Michael Penn Courses

Maximize the Area of One Ellipse

Explore a fascinating geometry problem involving ellipses inscribed in a circle, focusing on maximizing the area of one ellipse through mathematical analysis and problem-solving techniques.

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

The Genesis of Vertex Algebras

Explore the historical development of vertex algebras with Richard Borcherds, covering key concepts like Leech lattice, Dinkin diagrams, and string theory connections.

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

A Nice Approach to a Famous Sum

Explore an innovative method for calculating a well-known mathematical series, offering a fresh perspective on a classic problem in number theory and analysis.

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

A Number Theory Problem from Morocco

Explore a challenging number theory problem from a Moroccan math contest, guided by an expert's step-by-step solution and insightful explanations.

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

So Many Powers of 2

Explore fascinating mathematical properties and patterns related to powers of 2, uncovering intriguing relationships and insights in number theory and algebra.

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

Problem Solving - Complex Number Basics

Explore essential complex number techniques for problem-solving contests, covering arithmetic operations, Euler's formula, and nth roots of unity with practical examples.

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

Vertex Algebras - The Non-Negative Products

Explore the structure of non-negative products in vertex algebras, delving into advanced mathematical concepts and their applications in algebraic theory.

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

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