Combinatorics Courses and Certifications

Michael Penn

On Means of Binomial Coefficients

Explore limits related to arithmetic and geometric means of binomial coefficients, with strategies for solving complex mathematical problems in this advanced mathematics lecture.

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

Michael Penn

A Subfactorial Limit - Exploring Derangement Probabilities

Explore the fascinating world of subfactorial limits through examples, cases, and recursion, uncovering mathematical insights and problem-solving techniques.

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

Wrath of Math

The Game of Mousetrap - Mathematical Analysis and Permutations

Explore the mathematical mysteries behind the simple game of mousetrap, from Cayley's 1800s analysis to permutations, derangements, and modular variations.

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

MindYourDecisions

Brain Busting Apple Interview Puzzle - Paths On Grid

Uncover the surprising mathematical pattern behind Apple's brain-busting interview puzzle about counting paths on a grid using both computational and elegant shortcut methods.

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

Counting Problems - Combinations and Pascal's Triangle Identity C(n, k) = C(n − 1, k) + C(n − 1, k − 1)

Explore combinatorics through Pascal's triangle and binomial coefficients, uncovering the mathematical beauty of counting arrangements and combinations in this engaging talk.

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

Insights into Mathematics

Four Basic Combinatorial Counting Problems in Data Structures - Math Foundations 162

Explores four fundamental combinatorial counting problems for lists, ordered sets, sets, and multisets, providing insights into mathematical data structures and their enumeration.

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

Paul G. Allen School

Coding for Sunflowers - Theory Seminar

Explore recent advancements in the sunflower conjecture, simplifying proofs and discussing set theory implications in this mathematical theory seminar by Anup Rao.

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

Simons Institute

Improved Bounds for the Sunflower Lemma

Explore recent progress on the sunflower conjecture, examining structure vs pseudo-randomness and connections to DNF simplification under random restrictions.

• YouTube
• 1 hour 50 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

Institute for Advanced Study

The Ramsey Numbers - New Results and New Perspectives

Explore fundamental Ramsey numbers in combinatorics, recent advancements, and connections to high-dimensional random variable geometry with Julian Sahasrabudhe.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Michael Penn

A Classic Selection Problem in Mathematics

Master fundamental problem-solving techniques through a classic selection problem in mathematics, focusing on combinatorial analysis and strategic solution approaches.

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

TabletClass Math

Solving Outfit Combinations Using the Fundamental Counting Principle

Master the Fundamental Counting Principle through a real-world outfit combinations challenge, applying multiplication and permutations to solve practical math problems.

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

Michael Penn

Lah Numbers and an Appearance of Exponential Generating Functions

Explore Lah Numbers and their connection to exponential generating functions through mathematical analysis and problem-solving techniques.

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

Wrath of Math

Meet the Stirling Numbers of the Second Kind

Explore Stirling numbers of the second kind, from basic identities to the general formula, learning recurrence relations, the Stirling triangle, and connections to combinatorial concepts through examples and proofs.

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

Wrath of Math

Counting Rhyme Schemes Using Bell Numbers and Partitions

Explore the mathematical intricacies of counting rhyme schemes through Bell numbers, partitions, and recursive formulas in poetry analysis - from basic patterns to complex calculations.

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