Astro2020 Science White Paper: First Stars and Black Holes at Cosmic Dawn with Redshifted 21-cm Observations

The cosmic dawn refers to the period of the Universes history when stars and black holes first formed and began heating and ionizing hydrogen in the intergalactic medium (IGM). Though exceedingly difficult to detect directly, the first stars and black holes can be constrained indirectly through measurements of the cosmic 21-cm background, which traces the ionization state and temperature of intergalactic hydrogen gas. In this white paper, we focus on the science case for such observations, in particular those targeting redshifts z $gtrsim$ 10 when the IGM is expected to be mostly neutral. 21-cm observations provide a unique window into this epoch and are thus critical to advancing first star and black hole science in the next decade.