The first puzzle was here. You were asked to show that if group is defined as having a left identity e and every element g has a left inverse h with hg = e, then in fact the structure satisfies the normal definition of a group, so that e is also a right identity and [...]
Maths is a curious subject, which is reflected in its practitioners. Even by academic standards, mathematicians tend to come across as distinctly odd. For most of the world, maths means a school exam which they did not enjoy. A modest proportion can probably do some basic mental arithmetic and occasionally find that useful, although most [...]
I first took an interest in this topic when banking chiefs started parading before the Treasury Select Committee three years ago. I returned to it when Richard Williamson apologised to the pope shortly afterwards. Recently, claims Christina Patterson in today’s i, sham apologies have been coming thick and fast. Her main concern was l’affaire PIP. [...]
My local remainder/discount bookshop had a “sale” recently. That turned out to mean that they had a handful of books at 99p each instead of the usual £3.99 upwards. One was a complete works of Robert Burns (650pp, hardback). Having watched with interest the crowds along the Thames humming and fluffing their way through Auld [...]
This is based on the attack ad that sank Romney when he ran against Ted Kennedy in the 1994 Senate election. The new version, apparently starring the same cast of heart-broken ordinary citizens whose lives were allegedly destroyed by Romney as Gordon Gekko incarnate, has now been remade and re-released by a SuperPAC loyal to [...]
