Michael Penn Courses

A Quaternion Version of Euler's Formula

Explore a quaternion extension of Euler's formula, connecting complex numbers to 3D rotations and expanding mathematical understanding beyond traditional complex analysis.

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

A Physicist's Favorite Function

Explore a physicist's perspective on mathematical functions, blending humor and science to illuminate key concepts in continuity and piecewise functions.

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

A Neat Parameterized Integral Identity

Explore a fascinating parameterized integral identity, uncovering its mathematical intricacies and applications in this engaging tutorial led by Michael Penn.

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

Fresnel Integrals

Comprehensive exploration of Fresnel integrals, covering their mathematical properties, applications, and problem-solving techniques in just 20 minutes.

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

Find a Closed Form for This Intimidating Sequence

Explore a challenging sequence problem with creative problem-solving techniques and mathematical insights to find its closed form solution.

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

How to Create the Best Contest Problems

Insights on crafting engaging math contest problems from two expert educators. Learn techniques for designing challenging, creative, and thought-provoking mathematical puzzles.

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

What Does the Quantum Binomial Actually Do?

Explores the quantum binomial's role in quantum mechanics, explaining its mathematical properties and applications in describing quantum systems.

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

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