This teaching resource provides lecture notes and slides for a class on mathematical modeling of mammalian signaling pathways. This lecture was part of the course .Cell Signaling Systems: A Course for Graduate Students. and focused on quantitative modeling. The lecture describes how different types of mathematical representations are applied to different signaling systems to provide insight into how a signaling system controls cell behavior. The development of an ordinary differential equation.based model for a bistable switch and the predictions that can be obtained from the model are described. The lecture concludes with a description of how models can be tested experimentally and modified when the details of the models and the resultant predictive behavior are not confirmed by experimentation.