  A major goal of cosmology is to obtain sensitive, high resolution maps of the
Cosmic Microwave Background (CMB) anisotropy. Such maps, as would be produced
by the recently proposed Microwave Anisotropy Probe (MAP), will contain a
wealth of primary information about conditions in the early universe. To
mitigate systematic effects when observing the microwave background, it is
desirable for the raw data to be collected in differential form: as a set of
temperature differences between points in the sky. However, the production of
large (mega-pixel) maps from a set of temperature differences is a potentially
severe computational challenge. We present a new technique for producing maps
from differential radiometer data that has a computational cost that grows in
the slowest possible way with increasing angular resolution and number of map
pixels. The required central processor (CPU) time is proportional to the number
of differential data points and the required random access memory (RAM) is
proportional to the number of map pixels. We test our technique, and
demonstrate its feasibility, by simulating one year of a space-borne anisotropy
mission.
