Michael Penn Courses

A Cornucopia of Proofs

Learn various proof-writing techniques with Michael Penn in less than an hour. Randolph College Math and Science.

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

Differential Forms - Boundaries of M-Cells and M-Chains

Explore the concept of boundaries in differential forms, focusing on m-cells and m-chains. Learn to calculate examples and understand their mathematical significance in this concise tutorial.

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

Differential Forms - Integrals of M-Forms Over M-Chains

Explore m-cells, m-chains, and integration of differential forms over various dimensions, with practical examples for 0, 1, and 2-forms and chains.

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

The Heisenberg Algebra Part 1

Introduction to the Heisenberg vertex algebra, an algebraic model of one free boson. Explore the foundations of this complex mathematical concept and its applications in quantum mechanics.

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

An Aesthetic Double Integral

Explore an elegant calculation of a double integral, showcasing refined mathematical techniques and aesthetic problem-solving approaches in advanced calculus.

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

Real Analysis - The Fundamental Theorem of Calculus

Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.

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

Two from Africa

Solve challenging math problems from the 2004 Pan-African Math Olympiad, enhancing problem-solving skills and mathematical reasoning abilities.

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

What Is an Integer Partition?

Explore integer partitions in mathematics, their properties, and applications. Learn about this fundamental concept through examples and insights from a university-level talk for high school teachers.

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

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video