Michael Penn Courses

Fibonacci's Favorite Linear Algebra Problem

Explore a fascinating linear algebra problem connected to the Fibonacci sequence, presented with clear explanations and mathematical insights.

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

How to Take a Walk and Miss Every Rational Number

Explore the mathematical concept of creating a path that avoids all rational numbers, using clever techniques from real analysis and number theory.

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

Behind the Internet's Favorite Integration Trick

Uncover the mathematical principles and derivation behind a popular integration technique that has gained widespread attention online, explained by mathematician Michael Penn.

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

The Best Proof That the Real Numbers Are Uncountable

Discover the most elegant and compelling proof demonstrating why real numbers cannot be countable in this mathematical exploration of Cantor's diagonal argument.

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

From an Integral to a Differential Equation

Discover how to transform integral equations into differential equations, exploring the mathematical techniques and principles behind this conversion process.

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

A Non-Unique Limit in Calculus

Explore the concept of non-unique limits in mathematics, understanding when and why limits may not have a single value and how to approach these mathematical scenarios.

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

Two Nice Superfactorial Problems in Advanced Mathematics

Dive into challenging mathematical problems involving superfactorials, exploring solution strategies and advanced computational techniques.

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

A Non-Standard Irrationality Proof in Mathematics

Explore a unique mathematical demonstration of irrationality using non-conventional proof techniques and logical reasoning methods.

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

Solving the Viral Square Root Problem - A Mathematical Explanation

Delve into a step-by-step explanation of a viral mathematical puzzle involving square roots, guided by an experienced mathematics professor.

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

Can You Solve This Infinite Equation?

Unlock the secrets of solving complex infinite equations through step-by-step mathematical analysis and problem-solving techniques in this engaging 17-minute exploration.

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

How Likely Are Real Solutions - Probability in Polynomial Equations

Explore probability concepts in determining when mathematical equations yield real solutions rather than complex ones.

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

The "Ultimate" Product Rule

Discover an advanced extension of the product rule for differentiation that goes beyond the basic two-function case in this concise mathematical exploration.

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

Triangles in the Complex Plane

Explore geometric properties and relationships of triangles using complex number representations and coordinate systems.

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

A Surprising Exponential Closure in Mathematical Analysis

Explore an intriguing mathematical concept examining the unexpected closure properties of exponential functions and their fascinating implications.

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

Lifting the Exponent - A Mathematical Tool for Contest Problem Solving

Master the lifting exponent technique - a powerful mathematical tool for solving complex contest problems and improving your problem-solving capabilities in competitive mathematics.

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