## 09 DecMorley's Theorem

INTRODUCTION: One of the most elementary theorems in elementary geometry was discovered about 1899 by F. Morley (whose son Cristopher wrote novels such as Thunder on the Left). He mentioned it to his friends, who spread it over the world in the form of mathematical gossip....

## 30 NovWeirstrass' M-Test

We shall state and prove a very important result in Real Analysis called the Weirstrass' M-Test. The statement of the theorem is give below. Let \$\$\$\$ be a sequence of positive real numbers such that \$\$mid f_n(x) mid leq M_n\$\$ for \$\$x in D\$\$, \$\$n in...

## 05 AugTIFR Graduate School Question Paper-2011

The Tata Institute of Fundamental Research (TIFR), Mumbai organises its entrance exam for the Graduate Studies program. The 2011 paper can be found here. We are grateful to Mr. Uday Bhaskar Sharma (The Institute of Mathematical Sciences, Chennai) for providing us the question paper. [ad#ad-2]...

## 30 Jul20 টা বিখ্যাত অবীজীয় সংখ্যা

এটা পূৰ্ণ সংখ্যা আৰু এটা স্বাভাৱিক সংখ্যাৰ হৰণফল হিচাপে প্ৰকাশ কৰিব পৰা সংখ্যাবোৰক পৰিমেয় সংখ্যা বোলে আৰু এইদৰে যিবোৰ সংখ্যাক প্ৰকাশ কৰিব নোৱাৰি সেইবোৰক অপৰিমেয় সংখ্যা বোলে। পৰিমেয় সহগ বিশিষ্ট কোনো বিজগণিতীয় সমীকৰণৰ মূল হিচাপে প্ৰকাশ কৰিব পৰা সংখ্যাবোৰ হ’ল বীজীয় সংখ্যা আৰু যিবোৰ সংখ্যা...

## 24 JulISI 2009 Question Paper

The Indian Statistical Institute is a premier institute of India, and we give below the question paper for its BMath programme held in 2009.   Click Here   [ad#ad-2]...

## 14 MayNapier's Constant "e" is Transcendental

This theorem was first proved by Hermite in 1873. The below proof is near the one given by Hurwitz. We at first derive a couple of auxiliary results. Let \$\$f(x)\$\$ be any polynomial of degree \$\$ mu\$\$ and \$\$ F(x)\$\$ the sum of its derivatives, \$\$displaystyle F(x)...

## 13 MaySome Mathematics Brain Teasers

1. The greatest number of Mondays that can occur in the first 45 days of a year is ___? Ans: 7 If the first day is a Monday, then every seventh day is also a Monday, and Monday falls on the following numbered days: 1, 8, 15,...

## 21 AprThe Albert Einstein Quiz

It is said that this quiz was made up by Albert Einstein and according to him 98% will not solve it. There is a row of five houses, each having a different colour. In these houses live five people of various nationalities. Each of them nurtures...