Math 570-1: Geometry and Topology ( 4 hours course)
References:
1- Topology a first course, Munkres, second edition, Prentice Hall, 2000.
2- Introduction to Topology, Crump Baker.
3- Calculus on Manifolds, A modern approach to Classical heorems of Advanced Calculus, W. Benjamin, 1965.
4- Differentiable Manifolds, Matsushima, Marcel Dekker, 1972.
5- Introduction to Differentiable Manifolds and Riemannian Geometry, Boothby, Academic press, 1975.
Description of the course:
Connected spaces, Path connected spaces, Connected components, locally connected spaces, Quotient sacpes. The separation axioms( Hausdorff, Regular, Normal).
Differentiable manifolds, submanifolds of R^n and classical Lie groups, Tangent spaces, Differentiable mappings between manifolds. Inverse and implicit function theorems on manifolds.
There will be weekly home works and one mid term exam. Then a final exam out of 50 points.