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
• Self-Paced
• 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
• Self-Paced
• Free Video

Generalizing the Internet's Favorite Integral

Explore a mathematical journey generalizing a popular integral, delving into advanced techniques and uncovering surprising connections in calculus and analysis.

• YouTube
• 15 minutes
• Self-Paced
• Free Video

Breaking a Large Square into Smaller Parts - Optimal Methods

Explore optimal methods for dividing large squares into smaller parts, enhancing problem-solving skills and geometric understanding.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

E is Irrational - The Best Proof

Explore the most compelling proof of e's irrationality in this engaging mathematical demonstration, offering clear insights into this fundamental concept.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Solving a Higher Degree Diophantine Equation

Explore techniques for solving complex Diophantine equations of higher degrees, enhancing problem-solving skills in number theory and algebraic manipulation.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Integral Analysis - Lessons from a Complex Problem

Explore the rich insights and techniques hidden within a complex integral, uncovering multiple mathematical concepts and problem-solving strategies.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Solutions from My First Calculus 1 Exam

Explore solutions to a Calculus 1 exam, gaining insights into problem-solving techniques and common challenges faced by students in introductory calculus.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

A Nice Geometry Puzzle

Solve an engaging geometry puzzle that challenges your problem-solving skills and enhances your understanding of geometric principles.

• YouTube
• 14 minutes
• Self-Paced
• Free Video

A Nice Relation Between e and π - Mathematical Constants Explored

Explore a fascinating relationship between pi and e, uncovering the elegant connection between these fundamental mathematical constants.

• YouTube
• 14 minutes
• Self-Paced
• Free Video

The Only Real Cross Product is Three-Dimensional

Explore the unique properties of 3D cross products, their mathematical significance, and why they don't exist in other dimensions. Gain insights into vector algebra and spatial geometry.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Mobius Inversion - Number Theory's Secret Weapon

Explore Mobius Inversion, a powerful technique in number theory. Learn its applications and significance in solving complex mathematical problems and understanding number relationships.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Two Nice Approximations for n! - Factorial Calculation Methods

Explore two effective approximations for calculating factorials, enhancing your understanding of mathematical estimation techniques and their applications.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

The Strangest Circle - Mathematical Curiosities and Paradoxes

Explore a fascinating mathematical concept: a circle with peculiar properties that challenge conventional geometry, offering unique insights into advanced mathematical thinking.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Surprising Patterns in the Signs of Derivatives

Explore intriguing patterns in derivative signs, uncovering unexpected relationships and insights in calculus. Enhance your mathematical intuition and problem-solving skills.

• YouTube
• 22 minutes
• Self-Paced
• Free Video