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Instructor Office Hours |
Mondays 1:30-2:30, Wednesdays 3:00-4:00, in Room 318 Eckhart Hall, and by appointment. |
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Asaf Hadari | |||
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College Fellow Office Hours |
Tuesdays, 4-6, in Room 17 Eckhart Hall, and by appointment. |
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Class Meeting Times |
Tuesdays and Thursdays, 9:00-10:20, Room 203 Eckhart Hall. |
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Textbook |
Differential Topology, by Victor Guillemin and Alan Pollack |
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Exams |
In-Class Exam: Thursday, May 3rd Solutions |
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Syllabus |
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College Fellow Problem Session |
Wednesdays, 7:00 pm, in Room 312 Eckhart Hall. |
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Topics Covered |
Manifolds, tangent spaces, derivative, inverse function theorem, submersions, immersions, transversality, Preimage Theorem, homotopy, stability, Sard's Theorem, Morse functions, Whitney Embedding Theorem, tangent bundle, manifolds with boundary, intersection theory mod 2, oriented manifolds, oriented intersection theory, degree of a map, Brouwer Degree Theorem, vector fields, vector fields on spheres, Euler characteristic, Poincare-Hopf Index Theorem, Gauss map, exterior algebra, differential forms, exterior derivative, Stoke's theorem, cohomology, Thom's cobordism ring, and genera. |
Homework: Homework is due at the beginning of class on Thursdays. All exercises are in the textbook.
Due |
Homework Assignment |
April 5th |
Read 1.1-1.4 |
April 12th |
Read 1.5-1.6 |
April 19th |
Read 1.7-1.8 |
April 26th |
Read 2.1-2.4 |
May 3rd |
Read 2.5-2.6 |
May 10th |
Read 3.1-3.3,3.5 |
May 17th |
Read 3.7,4.1-4.3 |
May 24th |
Read 4.4 |
Wednesday |
Read 4.5 |
Practice Problems |
Remark: The code for this site goes back to Miklos Abert – who got it from someone else.