Free Online Calculus Text Books
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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.
Dedekind’s Theory of Real Numbers
Most math students encounter real numbers without ever seeing how they're actually constructed. You use \( \pi \) and \( \sqrt{2} \) throughout calculus, but nobody explains what these objects…
20+ Free Algebra Books for Students & Teachers (PDF Ebooks)
20+ Free Algebra Books for Students & Teachers handpicked and reviewed. Practical recommendations based on real testing and experience.
D’Alembert’s Ratio Test of Convergence of Series
The D'Alembert Ratio Test is one of the most useful tools for determining whether an infinite series converges or diverges. If you're studying real analysis or calculus, you'll use this…
Essential Steps of Problem Solving in Mathematical Sciences
Problem solving is more than just finding answers. Learning how to solve problems in mathematics is simply to know what to look for. Mathematics problems often require established procedures. To…
Bhaskara II’s Lilavati: Complete Reference Guide (Download PDF)
Lilavati is a 12th-century mathematics treatise that reads like poetry. Written by Bhaskara II (also known as Bhaskaracharya), it wraps arithmetic, algebra, and geometry inside riddles about bees, snakes, peacocks,…
The Collatz Conjecture: Unsolved but Useless
A comprehensive guide with practical insights and actionable advice.
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Gamma function is one of the most important special functions in mathematics. It extends the factorial to non-integer values. The Beta function is its close relative, and together they…
Mystery of Missing Money – 1 Rupee by Shakuntala Devi
Two women sell marbles at a market. One charges 3 marbles for ₹1. The other charges 2 marbles for ₹1. They each have 30 unsold marbles at the end of…
Understanding Poincare Conjecture
In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked:…
Derivative of x squared is 2x or x ? Where is the fallacy?
A comprehensive guide with practical insights and actionable advice.
Solving Ramanujan’s Puzzling Problem
Here's a problem that looks impossible at first glance. You've got infinitely many nested square roots, each level multiplied by an increasing integer. How do you even begin to evaluate…