MATH 642 - Differential Geometry

(3 units)

Geometry of curves and surfaces in space; Frenet’s formulas; Cartan’s frame fields, Gaussian curvature; intrinsic geometry of surface; congruence of surfaces; the Gauss-Bonnet theorem.

Units of Lecture: 3
Offered: Every Fall - Odd Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. analyze the intrinsic geometry of curves in space, such as arclength and curvature.
2. analyze the intrinsic geometry of surfaces in space, such as surface area, Gaussian curvature.
3. determine whether two surfaces cannot be related by an isometric bijection, due to different intrinsic geometry.
4. use the Gauss-Bonnet theorem to relate the geometry of an oriented surface without boundary to its topology.

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