I will focus on two important themes in contemporary ecology that draw upon mathematical tools: the dynamics of populations in space and management of populations. I will consider both deterministic and stochastic models of spatial population dynamics. For the management questions, I will consider both the issue of controlling invasive species in space and approaches for maintaining endangered species. Mathematical tools will be diverse, ranging from partial differential equations to stochastic models to different optimization approaches. Issues of time scales and the interface between models and data will be emphasized.