Michael Penn Courses

Matrix Exponentials, Determinants, and Lie Algebras

Explore matrix exponentials, determinants, and Lie algebras in this advanced mathematics video, delving into their properties and relationships for a deeper understanding of linear algebra concepts.

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

When "=" Isn't Quite Equal

Explore the nuances of mathematical equality, examining cases where the "=" symbol may not represent true equivalence. Gain insights into precise mathematical reasoning.

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

What Is It Like to Be a Pure Mathematician?

Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.

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

The Return of Big Integrals

Explore advanced integration techniques for complex mathematical problems, enhancing problem-solving skills and deepening understanding of calculus concepts.

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

An Irrational Sum

Explore the fascinating world of irrational numbers through an intriguing sum, delving into mathematical concepts and problem-solving techniques.

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

An Algebra for String Theory - The Virasoro Algebra

Explore the Virasoro algebra, a fundamental concept in string theory, and its applications in theoretical physics and mathematics.

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

Collatz Conjecture - The Interns' Inception

Explore the Collatz Conjecture, its examples, arguments, and related mathematical concepts like expected values and Gaussian integers in this engaging mathematical discussion.

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

The Witt Algebra

Explore the Witt Algebra, a crucial algebraic structure. Learn about Laurent polynomials, derivations, and proof by induction in this comprehensive mathematical exploration.

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

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