Author: Kazi Abu Rousan C is hard but fast But you need to be on guard to last. Python is easy but slow But you can use it to glow. But if you have julia Beautiful rhythms will flow. ---Me Julia is a high-level, high-performance, dynamic programming language. Most of you guys have heard or […]
Dear student, In the past few years several Cheenta students reached the top 300 universities in the world. These universities include Oxford, UCLA, NUS, MIT and University of Edinburgh. We have gradually shaped a success pathway for students that works in the long run. This pathway can be useful for you as well.There two components of this success path: Component 1: Performance […]
Author: Kazi Abu Rousan There are some problems in number theory which are very important not only because they came in exams but also they hide much richer intuition inside them. Today, we will be seeing one of such problems. Sources: B.Stat. (Hons.) and B.Math. (Hons.) I.S.I Admission Test 2012 problem-2. B.Stat. (Hons.) and B.Math. […]
Author: Kazi Abu Rousan Where are the zeros of zeta of s? G.F.B. Riemann has made a good guess; They're all on the critical line, saith he, And their density's one over 2 p log t. Source https://www.physicsforums.com/threads/a-poem-on-the-zeta-function.16280/ If you are a person who loves to read maths related stuff then sure you have came […]
Problem If $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ then $\sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}$ is equal to (A) $\frac{{\pi}^2}{24}$ (B) $\frac{{\pi}^2}{8}$ (C) $\frac{{\pi}^2}{6}$ (D) $\frac{{\pi}^2}{3}$ Hint Try to write the summation as sum of square of reciprocal of odd numbers and even numbers and take the advantage of the infinite sum Solution $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ $\Rightarrow \sum_{n=1}^{\infty} \frac{1}{(2n)^2} + \sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}= […]
Probability theory is nothing but common sense reduced to calculation. Pierre-Simon Laplace Today we will be discussing a problem from the second chapter of A First Course in Probability(Eighth Edition) by Sheldon Ross. Let's see what the problem says: Describing the Problem The problem(prob-48) says: Given 20 people, what is the probability that among the […]
PROBLEM Let $p$ be an odd prime.Then the number of positive integers less than $2p$ and relatively prime to $2p$ is: (A)$p-2$ (B) $\frac{p+1}{2} $(C) $p-1$(D)$p+1$ SOLUTION This is a number theoretic problem .We can solve this problem in 2 different methods. Let us see them both one by one Method -1 Let us look […]
There should be no such thing as boring mathematics. Edsger W. Dijkstra In one of our previous post, we have discussed on Mandelbrot Set. That set is one of the most beautiful piece of art and mystery. At the end of that post, I have said that we can calculate the value of $\pi $ […]
Author: Kazi Abu Rousan The pure mathematician, like the musician, is a free creator of his world of ordered beauty. Bertrand Russell Today we will be discussing one of the most fascinating idea of number theory, which is very simple to understand but very complex to get into. Today we will see how to find […]
Problem Let $f$:$\mathbb{R} \rightarrow \mathbb{R}$ be a continous function such that for all$x \in \mathbb{R}$ and all $t\geq 0$ f(x)=f(ktx) where $k>1$ is a fixed constant Hint Case-1 choose any 2 arbitary nos $x,y$ using the functional relationship prove that $f(x)=f(y)$ Case-2 when $x,y$ are of opposite signs then show that $$f(x)=f(\frac{x}{2})=f(\frac{x}{4})\dots$$ use continuity to […]
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