Groups and Homomorphisms

One often sees that proving theorems about groups and related structures can involve clever reasoning and ingenuity. I will be collecting, when possible, problems which use such reasoning, because what is more disorienting than not being able to re-use a clever method you discovered a few weeks ago? Problem 1: Show that has the same number…

Starting off: The notion of a group

In this series of posts exploring the Rubik’s Cube, the notion of a group is going to be central. A set and an operation @ (like +, *, – ) are said to form a group if they satisfy the following conditions. (The text above looks different because I had to first type it in Tex and then take…

Taking on the Rubik’s Cube

Group theory is so often seen as a highly abstract area of Mathematics and it seems difficult to imagine how it could be applied in the real world. Perhaps it seems as an area that mathematicians love for its pure beauty and its fascinating structures and reasoning. However that is not very much true. While…

Number Theory : The Queen of Mathematics

The Prince of Mathematics, Carl Friedrich Gauss once famously said : Mathematics is the Queen of the Sciences and Number theory is the Queen of Mathematics. This statement though highly debatable, does find resonance in many of the great mathematicians of both the past and the present (and most probably this will be true of…