## Two Interesting Math Problems

Problem1: Smallest Autobiographical Number: A number with ten digits or less is called autobiographical if its first digit (from the left) indicates the number of zeros it contains,the second digit the number of ones, third…

## Fox – Rabbit Chase Problems

Part I: A fox chases a rabbit. Both run at the same speed $v$ . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs…

## Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $x$ but do not possess a derivative for any value. We now consider the celebrated function…

## Memory Methods

Memory, in human reference, is the ability to store retain and recall information when needed. Without hammering the mind in the definitions, let we look into the ten methods of boosting our memory:  1. Simple…

## Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails for few more related articles. I have tried to list almost all freely available Calculus texts. Here…

## Dedekind’s Theory of Real Numbers

Intro Let $\mathbf{Q}$ be the set of rational numbers. It is well known that $\mathbf{Q}$ is an ordered field and also the set $\mathbf{Q}$ is equipped with a relation called "less than"…

## Free Online Algebra and Topology Books

This is a brief list of free e-books on Algebra, Topology and Related Mathematics. I hope it will be very helpful to all students and teachers searching for high quality content. If any link is…

## Applications of Complex Number Analysis to Divisibility Problems

Prove that ${(x+y)}^n-x^n-y^n$ is divisible by $xy(x+y) \times (x^2+xy+y^2)$ if $n$ is an odd number not divisible by $3$ . Prove that ${(x+y)}^n-x^n-y^n$ is divisible by $xy(x+y) \times {(x^2+xy+y^2)}^2$…

## Consequences of Light Absorption – The Jablonski Diagram

All about the Light Absorption’s theory on the basis of Jablonski diagram. According to the Grotthus – Draper Law of photo-chemical activation: Only that light which is absorbed by a system, can bring a photo-chemical change.…