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    \centerline{\it Math 438, Fall 2000  }

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\centerline{\bf   Syllabus and tentative schedule  }


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\begin{enumerate}

\item {\it Curves:} (week 1-3, one homework, one take-home mid-term), parametrized curves, regular curves, arc-length, vector
product, the local theory of curves, the local canonical curves, global properties of curves.

\item {\it  Regular surfaces}; (week 4-5, one  homework assignment), regular surfaces, inverse images of regular values, change of parameters, the tangent plane, the differential of a
map, the first fundamental form, area, orientation;

\item  {\it The Geometry of the Gauss maps}; (week 6-7, one homework set, one take-home mid-term exam), the second fundamental form, Gauss map in local coordinates, ruled surfaces, minimal surfaces, constant mean curvature surfaces.

\item  {\it The intrinsic geometry of surfaces:} (week 8-10, one homework set); Isometries, conformal maps, geodesics, parallel transport, the Gauss-Bonnet Theorem.

\item {\it  Global differential geometry:} (week 11-13, one homework set, take-home final exam), the variational formulas, surfaces of constant
Gauss curvature,
Chern-Lashof formula.


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\end{enumerate}


   If you have any further questions about Math 438, please feel free
to contact Professor Cao at 631-8847.
















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