Starting with multi-variable calculus, this course will develop the theme of invariants attached to the intrinsic and extrinsic geometry of curves and surfaces. Using local coordinates, invariants will be defined, which will later turn out to be independent of the choice of coordinates. The contrasts between intrinsic and extrinsic concepts will be emphasized. The notion of a smooth submanifold will be explored in detail, as will various notions of curvature. The various notions of curvature of surfaces are related to curvature and torsion of curves. The contrast between local and global phenomena is also emphasized. In the past the course has dealt with surfaces of revolution, ruled surfaces, minimal surfaces, special curves on surfaces, Gauss's "Theorema Egregium" and the Gauss-Bonnet theorem.
1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (MATH461, MATH240, MATH341); and must have completed two 400-level MATH courses with a minimum grade of C- (not including MATH461, 478, and 480's).
Level of Rigor
Elementary Differential Geometry, by Andrew Pressley
Diff. Geometry of Curves & Surfaces, by Manfredo Do Carmo
Computer science, physics
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Students interested in grad school in MATH should consider this course