Generating Functions Courses and Certifications

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

Insights into Mathematics

Combinatorics - Math History - NJ Wildberger

Explore combinatorics through historical examples, counting problems, graph theory, and generating functions. Delve into partitions, Fibonacci numbers, Catalan sequence, and famous theorems in this engaging mathematical journey.

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

Kimberly Brehm

Discrete Math II - Combinatorics

Explore advanced combinatorics, including permutations, generating functions, recurrence relations, graph theory, and algorithms, enhancing problem-solving skills in discrete mathematics.

• YouTube
• 12 hours
• On-Demand
• Free Video

3Blue1Brown

Olympiad Level Counting - How Many Subsets of {1,…,2000} Have a Sum Divisible by 5?

Explore advanced counting techniques using generating functions and complex numbers to solve a challenging subset sum problem, with applications to Olympiad-level mathematics.

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

ICTP Mathematics

Invariants of Manifolds from 6 Dimensions

Explore advanced mathematical concepts in gauge theories and differential invariants, focusing on invariants of manifolds from 6 dimensions and their applications in theoretical physics.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Michael Penn

How Is This Huge Function Useful

Explore the utility of a complex function through examples, recursion, generating functions, and differential equations in this engaging mathematical analysis.

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

Michael Penn

What Is It Like to Be a Pure Mathematician?

Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.

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

Michael Penn

Difference at Distance 1 - Number Theory

Explore number theory concepts focusing on difference 2 at distance 1, with examples, proofs, and generating functions to deepen understanding of this mathematical topic.

• YouTube
• 30 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

Michael Penn

Generating Functions - Number Theory

Explore generating functions in number theory, learning their applications and techniques for solving complex mathematical problems.

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

Michael Penn

Catalan Numbers - Generating Function and Closed Form

Explore generating functions and closed forms for Catalan numbers, building on recursion concepts to derive a comprehensive understanding of this important mathematical sequence.

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

Michael Penn

Some Identities Involving the Riemann-Zeta Function

Explore the Riemann-Zeta function, its generating function for positive even integers, and derive sum identities in this mathematical deep dive.

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

Fields Institute

Motivic Hochschild Homology Over Algebraically Closed Fields

Explore Hochschild homology in motivic spectra, uncovering torsion classes and connections to Steenrod algebra. Gain insights into algebraic geometry and homotopy theory applications.

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

ICTP Mathematics

Computation of the Vertical Vafa-Witten Invariants II

Explore advanced algebraic geometry concepts, focusing on vertical Vafa-Witten invariants computation using localization on Hilbert schemes of points for toric surfaces.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

ICTP-IGAP Algebraic Geometry Seminar on Vertical Vafa-Witten Invariants

Explore Vafa-Witten invariants, focusing on vertical components. Examine moduli space fixpoint loci, generating functions, and conjectural formulas for both vertical and horizontal invariants.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video