# Dot products and duality | Essence of linear algebra, chapter 9

Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what’s going on with the dot product, and the connection between its numerical computation and … Continue reading Dot products and duality | Essence of linear algebra, chapter 9

# Waves: Light, Sound, and the nature of Reality

Physics of waves: Covers Quantum Waves, sound waves, and light waves. Easy to understand explanation of refraction, reflection, and many other topics. Important correction: In the section of refraction, the colors are reversed. Violet light slows down in water more … Continue reading Waves: Light, Sound, and the nature of Reality

# Laplace Transform Explained and Visualized Intuitively

Pierre-Simon, marquis de Laplace (/ləˈplɑːs/; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827)  Pierre-Simon, marquis de Laplace was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and … Continue reading Laplace Transform Explained and Visualized Intuitively

# Divergence and curl: Maxwell’s Equations, fluid flow and more

Maxwell’s equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. … Maxwell first used the equations to propose that light is an electromagnetic phenomenon. Introduction to Maxwell’s Equations James … Continue reading Divergence and curl: Maxwell’s Equations, fluid flow and more

# But what is a partial differential equation? | DE2

Typo corrections: – At 1:33, it should be “Black-Scholes” – At 16:21 it should read “scratch an itch”. If anyone asks, I purposefully leave at least one typo in each video, like a Navajo rug with a deliberate imperfection as … Continue reading But what is a partial differential equation? | DE2

# Riemann’s paradox: pi = infinity minus infinity

With the help of a very famous mathematician the Mathologer sets out to show how you can subtract infinity from infinity in a legit way to get exactly pi. Thank you very much to Danil Dmitriev the official Mathologer translator … Continue reading Riemann’s paradox: pi = infinity minus infinity

# The Infinite Hotel Paradox – Jeff Dekofsky

The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it’s completely booked but one person wants to check in? What about … Continue reading The Infinite Hotel Paradox – Jeff Dekofsky