Topic for Spring 2023: Differential Geometry
Prerequisites: MATH 230 and MATH 250, or MATH 300
This course will study geometry from the perspective of "differential geometry". Topics will include tangent spaces, tangent quadrics, and tangent cubics which we will use to approximate curves and surfaces near a point. We will also investigate curvature. What does it mean that mass "curves" spacetime? Other topics to appear include manifolds, the classification of all possible 2-dimensional manifolds, and projective space, with all its wonderful "points at infinity".