Michael Penn Courses

One of My Favorite Identities

Explore a fascinating mathematical identity, delving into its properties, applications, and significance in the field of mathematics.

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

Why Are There No 3 Dimensional "Complex Numbers"?

Explores the mathematical reasons behind the absence of 3D complex numbers, delving into algebra, quaternions, and the limitations of number systems beyond 2D complex planes.

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

Can You Define Trig Functions via a Differential Equation

Explore an unconventional approach to defining trigonometric functions using differential equations, offering a fresh perspective on these fundamental mathematical concepts.

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

A Unique Approach to the Half-Derivative

Explore a novel perspective on the half-derivative concept, delving into its mathematical intricacies and applications in advanced calculus and analysis.

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

The Craziest Definition of the Derivative You Have Ever Seen

Explore an unconventional approach to defining derivatives, offering a fresh perspective on calculus concepts and challenging traditional mathematical thinking.

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

Convoluted Fibonacci Numbers

Explore the intriguing concept of convoluted Fibonacci numbers, delving into their mathematical properties and unique characteristics in number theory.

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

Groups With Four Members

Explore the mathematical properties and structures of groups with four members, uncovering their unique characteristics and applications in abstract algebra.

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

Deriving Euler's Formula Four Ways

Explore four distinct derivations of Euler's formula, uncovering its mathematical beauty and significance in complex analysis and beyond.

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

Unveiling the Most Diabolical Algebraic Identity Ever

Explore a mind-bending algebraic identity that challenges conventional mathematical thinking and expands problem-solving skills.

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

Where Limits Aren't What They Seem

Explore mathematical limits beyond conventional understanding, uncovering surprising insights and challenging preconceptions in this thought-provoking exploration of advanced calculus concepts.

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

This Function Knows Your Phone Number

Explore a humorous mathematical puzzle involving recursive phone numbers and exponential functions, blending math concepts with comedic storytelling.

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

A Suspicious and Tricky Combination - A Functional-Differential Equation

Explore the intriguing world of functional-differential equations, combining two complex mathematical concepts for a challenging and insightful problem-solving experience.

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

What Does "Same" Mean in Math? It Depends.

Explores the nuanced concept of "sameness" in mathematics, examining various contexts where equality and equivalence have different interpretations and implications.

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

A Wallis-Type Product for E

Explore a Wallis-type product representation for the mathematical constant e, delving into its derivation and significance in number theory and analysis.

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

Gamma Reflection via Double and Contour Integration

Explore gamma function reflection using double and contour integration techniques, enhancing understanding of complex analysis and special functions in mathematics.

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