Michael Penn Courses

A PHInominal Differential Equation

Explore a fascinating differential equation with unique properties and solutions, delving into advanced mathematical concepts and problem-solving techniques.

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

How Is This Huge Function Useful

Explore the utility of a complex function through examples, recursion, generating functions, and differential equations in this engaging mathematical analysis.

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

The Derivative Is a Lie

Explore the concept of derivatives through a whimsical narrative, blending mathematical concepts with creative storytelling to make complex ideas more accessible and engaging.

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

The Most Interesting Differential Equation You Have Seen

Explore a fascinating differential equation through an entertaining superhero-themed narrative, blending mathematics with creative storytelling.

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

The Quantum Factorial Is Upon Us

Explore the quantum analog of the factorial function, examining inversions and the N=4 case. Delve into advanced mathematical concepts with clear explanations and examples.

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

Will You Survive This Differential Equation?

Explore a challenging differential equation using integrating factors and clever tricks to find the solution in this engaging mathematical problem-solving session.

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

The Universal Enveloping Algebra

Explore the concept of universal enveloping algebra, its construction, properties, and applications in abstract algebra and representation theory.

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

Balancing Numbers

Explore the concept of (co) balancing numbers, a fascinating mathematical topic that challenges your problem-solving skills and deepens your understanding of number theory.

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

What Mathematicians Mean When We Use Super as a Prefix

Explore the mathematical meaning of "super" as a prefix, delving into its applications and significance in various mathematical contexts.

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

The Average Distance Between Points on a Square

Explore the mathematical concept of average distance between points on a square through coordinates, distance formula, and integral calculus. Gain insights into geometric problem-solving.

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

Measuring Infinite Dimensions

Explore the concept of measuring infinite dimensions in mathematics, delving into advanced topics related to infinite-dimensional spaces and their properties.

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

One of the First Transcendental Numbers - Liouville's Constant

Explore Liouville's Constant, one of the earliest discovered transcendental numbers, and its significance in mathematics. Gain insights into this unique numerical concept and its properties.

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

Generalizing the Right Angle

Explore the concept of generalizing right angles, extending geometric principles beyond traditional 90-degree angles for a deeper understanding of mathematical relationships.

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

A Gnarly Inverse Trig Integral

Explore a challenging inverse trigonometric integral, delving into advanced calculus techniques for solving complex mathematical problems.

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

This Is a Circle

Explore the fascinating properties and applications of circles in mathematics, from basic geometry to advanced concepts, enhancing your understanding of this fundamental shape.

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