## 02 AugIMO 2012

The 53rd International Mathematical Olympiad (IMO) was held this year at Mar del Plata, Argentina. The question papers can be downloaded here. The 52nd IMO was held last year at the Netherlands. The IMO problem short-list with the solutions of that IMO can be downloaded here. The...

## 12 JulThe Flower Puzzle

Consider the following puzzle: There are three temples say A, B and C. A priest takes with him some flowers and visits A. The flowers instantly double itself, and the priest keeps some of those flowers in A and proceeds towards B. At B also the...

## 24 AprA geeky party trick

You are at a friend’s place having good time together, watching TV, maybe playing classic video games, or whatever you are in mood for. Soon it all gets pretty boring. You are in mood for some fun and you want to have a bet with...

## 12 AprRamanujan Magic Square

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the...

## 08 AprHilbert's Axioms of Geometry

David Hilbert was a German mathematician who is known for his problem set that he proposed in one of the first ICMs, that have kept mathematicians busy for the last century. Hilbert is also known for his axiomatisation of the Euclidean geometry with his set...

## 27 FebNumber magic

Recently I found all the 22 existing ways to put 0 to 9 in the equation of a product such that each number occurs exactly once. And here they are: 5694×3=17082 6819×3=20457 6918×3=20754 8169×3=24507 9168×3=27504 3907×4=15628 7039×4=28156 9127×4=36508 5817×6=34902 3094×7=21658 4093×7=28651 9304×7=65128 9403×7=65821 594×27=16038 495×36=17820 402×39=15678 396×45=17820 715×46=32890 367×52=19084 297×54=16038 927×63=58401 345×78=26910   Also, as an extension, did the same after excluding zero: 1738×4= 6952 1963×4= 7852 483×12= 5796 297×18= 5346 198×27= 5346 157×28= 4396 186×39=...

## 26 FebA closer look into a well-known quotient ring

The ring \$\$Z[i]={a+ib: a,b in Z, i^{2}=-1}\$\$  is quite a well- known ring in Algebra. Further, being a principal ideal domain, every ideal of \$\$Z[i]\$\$  is generated by a single element say \$\$a+ib in Z[i]\$\$ and so can be taken in the form \$\$<a+ib>={(x+iy)(a+ib): x,y...

## 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]...