Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. Prime Generating Formulas We all know how hard it is to predict a formula for prime numbers!…

# Writing

I am an experimental Windows user. I find, install and experiment with several new applications on my Windows PC every week. Most of the applications and tools I have installed are directly or indirectly about desktop publishing. Some of them are aimed to help me with my study and some others are for web development. In…

What is a backlink? In the language of SEO, a backlink to your site is an HTTP URL from any other site which points to one of your webpages. Backlinks help bloggers and webmasters meet more traffic, better search engine reputation and gain better algorithmic parameters like Google Page Rank, Alexa Rank, Moz Rank, Domain…

‘Symmetry’ has a special meaning in physics. A picture is said to be symmetrical if one side is somehow the same as the other side. Precisely, a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation. For example, if we look at a…

It was mid 2012, the first time I installed TeXstudio version 2.3, on my PC. ‘Peaceful‘ was the word I used to describe it then after. TeXstudio has now gradually inched to version 2.12.22 and by time being even more peaceful and wonderful. Wonder why did I call it ‘peaceful’? Writing LaTeX is a real pain, when you are willing to…

If you are starting a blog then WordPress can be an exciting platform because it’s free, user-friendly and has a variety of plugins that give you many options. It is also known to be a powerful content management system, which is an added advantage. Moreover business owners and individuals alike can benefit from it because…

About This post is actually a summary of a research project I took under INSPIRE-SHE Scholarship Program by the Dept. of Science and Technology, Govt. of India. My plan was to make the content open-source on the web that faults could be corrected by time. The language is simple and very easy to understand and the…

An old yet beautiful untabled listing of highly interactive mathematics related articles and papers available online.

Long post and page URLs can be annoying. Take an example: https://gauravtiwari.org/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/ (one of the most popular posts from my blog). Will you like to write these (about) a hundred characters? Or will you prefer URL shorteners, like bit.ly or wp.me, instead? As a third option, you may say, “I can just copy and paste the URLs to…

What is Logic? If mathematics is regarded as a language, then logic is its grammar. In other words, logical precision has the same importance in mathematics as grammatical accuracy in a language. As linguistic grammar has sentences, statements— logic has them too. After we discuss Sentence & Statements, we will proceed to further logical theories.…

In this note/article, I will discuss what Fermat Numbers are and what some important theorems & examples are associated with them. Definition and Examples Fermat Numbers, a class of numbers, are the integers of the form $ F_n=2^{2^n} +1 \ \ n \ge 0$ . For example: Putting $ n := 0,1,2 \ldots$ in $…

Looking for free PDF algebra and topology books online? I have gathered a 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 broken, please email me at gaurav@gauravtiwari.org. Let’s start. Abstract Algebra Online by Prof. Beachy This…