Ensembles in statistical physics are collections of macroscopically identical but essentially independent systems. I explain the three main types: microcanonical, canonical, and grand canonical ensembles, their defining properties, and when…
This paper presents a statistical analysis of 20 years of meteorological data from the Pantnagar weather station in Uttarakhand, India. Conducted under the INSPIRE-SHE Scholarship Program, the research examines temperature,…
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I present the classic proofs of irrationality for square root of…
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know why it's true? Most people don't. I show you the…
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But proving it rigorously is where things get interesting. I cover…
India declared 2012 as the National Mathematical Year to celebrate Srinivasa Ramanujan's 125th birth anniversary. The government honored one of history's greatest self-taught mathematicians whose contributions to number theory, infinite…
Dr. SMRH Moosavi has claimed to derive a general formula for finding the nth prime number. I present his claim, the formula, and the surrounding mathematical context. Whether this constitutes…
You can figure out what day of the week any date falls on. No calendar needed. Just arithmetic. I'll teach you a genuine mathematical formula that works for any date…
Equations are the reason we can solve problems in seconds that would take hours of guesswork. I cover the basics: what equations are, how they work, types of equations, and…
Long URLs are a pain when sharing links on social media, emails, or podcasts. WordPress has a built-in shortlink system most people don't know about, plus several third-party solutions that…
Numbers are the alphabet of mathematics. But here's what most people never learn: all the complex numbers you encounter, from imaginary numbers to quaternions, are built from a few simple…
Logic is the grammar of mathematics. You can have brilliant mathematical intuition, but without logical precision, you can't communicate your ideas or verify they're correct. I walk you through propositions,…
