Coordinates: Mondays and Wednesdays, 11:30 AM - 1 PM in MC 108.
Instructor: Rasul Shafikov, MC 112, . Office Hours: Tuesdays, 1 PM - 2:30 PM.
Announcements: There will be no class on Wed, Nov. 2.
Textbook: Smooth manifolds by J. Lee. Springer, 2002
Course Description: Manifold structures appear everywhere in mathematics and in physics. The goal of the course is to give a gentle, yet rigourous introduction to basic notions associated with smooth (diﬀerentiable) manifolds such as smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, diﬀerential forms, foliations, etc. Unlike a course in diﬀerential geometry we will NOT be discussing the curvature tensor or connections.
Prerequisites: Basic undergraduate linear algebra, real analysis, and a course in general topology. In particular, we will be working with covering spaces. These will be brieﬂy discussed at the beginning of the course, but it is recommended that a student should at least be familiar with the notion of the fundamental group and covering spaces.
Assignments: Homework will be assigned biweekly, and will include routine exercises as well as some challenging problems.
Exams: There will be a Midterm and a Final Exam.
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