Dr. Paul Stanford departed from our recent lectures on applied
mathematics and contest preparation to give our students a
glimpse into the fascinating world of pure mathematics. Dr.
Stanford is particularly skilled at teaching deep ideas without
the need to resort to complex algebra, I’ll attempt in this
recap to do his lecture a small bit of justice. Dr. Stanford
began with one of the simplest concepts, points on a plane and
arrows connecting those points. Many of these arrows considered
together and connecting a set of points yield all sorts of
interesting directed graphs or “digraphs.“ This idea becomes
more interesting when restrictions are imposed such as the rule
that no two arrows can originate from the same point. When a
sequence of arrows loop back upon themselves they form a shape
like a “hairy circle” from the title of the lecture. Dr.
Stanford further restricted the cases with the following rules:
no two arrows can connect to the same point and no symmetry is
allowed. These restrictions yielded on