Michael Penn Courses

Are These the Only Square Fibonacci Numbers?

Explore the intriguing connection between Fibonacci numbers and perfect squares, examining which Fibonacci numbers are also square numbers and the mathematical reasoning behind this phenomenon.

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

A Stylized Integral

Explore a unique mathematical challenge involving a stylized integral, delving into advanced calculus techniques and problem-solving strategies.

• YouTube
• 24 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

The Dilogarithm - A Favorite Special Function

Explore the dilogarithm function, its properties, and applications in mathematics. Gain insights into this intriguing special function and its significance in various mathematical contexts.

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

The Quantum Derivative

Explore the concept of quantum derivative, its applications, and mathematical foundations in this concise tutorial on advanced calculus and quantum mechanics.

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

How the Power Set Forms a Ring

Explore how the power set forms a ring in this mathematical demonstration, showcasing set theory principles and algebraic structures.

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

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

Infinitely Many Primes of the Form

Explore the fascinating world of prime numbers and their unique patterns in this engaging mathematical discussion on infinite prime sequences.

• YouTube
• 24 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

Euler's Other Constant

Explore Euler's lesser-known constant, its properties, and significance in mathematics. Gain insights into this fundamental mathematical concept beyond the famous Euler's number.

• YouTube
• 23 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

Finding a Taylor Series Using Differential Equations

Explore an innovative approach to deriving Taylor series using differential equations, offering a fresh perspective on this fundamental mathematical concept.

• YouTube
• 24 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

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