Shifrin T. Differential geometry. A first course in curves and surfaces

University of Georgia, 2021. — 128 p.This course is an in-person lecture course with in-class quizzes and graded homework. The official schedule for the course is provided on the the course webpage. Homework due dates are provided in Gradescope (see below) and aren’t listed on the webpage. You are expected to read the notes and the book sections before coming to class. There will be a brief quiz at the start of some classes (quiz dates are announced in advance on the webpage). You aren’t expected to completely understand after this first reading, but it will prepare you to get much more out of the lecture and class activities.
Students will develop an understanding of the geometry of curves and surfaces, including curvature and torsion fortudents will develop an understanding of the geometry of curves and surfaces, including curvature and torsion for space curves and Gauss and mean curvature for surfaces. The course will include discussion of the geometry of three dimensional space, and end with the Gauss-Bonnet theorem. At the end of the course, students should be prepared for a graduate course in Riemannian geometry space curves and Gauss and mean curvature for surfaces.