Michael Penn Courses

Ultra-Mega Differential Equations Review Problem

Comprehensive review of differential equation techniques, covering calculus concepts and various solving methods through an in-depth problem-solving demonstration.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

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

Real Analysis - L'Hospital's Rule - Infinity-Infinity Case

Rigorous proof of L'Hospital's rule for infinity/infinity case, demonstrating its application in calculating limits of indeterminate forms in real analysis.

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

Problem Solving - Using Symmetry

Explore the power of symmetry in problem-solving, uncovering elegant solutions to complex mathematical challenges through practical examples and insightful explanations.

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

A Nice Integral

Explore advanced integration techniques using Feynman's trick and Fubini's theorem to solve a challenging integral, enhancing problem-solving skills in mathematical analysis.

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

A Commutative Vertex Algebra

Explore the universal commutative vertex algebra with one generator, demonstrating how to give a polynomial ring vertex algebra structure through an in-depth mathematical analysis.

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

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

The Normally Ordered Product

Explore the concept of normally ordered product in vertex algebras, its definition, and importance in understanding vertex operator structures.

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

A Wallis Type Infinite Product

Explore the evaluation of an infinite product related to the famous Wallis product, delving into advanced mathematical concepts and techniques.

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

The Vector Spaces for Vertex Algebras

Explore key vector spaces for vertex algebras: polynomial rings, exterior algebras with infinite variables, and universal enveloping algebra of the Virasoro Lie algebra. Gain essential understanding for advanced algebraic studies.

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

Differential Forms - The Minkowski Metric and the Hodge Operator

Explore the Minkowski inner product's lifting to 2 and 3 forms and its impact on the Hodge operator in this advanced mathematics video lecture on differential geometry.

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

Differential Forms - The Hodge Operator via an Inner Product

Explore the generalized Hodge operator for m-forms using inner products, advancing understanding of differential geometry and mathematical physics concepts.

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

A Sum Two Ways

Explore two distinct methods for calculating the closed form of an intriguing infinite series, demonstrating advanced mathematical techniques and problem-solving approaches.

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

A Gentle Description of a Vertex Algebra

Explore the concept of vertex algebra through associative, Lie, and Poisson algebras. Learn its definition and gain intuition for understanding its components in this mathematical journey.

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

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