Michael Penn Courses

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

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

A Great Proof of the Euler-Mascheroni Constant Identity

Explore a captivating proof of a fascinating mathematical identity, delving into elegant reasoning and surprising connections that illuminate the beauty of number theory.

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

The Duality Between Quaternions and Vectors

Explore the fascinating relationship between quaternions and vectors, uncovering their dual nature and applications in mathematics and physics.

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

The Best Ever Approach to This Derivative

Descubre un enfoque innovador y eficaz para resolver derivadas complejas, mejorando tu comprensión y habilidades en cálculo diferencial.

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

Solving a Mixed Diophantine Equation

Explore a fascinating mixed Diophantine equation, unraveling its complexities and discovering elegant solutions through step-by-step mathematical reasoning.

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

How to Find All Prime Numbers

Explore efficient methods for identifying prime numbers, including the Sieve of Eratosthenes algorithm and other mathematical techniques for prime number generation.

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

An Integral Connection Between Trigonometry and Logarithms

Explore the fascinating link between trigonometry and logarithms through an integral, revealing unexpected mathematical connections and deepening understanding of both concepts.

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

Conquer Tricky Sums with This Nice Trick

Learn a clever technique to simplify complex summations, enhancing your mathematical problem-solving skills and boosting your confidence in tackling challenging calculations.

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

An Amazing Approach to a Classic Integral

Explore an innovative approach to solving a classic integral, demonstrating unique problem-solving techniques and mathematical insights.

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

A Discovery of Irrationality from 470 BC

Explore the ancient Greek discovery of irrational numbers, a mathematical breakthrough that challenged fundamental beliefs and shaped the foundations of modern mathematics.

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