  The dense vortex matter structure and associated magnetization are calculated
for type-II superconducting mesoscopic disks. The magnetization exhibits
generically first-order phase transitions as the number of vortices changes by
one and presents two well-defined regimes: A non-monotonous evolution of the
magnitude of the magnetization jumps signals the presence of a vortex glass
structure which is separated by a second-order phase transition at $H_{c2}$
from a condensed state of vortices (giant vortex) where the magnitude of the
jumps changes monotonously. We compare our results with Hall magnetometry
measurements by Geim et al. (Nature 390, 259 (1997)) and claim that the
magnetization exhibits clear traces of the presence of these vortex glass
states.
