Vision science combines ideas from physics, biology, and psychology. The language and ideas of mathematics help scientists communicate and provide an initial framing for understanding the visual system. Mathematics combined with computational modeling adds important realism to the formulations. Together, mathematics and computational tools provide a realistic estimate of the initial signals the brain analyzes to render visual judgments (e.g., motion, depth, and color). This chapter first traces calculations from the representation of the light signal, to how that signal is transformed by the lens to the retinal image, and then how the image is converted into cone photoreceptor excitations. The central steps in the initial encoding rely heavily on linear systems theory and the mathematics of signal-dependent noise. We then describe computational methods that add more realism to the description of how light is encoded by cone excitations. Finally, we describe the mathematical formulation of the ideal observer using all the encoded information to perform a visual discrimination task, and Bayesian methods that combine prior information and sensory data to estimate the light input. These tools help us reason about the information present in the neural representation, what information is lost, and types of neural circuits for extracting information.