Everywhere Continuous Non-differentiable Function
Weierstrass shocked the mathematical world in 1872 by constructing a function that's continuous everywhere but differentiable nowhere. Not at a…
Math
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.
Free Online Calculus Text Books
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have…
Dedekind’s Theory of Real Numbers
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts.…
20+ Free Algebra Books for Students & Teachers (PDF Ebooks)
I've compiled 20+ free algebra and topology ebooks. Not sketchy PDFs from torrent sites. Real textbooks that professors and universities…
D’Alembert’s Ratio Test of Convergence of Series
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges.…
Essential Steps of Problem Solving in Mathematical Sciences
Problem solving in mathematics isn't about memorizing formulas. It's about knowing what to look for. I break down the essential…
Bhaskara II’s Lilavati: Complete Reference Guide (Download PDF)
Lilavati is a 12th-century mathematics treatise that reads like poetry. Written by Bhaskara II, it wraps arithmetic, algebra, and geometry…
The Collatz Conjecture: Unsolved but Useless
Pick any positive integer. If it's even, halve it. If it's odd, triple it and add one. Repeat. You always…
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Dirichlet theorem connects the Gamma and Beta functions to evaluate complex multiple integrals. Liouville extended it further, making it…
Mystery of Missing Money – 1 Rupee by Shakuntala Devi
Shakuntala Devi's missing money puzzle is a classic in mathematical logic. Two women sell marbles at different rates. When they…
Understanding Poincare Conjecture
In 1904, Poincare asked a deceptively simple question: if a three-dimensional shape is simply connected, must it be a sphere?…
Derivative of x squared is 2x or x ? Where is the fallacy?
Here's a mathematical fallacy that trips up even sharp students. Can you prove that the derivative of x squared is…