Differentiable Manifolds

Homework:

Problem set 1: problems 1-4, due Monday, Sept. 23, in class.

Problem set 2: problems 5-10, due Monday, October 12, in class.

Problem set 3: problems 11-15, due Wednesday, November 11, in class.

MW 10:00-11:20, Smith Hall 204

Instructor	Prof. John Loftin, 309 Smith Hall, Phone: (973)353-5156, ext. 3910.
Email	loftin AT rutgers DOT edu Email is the best way to get in touch with me.
Website	http://andromeda.rutgers.edu/~loftin (this syllabus is attached to the website)
Department Website	http://math.newark.rutgers.edu/
Prerequisites	General topology (topological spaces, Hausdorff property, quotient topology, compactness, connectedness, covering spaces)
Course Material	Topological Manifolds Definitions Group Actions Some Advanced Calculus Differentiable Maps Implicit and Inverse Function Theorems Existence and Uniqueness of ODEs Change of Variables in Integration Differentiable Manifolds Submanifolds Differentiation on Manifolds Vector Fields Vector Bundles Riemannian Metrics Existence of Riemannian Metrics (Partitions of Unity) Geodesics Distance Normal Coordinates The Exponential Map Curvature Integration on Manifolds Multilinear Algebra and the Determinant Differential Forms Orientation and Volume Forms Manifolds with Boundary Stokes' Theorem More on Curvature Flatness and the Fundamental Group Complete Riemannian Manifolds of Negative Curvature
Text	An Introduction to Differentiable Manifolds and Riemannian Geometry, by William Boothby, published by Academic Press.
Homework	Homework will be assigned periodically. Students are encouraged to work together on the homework (but you must write up your own problem sets---no copying).
Exams	We may have an in-class midterm exam, and probably a take-home final.
Office Hours	M 1-2pm, W 11:30-12:30, in 309 Smith Hall. You may see me any time during office hours without an appointment. You may also make an appointment to see me at other times.