Pen Paper And PHP

A Possible Proof of Collatz Conjecture

Our reader Eswar Chellappa has sent his work on the solution of '3X+1' problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that: $$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even } \\ 3x+1, & \text{ if } x \text{ is odd} \end{cases}$$ Then the iterates of…


8 big online communities a math major should join

Online communities are the groups of web savvy individuals who share communal interests. A community can be developed with just a single topic or by a bunch of philosophies. A better community binds its members through substantial debates. Mathematics is a very popular communal interest and there are hundreds of online communities formed in both Q&A and debate styles. Some mathematical communities are so immense that they serve two or three discussions every minute. If you are a math student,…

Unlocked Lock

New Math Series: Selected Topics in Functional Analysis

This series of study notes is aimed for post-graduate (M.A/M.Sc.) students of Indian & international universities. The study of functional analysis can be started after basic topology and set theory courses. In this introductory article we will start with some elementary yet important definitions and notations from analysis. We will finish this article with the definition of Norm & Normed Linear spaces derivedfrom the notions of linear spaces. An elementary treatise of examples and their completeness of Normed (linear) Spaces will…

Useful Php Scripts

Effective PHP Scripts to use for your WordPress blog

WordPress plugins are effective and easier to use. They do what they are meant to. You can get WP plugins for almost any tweak you want to do with your site. But there are still a few tweaks that can't be done by plugins. Or, if they could be done -- plugins might build seriously more load on your site. To solve this, you can always place some PHP scripts which run into your WordPress' site's front-end to offer wanted results. This process doesn't need installation of plugins and hence strengthens your site's security and keeps bloat away. Here is the list of some highly useful PHP scripts to use for your WordPress blog. This list is expandable and will surely expand to larger number of scripts as time moves on. All the codes listed below are error-proof and tested by me on my blogs.
Iit Jee Inception Program

UFaber Gives Wings to IIT Aspirants Dreams – Free Webinar on IIT JEE Inception Program

It is a dream harbored by many young minds across the country and for good reason. Yes, that’s right, we are talking about the coveted IITs here. With each passing year, the competition gets even tougher. While some, with their shrewd tactical approach to studies, proper guidance and hard work crack the entrance exam, the unlucky ones are left wondering where exactly did they go wrong.