  This set of lecture notes presents a pedantic derivation of the connection
between the $ {\hat A} $-genus of spacetime's loop space and the genus one
partition function of the $ N=1/2 $ sigma model. It concludes with some remarks
on possible generalizations of the $ {\hat A} $-genus which follow naturally
from the `stringy' point-of-view but have yet to be explored mathematically.
This set of lecture notes is geared towards a mathematical audience unfamiliar
with the $ N=1/2 $ sigma model.
