# Spring 2007

 Instructor Dr. Thomas M. Fiore Email Instructor Office Hours Mondays 1:30-2:30, Wednesdays 3:00-4:00, in Room 318 Eckhart Hall, and by appointment. College Fellow Asaf Hadari Email College Fellow Office Hours Tuesdays, 4-6, in Room 17 Eckhart Hall, and by appointment. Class Meeting Times Tuesdays and Thursdays, 9:00-10:20, Room 203 Eckhart Hall. Textbook Differential Topology, by Victor Guillemin and Alan Pollack Exams In-Class Exam: Thursday, May 3rd Solutions Final: Tuesday, June 5th, 8am-10am, in Eckhart 203. Solutions Syllabus College Fellow Problem Session Wednesdays, 7:00 pm, in Room 312 Eckhart Hall. 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 Pages 5-7: Problems 2,3,4,5,12,13,14,16,17 Pages 11-13:1,2,4,9,10,11,12 April 12th Read 1.5-1.6 Pages 18-19: Problems 2,5,9,10, Extra Credit: 7 Pages 25-27: Problem 1 April 19th Read 1.7-1.8 Pages 25-27: Problems 2,7,10 Pages 32-33: Problems 4,5,7 April 26th Read 2.1-2.4 Pages 37-39: Problems 1,2,7,10 Pages 45-48: Problems 6 Pages 55-56: Problems 6,7 May 3rd Read 2.5-2.6 Pages 62-63: Problems 7,8 Pages 66-67: Problem 7 (no need to do 6) Prepare for Exam on May 3rd by redoing all old problems you may have missed, reviewing class notes, and doing additional practice problems. May 10th Read 3.1-3.3,3.5 May 17th Read 3.7,4.1-4.3 Page 83: Problem 4 Page 103: Problems 2,4,6,13 Page 117: Problems 1,7 Bonus: Page 117: Problem 9 May 24th Read 4.4 Page 139: Problem 3,10,11,18 Page 150: Problem 3 Wednesday May 31st Read 4.5 Page 160: Problems 6,10 (no need to do 8,9) Page 172: Problems 5,7,8 (no need to do 3) Practice Problems for Final

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