Michael Penn Courses

Flattening a Curve - Stereographic Projection

Explore stereographic projection, a fascinating mathematical technique for mapping curved surfaces onto flat planes, with applications in cartography and complex analysis.

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

Difference at Distance 1 - Number Theory

Explore number theory concepts focusing on difference 2 at distance 1, with examples, proofs, and generating functions to deepen understanding of this mathematical topic.

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

What Is the Free Vector Space?

Explore the concept of free vector space through clear definitions, illustrative examples, and practical applications in this concise mathematical tutorial.

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

What Is a Tensor Anyway? - From a Mathematician

Explore tensors from a mathematician's perspective, delving into their definition, properties, and applications in various mathematical fields.

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

Ramanujan's Famous Mod 5 Congruence - Number Theory

Explore Ramanujan's famous (mod 5) congruence in number theory, delving into its mathematical significance and applications. Gain insights into this intriguing concept through clear explanations and examples.

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

Ramanujan's Theta Functions - Number Theory

Explore Ramanujan's theta functions in number theory, delving into their properties, applications, and significance in mathematical research and problem-solving.

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

Introduction to Product-Sum Identities - Number Theory

Explore fundamental concepts of product-sum identities in number theory, learning key techniques for solving mathematical problems and understanding their applications.

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

How to Use Generating Functions with Integer Partitions - Number Theory

Explore generating functions in integer partitions, including unrestricted and restricted cases, with applications to odd parts and rational functions in number theory.

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

Every Calculus Teacher I Know Skips This

Uncover a crucial calculus concept often overlooked by instructors. Gain insights into an important but frequently omitted topic, enhancing your understanding of calculus fundamentals.

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

Generating Functions - Number Theory

Explore generating functions in number theory, learning their applications and techniques for solving complex mathematical problems.

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

Introduction to Integer Partitions - Number Theory

Explore integer partitions in number theory, learning key concepts and applications. Gain insights into this fundamental mathematical topic through clear explanations and examples.

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

The Derivative Is Everywhere

Explore the ubiquitous nature of derivatives in mathematics and their applications across various fields, enhancing your understanding of this fundamental calculus concept.

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

Quadratic Forms - Number Theory

Explore quadratic forms in number theory, delving into their properties, applications, and significance in mathematical analysis.

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

Sums of Squares - Number Theory

Explore number theory concepts focusing on sums of squares, including a theorem and its proof, enhancing mathematical understanding and problem-solving skills.

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

Square Roots Mod P - Number Theory

Explore square roots in modular arithmetic, a key concept in number theory. Learn proofs, work through examples, and gain practical problem-solving skills in this engaging mathematical exploration.

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