MATH 3B03

GEOMETRY

Undergraduate

Fall 2026 · C01

Readings

eText Elementary Differential Geometry - 6 Month Access Ed: 2
Pressley · 2 · Required
ISBN 9781848828919; 9781848828902

Fall 2026 · C01

Smooth curves (1.1, 1.2)
Arclength and Tangent Vectors (1.3,1.4)
Curvature of plane curves, closed curves, and Hopf's umlaufsatz (2.1, 3.1)
Isoperimetric inequality (3.1, 3.2)
Introduction to surfaces (4.1-4.3)
Tangent plane, derivatives, normals, orientability (4.4, 4.5)
First fundamental form (metric tensor) and lengths of curves (6.1)
Local isometries (6.2, 6.4)
Second fundamental form (7.1)
The Gauss map, Weingarten map (7.2)
Geodesic and normal curvatures, parallel transport (7.3,7.4)
Gaussian, mean, and principal curvatures (8.1)
Geodesics and minimal curves (9.1,9.2,9.4)
Gauss-Codazzi-Mainardi equations (10.1)
The Theorem Egregium (10.2)
Plateau's problem (12.1)
Minimal surfaces (12.2)
The Gauss Bonnet Theorem : (13.1-13.4)
Singularities of vector fields (13.7) *
An Introduction to Riemannian geometry*

Elementary Differential Geometry
Andrew Pressley · 2010 · 2nd · Required
Springer Undergraduate Mathematics Series
Elementary Differential Geometry Authors: Andrew Pressley Publisher: Springer Undergraduate Mathematics Series Publication Date: 2010 Edition: 2nd https://link.springer.com/book/10.1007/978-1-84882-891-9
See source
https://link.springer.com/book/10.1007/978-1-84882-891-9
See source

Fall 2025 · C01

Etext Elementary Differential Geometry - 6 Month Access Ed: 2
Pressley · 2 · Required
ISBN 9781848828919; 9781848828902

Sources