Mathematics Blog by Gaurav Tiwari. This section is dedicated to exploring various mathematical concepts and theories, transcending the boundaries of traditional high school and early college curriculums.
The mathematics topics here encompass various subfields, including algebra, calculus, number theory, geometry, topology, and more.
Every differential equation can be converted into an integral equation. Just integrate it. Sounds too simple, right? The details matter though. I walk through the conversion process step by step,…
Building on integral equation fundamentals, this article covers square integrable functions, norms, and the trial method for solving integral equations. I explain L2 spaces, why they matter for integral equation…
Integral equations look intimidating, but they're built from ideas you already know. I explain what integral equations are, their classification system (Fredholm vs Volterra, first vs second kind), and how…
I wrote this analysis in 2010 at age 17, obsessed with Ramanujan's nested radicals while studying under the INSPIRE-SHE scholarship. Fifteen years later, the mathematics still holds up. This complete…
Barry Martin's Hopalong Orbits Visualizer is a stunning WebGL experiment that renders abstract mathematical art in 3D. Using the Hopalong Attractor algorithm and three.js, it transforms simple equations into mesmerizing…
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and the key is grasping what sequences represent: ordered lists of…
Euler discovered a simple formula that generates 40 consecutive prime numbers: n squared plus n plus 41. Plug in 0 through 39 and every output is prime. I explore why…
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…
