Michael Penn Courses

Some Important Facts About Congruence Modulo N

Explore key properties of congruence modulo n, a fundamental equivalence relation in number theory. Learn arithmetic properties and computational techniques for this important concept.

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

Permutation Orbifolds of Vertex Operator Algebras

Explore permutation orbifolds in vertex operator algebras, delving into advanced algebraic structures and their applications in mathematical physics and string theory.

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

Some Example Calculations in the Heisenberg Vertex Algebra

Explore in-depth calculations within the Heisenberg vertex algebra, demonstrating advanced mathematical concepts and techniques in this specialized field of study.

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

The Number Theory You Need to Learn Abstract Algebra

Explore essential number theory concepts like division algorithm, Euclidean algorithm, and congruence modulo n, laying the foundation for abstract algebra studies.

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

Brush Up on Number Theory Tricks

Explore a viewer-suggested number theory problem, enhancing your problem-solving skills and deepening your understanding of mathematical concepts.

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

Proofs by Mathematical Induction

Explore the principle of mathematical induction through clear explanations and diverse examples, enhancing your ability to construct rigorous proofs in mathematics.

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

Basic Proofs Involving Sets

Learn techniques for proving fundamental set theory results, enhancing your mathematical reasoning skills and deepening your understanding of set operations and relationships.

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

A Cornucopia of Proofs

Learn various proof-writing techniques with Michael Penn in less than an hour. Randolph College Math and Science.

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

Differential Forms - Boundaries of M-Cells and M-Chains

Explore the concept of boundaries in differential forms, focusing on m-cells and m-chains. Learn to calculate examples and understand their mathematical significance in this concise tutorial.

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

Differential Forms - Integrals of M-Forms Over M-Chains

Explore m-cells, m-chains, and integration of differential forms over various dimensions, with practical examples for 0, 1, and 2-forms and chains.

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

The Heisenberg Algebra Part 1

Introduction to the Heisenberg vertex algebra, an algebraic model of one free boson. Explore the foundations of this complex mathematical concept and its applications in quantum mechanics.

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

An Aesthetic Double Integral

Explore an elegant calculation of a double integral, showcasing refined mathematical techniques and aesthetic problem-solving approaches in advanced calculus.

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

Real Analysis - The Fundamental Theorem of Calculus

Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.

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

Two from Africa

Solve challenging math problems from the 2004 Pan-African Math Olympiad, enhancing problem-solving skills and mathematical reasoning abilities.

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

What Is an Integer Partition?

Explore integer partitions in mathematics, their properties, and applications. Learn about this fundamental concept through examples and insights from a university-level talk for high school teachers.

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