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I've compiled 20+ free algebra and topology ebooks. Not sketchy PDFs from torrent sites. Real textbooks that professors and universities have made freely available. Covers abstract algebra, linear algebra, algebraic…
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges. I cover the theorem statement, proof, worked examples, and the…
When a molecule absorbs light, the energy has to go somewhere. It can trigger a chemical reaction, release heat, or emit light as fluorescence or phosphorescence. The Jablonski diagram maps…
Problem solving in mathematics isn't about memorizing formulas. It's about knowing what to look for. I break down the essential steps every math student needs: understanding the problem, devising a…
Lilavati is a 12th-century mathematics treatise that reads like poetry. Written by Bhaskara II, it wraps arithmetic, algebra, and geometry inside riddles about bees, snakes, and peacocks. I've created a…
Einstein gets all the credit for relativity, but Poincare was circling the same ideas years earlier. He was trying to salvage classical physics with modifications when the Michelson-Morley experiment shattered…
Pick any positive integer. If it's even, halve it. If it's odd, triple it and add one. Repeat. You always reach 1. At least, that's what every number ever tested…
The Dirichlet theorem connects the Gamma and Beta functions to evaluate complex multiple integrals. Liouville extended it further, making it even more powerful. I cover both theorems with complete proofs,…
Unimolecular reactions seem impossible. A single molecule just reacts on its own? Where does the energy come from? Lindemann solved this puzzle by proposing that molecules first get energized through…
Shakuntala Devi's missing money puzzle is a classic in mathematical logic. Two women sell marbles at different rates. When they combine forces, the math doesn't add up. Where did the…
In 1904, Poincare asked a deceptively simple question: if a three-dimensional shape is simply connected, must it be a sphere? This question stumped mathematicians for nearly a century until Grigori…
Cosmic rays aren't actually rays. They're high-energy particles from deep space that slam into Earth's atmosphere at nearly the speed of light. I explain what cosmic radiation is, how cosmic…
