Generating Functions Courses and Certifications

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

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

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

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
• Free Online Course (Audit)

Analytic Combinatorics

65 ratings at Coursera

Explore precise quantitative predictions of large combinatorial structures through symbolic methods, generating functions, and complex analysis for deriving accurate asymptotics.

• Coursera
• 17 hours
• On-Demand
• Free Online Course (Audit)

Combinatorics and Algorithms Design

Master combinatorial mathematics and algorithm design principles through advanced counting techniques, generating functions, recurrence relations, and problem-solving strategies.

• XuetangX
• On-Demand
• Free Online Course

Combinatorial Mathematics

Explore counting, arrangements, and finite systems in mathematics. Learn applications in computer science, cryptography, and more. Develop problem-solving skills for various fields.

• Swayam
• 16 weeks
• On-Demand
• Free Online Course

IIT Madras;  NPTEL

Combinatorics

Explore advanced counting techniques, generating functions, graph theory, and Polya theory. Gain insights into combinatorial structures and their applications in discrete mathematics.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Applied Probability

Tap into a framework for understanding the world around us, from sports to science.

• Brilliant
• 10-15 hours
• On-Demand
• Paid Course

Number Theory

Comprehensive exploration of number theory, covering foundational concepts to advanced topics like quadratic reciprocity, integer partitions, and Ramanujan's congruences.

• YouTube
• 16 hours
• 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

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

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