Differential geometry is the study of geometric properties of curves, surfaces, and their higher dimensional analogues using the methods of calculus. It has a long and rich history, and, in addition to its intrinsic mathematical value and important connections with various other branches of mathematics, it has many applications in various physical sciences. In this course, we will study differential manifolds, Riemannian metrics, Levi-Civita connections, curvature tensors, geodesics and space forms and possibly comparison theorems in Riemannian geometry.
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Real analysis