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We present a 1.1~mm census of dense cores in the Mon~R2 Giant Molecular Cloudwith the AzTEC instrument on the Large Millimeter Telescope (LMT). We detect295 cores (209 starless, and 86 with protostars) in a two square degree shallowsurvey. We also carry out a deep follow-up survey of 9 regions with low tointermediate ($3<A_V<7$) gas column densities and detect 60 new cores in thedeeper survey which allows us to derive a completeness limit. After performingcorrections for low signal-to-noise cores, we find a median core mass of $\sim2.1 \text{M}_{\odot}$ and a median size of $ 0.08$~pc. $46\%$ of the cores(141) have masses exceeding the local Bonor-Ebert mass for cores with T=12K,suggesting that in the absence of supporting non-thermal pressure, theseregions are unstable to gravitational collapse. We present the core massfunction (CMF) for various subdivisions of the core sample. We find that coreswith masses $>$10~$M_{\odot}$ are exclusively found in regions with high corenumber densities and that the CMF of the starless cores has an excess oflow-mass cores ($<$5~$M_{\odot}$) compared to the CMF of protostellar cores. Wereport a power law correlation of index $1.99 \pm 0.03$ between local core massdensity and gas column density (as traced by Herschel) over a wide range ofsize scales (0.3-5~pc). This power law is consistent with that predicted forthermal fragmentation of a self-gravitating sheet.

Early science with the Large Millimetre Telescope: An LMT/AzTEC 1.1 mm Survey of Dense Cores in the Monoceros R2 Giant Molecular Cloud