This is a team-taught course for students enrolled in the computational neuroscience graduate program. In my segment I cover three topics: convolution and filtering in primary visual cortex; frequency analysis and velocity computation in area MT; and optic flow and heading perception in area MSTd. In all cases I explain how mathematical models are crucial for formalizing ideas and generating testable predictions.

The figure illustrates a theory I developed with Richard Anderson called spiral space theory. It is a model of heading computation in which heading is identified as a position in a 4-dimensional space (only 3 dimensions are shown) with axes representing orthogonal types of flow. I cover this model in the course to emphasize that mathematical models are above all formalizations, sometimes purely graphical in nature.