Studying knots mathematically has proven to be
an exceptionally fertile area of study and, within the past few years,
applications to various other disciplines have been uncovered. Using the
methods outlined in the sample
problem on knots determine which of the following knots are equivalent.
Keep in mind that simply establishing that two knots have the same colouring
invariant does not establish that they are equivalent. (But it is an indication
that they might be).