Projection Theory
A graduate-level MIT OpenCourseWare course examining how a set X behaves under different orthogonal projections, a question not usually emphasized in standard analysis curricula but central to several active research areas. The course surveys applications of projection theory in harmonic analysis, analytic number theory, additive combinatorics, and homogeneous dynamics, introducing each topic, motivating its connection to projections, and proving representative results rather than the strongest known theorems. Materials follow MIT's OpenCourseWare model of lecture notes and course materials made freely available online, with no certificate offered. The course is aimed at advanced graduate students already comfortable with real analysis who want to see how a single geometric question threads through multiple branches of modern mathematics, building from foundational questions up to recent developments in the field.