Michael Penn Courses

A Nice Product From Ramanujan - Featuring 3 Important Constants

Explore Ramanujan's fascinating product involving three crucial mathematical constants, uncovering its significance and implications in number theory.

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

Beyond Real Numbers - Solving X + 1 = 0 in Different Number Systems

Explore solutions to x² + 1 = 0 in various number systems, expanding mathematical understanding beyond real numbers and into complex realms.

• YouTube
• 28 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

How to Integrate With Respect to Any Function

Master integration techniques for any function, enhancing your calculus skills and problem-solving abilities in mathematics.

• YouTube
• 24 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

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

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

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

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

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