Online communities are 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

# Education

Gaurav Tiwari is one of the top Education bloggers online, specializing in exam preparation, online learning and career development.

Linear Space or Vector Space over a field K Definition: The linear space over a field K is a non-empty set along with a function $+ : X \times X \to X$ called linear/vector addition (or just, ‘addition‘) and another function $ \cdot : K \times X \to X$ called scalar multiplication, such that for all elements $x, y, z, \ldots$ in $X$ and $1, k,

My personal mobile number 9565804301 is a prime number. What is a prime number? Any integer p greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. In other words, the natural numbers which are completely divisible by 1 and themselves only and have no other factors, are called prime numbers. 2 , 3,5,7,11,13… etc. are prime numbers [or just Primes].

‘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 base that is left and right symmetrical, then turn it 180°

Every person in the world likes to enjoy and leads his/her life happily. There are many ways to enjoy, and the first among them will definitely be a vacation or traveling to the world’s beautiful and historic places to admire the beauty of nature and get away from his daily routines. In this busy life it is not possible to visit the most wonderful destinations frequently,

1st April is a day of fun, humor and enjoyment. Even though, I have lot of fun puzzles on this blog, these ten are totally meant for today. Enjoy! PUZZLES 1. If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one matchstick in the matchbox, so what do you light first? 2. If the question you answered

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 write a long document or article, which in my case are

How many weeks are left before your final exams? Are you ready to score memorable grades? If not, you may just have to wait another 12 months to re-take exams and no student wants that to happen. GCSE students who fail won’t be able to pursue A-levels, and A-level students who fail (or get low grades) won’t get into their dream college. Did we get your

In this article we will define what are Macrostates and Microstates in Statistical Physics with examples and illustrations. Consider some (4, say) distinguishable particles. If we wish to distribute them into two exactly similar compartments in an open box, then the priori probability for a particle of going into any one of the compartments will be exactly 1/2 as both compartments are identical. If the four

This post explains the basic method of converting an integral equation into a corresponding differential equation.

A-level exams cannot be avoided by avid students with ages between 16 and 18 looking to go to college. These tests are extremely important and the marks obtained will most likely be your ticket to entering a good university. Getting ready for A-level exams means more than just reading notes and hoping for positive results; you must look forward for an exam revision and always remember

Infinitely many answers questions are possible to the answer, “No”. So, our real task should be to find one of THOSE many, which seems to be a perfect one. A simple and the first ever logical approach of giving answers to a question is to derive answers from the question, that is, replace some words of the question with reasonable ones and make a statement. (Conversely but )

If you’re a 16-year-old student preparing for any exam, you must know one thing – your brain needs special treatment. We have the power to understand so many things about our memory’s structure, which is why it’s our duty to find the best training strategies for the brain and prepare it for intensive testing. The process is all about working its neuro-plasticity, compel it to stay

Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the interval $(a,b)$ if $$\displaystyle {\int_a^b} {|y(x)|}^2 dx <\infty$$ or $$\displaystyle {\int_a^b} y(x) \bar{y}(x) dx <\infty$$. For further reading, I suggest this Wikipedia page. $y(x)$ is then also called ‘regular function’. The kernel $K(x,t)$ , a function of two variables is an $\mathfrak{L_2}$ – function if atleast one

It is so fun and enjoyable to travel through rail routes. Most of the people love to travel through rails instead of preferring to travel through the car. Travelling through rail is a good experience along with watching the beauty of nature and different sceneries when you travel long distances. Many of the people believe that it is safe to travel on rail routes, but sometimes

In this article I will explain what are Integral Equations, how those are structured and what are certain types of Integral Equations. What is an Integral Equation? An integral equation is an equation in which an unknown function appears under one or more integration signs. Any integral calculus statement like — $ y= \int_a^b \phi(x) dx$ can be considered as an integral equation. If you noticed

Every student or graduate knows how hard the first experience of passing exams is. Preliminary preparation starves the nervous system and the physical condition of the human body, however, the exam itself is always a stressful situation, which requires a candidate a great manifestation of mental and physical abilities. Therefore, just the knowledge of a subject is not enough for the exam. The examinee needs to

Exams have been haunting students forever, and although you’re willing to do whatever you can to retain essential information, sometimes you end up spending weeks studying with useless revision techniques. We’re accustomed to employing our own techniques when it comes to studying such as making sticky notes, highlighting, or drawing charts. However, recent studies conducted in the US have shown that many of the most famous