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.
Weierstrass shocked the mathematical world in 1872 by constructing a function that's continuous everywhere but differentiable nowhere. Not at a few points. At no points whatsoever. I walk through the…
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have made freely available online. This curated list covers single-variable calculus,…
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts. He showed how to build the real numbers rigorously from…
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…
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…
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,…
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…
Here's a mathematical fallacy that trips up even sharp students. Can you prove that the derivative of x squared is x instead of 2x? I'll show you the flawed proof,…
