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No matter what function I put in the r.mapcalc in the GRASS GUI I get a blank map full of null values. I even tried DEM+0 (I can see my DEM) and this also yielded a blank map.

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Perhaps you haven't set computational region correctly? Try running g.region before r.mapcalc:

g.region rast=DEM

This makes the computational region match the extent of your map DEM.

See also: http://grasswiki.osgeo.org/wiki/Computational_region

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