Date Submitted:

Changes proposed by: misrak

Catalog Pages referencing this course

Programs referencing this course

Columbian College of Arts and Sciences

Mathematics (MATH)

MATH

3848

Differential Geometry

Differential Geometry

Fall 2017

3

Course Type

Lecture

Default Grading Method

Letter Grade

No

No

MATH 2184 or MATH 2185; MATH 2233 and MATH 2971

Corequisites

30

Frequency of Offering

Term(s) Offered

Are there Course Equivalents?

No

No

Fee Type

No

Curves in space, regular surfaces, tensors, fundamental forms of a surface, Gauss–Bonnet theory, minimal surfaces; the geometry of the Gauss map.

A student who completes this course will know: * the properties of a curve and the concepts of curvature and torsion. * what is a regular surface and what is its Gauss map. * how to calculate the first and second fundamental forms of a surface and quantities such as arc length, surface area, principal curvatures, Gauss curvature and mean curvature. * the meaning of the covariant derivative and how to compute it. * the implications of Theorema Egregrium and the Gauss-Bonnet Theorem.

Uploaded a Course Syllabus

Course Attribute

CCAS - GCR: Q & L

Updated 04/07/17.

Key: 4858