MATC63 Differential Geometry (Winter 2025)

This course provides a first introduction to differential geometry, with a focus on the classical theory of curves and surfaces in Euclidean space.

Instructor: Prof. Robert (Bob) Haslhofer

Website: http://www.math.toronto.edu/roberth/C63.html

Lectures: Tuesday 2--3 in HLB106 and Thursday 1--3 in IC328

Office Hours: Tuesday 12--1 in IA4132

Grading Scheme: Homework 20%, Midterm 30%, Final exam 50%

There will be 5 homework assignments. Your lowest homework score will be dropped. There will be no makeup test! (If you miss the midterm for a valid reason, your grade will be reweighted as Homework 30%, Final 70%.)

Homework: via crowdmark

Weekly lecture notes: via quercus

Midterm Exam (in class): Feb 6 from 1--3

Final Exam: TBA

Prerequisites: MATB42 and MATB43

Textbook: T. Shifrin: Differential Geometry: A First Course in Curves and Surfaces

Secondary references:
M. Do Carmo: Differential geometry of curves and surfaces
A. Pressley: Elementary Differential Geometry

Topics to be covered: regular curves and surfaces in Euclidean space, local and global theory of curves, first and second fundamental form of surfaces, Gauss curvature and mean curvature, covariant derivative and parallel transport, Gauss-Bonnet theorem, geodesics, minimal surfaces and soap bubbles.