Generating Functions Courses and Certifications

Generating Functions for Catalan Numbers - Lecture 7

Discover how to derive generating functions for Catalan numbers and apply them to find explicit formulas in this MIT discrete mathematics lecture.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Michael Penn

Generating Functions and Combinatorial Identities

Explore techniques for manipulating generating functions to create new combinatorial sum identities, with an application to Fibonacci number sums.

• YouTube
• 24 minutes
• On-Demand
• Free Video

More on Generating Functions - Lecture 6

Explore advanced generating function techniques to solve linear recurrence equations and derive Fibonacci number expressions, plus learn two-variable generating functions.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

More Counting and Generating Functions - Lecture 5

Explore advanced counting techniques including the Cayley tree theorem proof and fundamentals of generating functions, their combinations, and mathematical applications.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Fields Institute

Automatically Computing Asymptotics of Sequences with Multivariate Rational Generating Functions

Discover techniques for automatically computing asymptotic behavior of sequences using multivariate rational generating functions in this mathematical analysis presentation.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Fields Institute

Asymptotics of Multivariate Algebraic Generating Functions

Explore the mathematical theory behind asymptotics of multivariate algebraic generating functions in this Fields Institute presentation by Tia Ruza from University of Waterloo.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Fields Institute

Non-algebraic Generating Functions in Pattern Avoidance

Explore non-algebraic generating functions in pattern avoidance with Miklos Bona from the University of Florida at the AofA 2025 conference.

• YouTube
• 17 minutes
• On-Demand
• Free Video

TrevTutor

Discrete Mathematics - Counting, Recurrence Relations, Generating Functions, Probability, Graph Theory

2 reviews

Master essential discrete mathematics concepts including combinatorics, probability, recurrence relations, generating functions, and graph theory through comprehensive examples.

• YouTube
• 10 hours 49 minutes
• On-Demand
• Free Video

Michael Penn

A Mysterious Chinese Contest Problem

Explore generating functions for integer partitions to solve a challenging math contest problem, enhancing problem-solving skills and deepening understanding of advanced mathematical concepts.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Michael Penn

So Many Factorials

Explore advanced mathematical techniques to evaluate complex factorial series, utilizing central binomial coefficients, generating functions, and trigonometric integrals for problem-solving.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Michael Penn

A Series Involving Harmonic Numbers - Featuring the Dilogarithm Function

Explore generating functions to calculate sums of series with harmonic numbers, featuring the dilogarithm function in advanced mathematical analysis.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Analysis of Algorithms

6 reviews

Explore algorithms through calculus, generating functions, and symbolic methods. Analyze structures like permutations, trees, and strings. Gain quantitative insights into large combinatorial structures.

• Coursera
• 21 hours
• On-Demand
• Paid Course

Mathologer

Explaining the Bizarre Pattern in Making Change for a Googol Dollars - Infinite Generating Functions

Explore the fascinating mathematics behind making change for a googol dollars, uncovering surprising patterns and using infinite generating functions to solve this complex problem.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Hall-Littlewood Polynomials, Affine Schubert Series, and Lattice Enumeration

Discover Hall-Littlewood-Schubert series and their applications to counting problems in algebra, geometry, and number theory through multivariate generating functions.

• YouTube
• 13 minutes
• On-Demand
• Free Video

Michael Penn

How to Use Generating Functions with Integer Partitions - Number Theory

Explore generating functions in integer partitions, including unrestricted and restricted cases, with applications to odd parts and rational functions in number theory.

• YouTube
• 30 minutes
• On-Demand
• Free Video