## 10 JanApplications of Sylow Theorems

Sylow Theorem's is Group Theory are an important mathematical tool. Below we give a simple application of the theorems. Theorem: If \$\$H\$\$ and \$\$K\$\$ are subgroups of \$\$G\$\$ and \$\$Hleq N_G(K)\$\$, then \$\$HK\$\$ is a subgroup of \$\$G\$\$. In particular, if \$\$K\$\$ is normal is \$\$G\$\$...

## 08 JanNEST 2012: Exam Alert

National Entrance Screening Test (NEST) is a compulsory test for students seeking admission to National Institute of Science Education and Research (NISER), Bhubaneswar and University of Mumbai - Department of Atomic Energy Centre for Excellence in Basic Sciences (UM-DAE CBS), Mumbai. Both NISER and UM-DAE...

## 16 DecTIFR PhD Entrance 2012 Question paper

The Tata Institute of Fundamental Research (TIFR) conducts  a graduate programme leading to the award of PhD degree in certain subjects.  The 2012 Mathematics question paper can be found here. We had also earlier posted the 2011 question paper here. [ad#ad-2]...

## 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 OctIndian National Mathematical Olympiad

The Indian National Mathematical Olympiad (INMO) is a prestigious Olympiad aimed at highly motivated high school students and pre college students. It is conducted all over the country in various centres. In Assam, Gauhati University is a centre. Please click here or here to get...

## 26 Sep2011 Assam State Olympiad Question Papers

The Assam Academy of Mathematics (AAM) organized the 2011 State Mathematics Olympiad in numerous centres all over Assam. The question paper for Category III (Class IX and X) can be found here, and the question paper for Category IV (Class XI and XII) can be...

## 05 AugInternational Mathematical Olympiad 2011

The International Mathematical Olympiad (IMO) is held every year in July where talented high school students participate in a grueling 9 hour exam spread over two days to tackle some of the most challenging mathematical problems. This year too it was held in Amsterdam where...

## 05 AugGATE 2011 Question Paper

The Graduate Apptitute Test in Engineering (GATE) is jointly organised by the Indian Institutes of Technology (IITs) and the Indian Institute of Science (IISc). The mathematics paper of the 2011 test can be found here. We are grateful to Mr. Uday Bhaskar Sharma (The Institute of...