MATH 739
New! Solutions to the midterm exam!
The final exam will
be a take-home exam. It will be distributed on the last day of class
(May 6) and due on Monday, May 10 at 5pm.
Tuesday/Thursday 1:30-2:45, KH 253
Professor: Goldin
Office: Science and Tech I, Room 207
Office Hours/Location: Tuesdays/Thursdays 2:45-3:45, and by appointment
Contact Information: EMAIL IS BEST:
rgoldin@gmu.edu
Course Description: This is an introductory course in
differential geometry. The prerequisites include MATH 621, MATH 631, and MATH
685. If you have not had these courses, please speak to me within the first week
of classes. We will cover the following topics, subject to time constraints
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Smooth manifolds, submanifolds
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Diffeomorphisms and other maps of manifolds
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Vector fields
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Vector bundles, including tangent and cotangent bundles.
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Lie groups and group actions
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Tensor algebra and differential forms
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Riemannian metrics and symplectic forms
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de Rham cohomology
The book for the course is Smooth Manifolds by John M. Lee. We will follow many aspects of the book (though not all), and the problem sets will come mostly from the book. If you have seen the book, you know we will not be covering the whole book but rather select chapters and sections.
Course activity: There will be approximately 8-10 problem
sets given over the semester. There will be one mid-term exam on March 18, and a final exam.
The midterm exam is in-class but OPEN BOOK. You may also have your notes. Depending on class sentiment,
the final exam may be take-home.
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Grade: The grade in this course will be evaluated as follows. Students will earn the higher of
Problem Sets: 50%
Midterm Exam: 20%
Final Exam: 30%
Problem Sets: 70%
Midterm Exam: 15%
Final Exam: 15%
Problem Sets: 60%
Final Exam: 40%