Advanced Counting: Generating Functions and Recurrence Relations
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Related lectures (26)
Counting with Recurrence Relations: Summary
Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.
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: Linear Homogeneous Recurrence Relations and Generating Functions
Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.
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.
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.
Generating Functions: Properties and Applications
Explores generating functions, Laplace transform, and their role in probability distributions.
Linear Combinations: Moment-Generating Functions
Explores moment-generating functions, linear combinations, and normality of random variables.
Pentagonal Number Theorem and Jacobi Identity
Covers the pentagonal number theorem, Jacobi identity, and modularity of eta and theta functions.
Extreme Value Models: Technical Derivation
MOOC: Selected Topics on Discrete Choice
Explores the technical derivation and properties of Multivariate Extreme Value models.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Thermal Partition Function: Feynman Diagrams
Covers the thermal partition function using Feynman diagrams and perturbation theory.
Linear Recurrence Relations: Solving Techniques and Examples
Explains linear homogeneous recurrence relations and provides solving techniques and examples.
Counting Problems: Solutions and Generating Functions
Covers counting problems using generating functions to find solutions.
Ramanujan Graphs: Generating Functions and Expander Graphs
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Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.
Functions: Limits, Continuity, Differentiability
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Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.
Generating Functions: Moments and Cumulants
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Explores generating functions for moments and cumulants, showcasing their role in distribution analysis.
Derivatives and Continuity in Multivariable Functions
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Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.
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