  We describe recent experimental efforts to perform polarization-resolved
optical spectroscopy of monolayer transition-metal dichalcogenide
semiconductors in very large pulsed magnetic fields to 65 tesla. The
experimental setup and technical challenges are discussed in detail, and
temperature-dependent magneto-reflection spectra from atomically thin tungsten
disulphide (WS$_2$) are presented. The data clearly reveal not only the valley
Zeeman effect in these 2D semiconductors, but also the small quadratic exciton
diamagnetic shift from which the very small exciton size can be directly
inferred. Finally, we present model calculations that demonstrate how the
measured diamagnetic shifts can be used to constrain estimates of the exciton
binding energy in this new family of monolayer semiconductors.
