  We present a set of compelling science cases for the ALMA Band 1 receiver
suite. For these cases, we assume in tandem the updated nominal Band 1
frequency range of 35-50 GHz with a likely extension up to 52 GHz; together
these frequencies optimize the Band 1 science return. The scope of the science
cases ranges from nearby stars to the re-ionization edge of the Universe. Two
cases provide additional leverage on the present ALMA Level One Science Goals
and are seen as particularly powerful motivations for building the Band 1
Receiver suite: (1) detailing the evolution of grains in protoplanetary disks,
as a complement to the gas kinematics, requires continuum observations out to
~35 GHz (~9mm); and (2) detecting CO 3-2 line emission from galaxies like the
Milky Way during the epoch of re-ionization, i.e., 6 < z < 10, also requires
Band 1 receiver coverage. The range of Band 1 science is wide, however, and
includes studies of very small dust grains in the ISM, pulsar wind nebulae,
radio supernovae, X-ray binaries, the Galactic Center (i.e., Sgr A*), dense
cloud cores, complex carbon-chain molecules, masers, magnetic fields in the
dense ISM, jets and outflows from young stars, distant galaxies, and galaxy
clusters (i.e., the Sunyaev-Zel'dovich Effect). A comparison of ALMA and the
Jansky VLA (JVLA) at the same frequencies of Band 1 finds similar sensitivity
performance at 40-50 GHz, with a slight edge for ALMA at higher frequencies
(e.g., within a factor of 2 for continuum observations). With its larger number
of instantaneous baselines, however, ALMA Band 1data will have greater fidelity
than those from the JVLA at similar frequencies.
