Michael Penn Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Real Analysis - Continuity

Explore the precise definition of continuity in real analysis, its equivalence to sequential continuity, and its connection to Calculus 1 limits. Gain a deeper understanding of this fundamental concept.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Problem Solving - The Pigeonhole Principle

Explore the pigeonhole principle through examples, including famous problems from Erdos and the 1994 Putnam Exam. Learn problem-solving techniques in mathematics.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Pi Is Irrational

Explore a simple proof demonstrating pi's irrationality, delving into mathematical concepts and reasoning behind this fundamental property of the famous constant.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Real Analysis - Subsequences

Explore subsequences in Real Analysis, including the Bolzano-Weirstrass Theorem. Learn key concepts and proofs to deepen your understanding of this fundamental mathematical topic.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Differential Forms - The Exterior Derivative and Vector Calculus

Explore the connection between classical vector calculus operators and differential forms, focusing on the exterior derivative and Hodge operator in this concise mathematical explanation.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Differential Forms - Integrating M-Forms

Explore the concept of integrating differential m-forms on m-dimensional hypersurfaces in R^n, including theory and practical examples to enhance understanding of this advanced mathematical topic.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

An Infinite Tangent Product

Explore the evaluation of an infinite tangent product using identities and telescoping techniques, delving into advanced mathematical concepts and problem-solving strategies.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Real Analysis - Algebraic Properties of Limits

Explore algebraic properties of limits in real analysis, proving classic theorems and enhancing understanding of fundamental mathematical concepts.

• YouTube
• 21 minutes
• Self-Paced
• Free Video