## Math 348 A1 Fall 2016

 Instructor / Office / Phone # Xinwei Yu / 527 CAB / (780)4925731 Email ;  Webpage xinwei2@ualberta.ca ;  http://www.math.ualberta.ca/~xinweiyu Location / Time SAB 336/ TR 11 - 12:20 Office Hours T 12:30 - 14:30; R 12:30 - 13:30; Or by appointment

Important Dates:
• Midterms (Temporary): Thursdays in class. One hour each. Sept. 29, Nov. 3.
• Final Exam (Temporary, check beartracks for final date/time/location): 12-Dec-2016 (Monday) @ 9:00 a.m.; Two hours.
• Deferred Exam: Saturday Jan. 14, 2017 @ CAB 563. You need to register at 8:30am.

Course Material

 Week Dates Lecture Notes Required (optional) Readings in the Textbook Homeworks Due on Fridays at 12p in Assignment Box 1 9/1 L01: Introduction 2 9/6, 9/8 Review of Curves and Surfaces in Calculus: L02: Prerequisites L03: Curves (p.9--12 of L03 will be covered in Lecture 4) 1.1, 1.2 (1.3, 1.4, 1.5) HW1 (Due 9/16) Solutions 3 9/13, 9/15 L04: Surfaces L05: Surfaces (cont) 4.1, 4.2, 4.3, 4.4, 4.5 (Before Def. 4.5.1) (4.5, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6) HW2 (Due 9/23) Solutions 4 9/20, 9/22 Transition from Calculus to Differential Geometry: L06: Curvature L07: Torsion, Frenet-Serret equations 2.1, 2.3 (2.2) HW3 (Due 9/30) Solutions 5 9/27 9/29 Review for Midterm 1 Midterm 1 (Solutions) 6 10/4, 10/6 L08: The first fundamental form L09: Examples and applications 6.1 (6.2, 6.3, 6.4, 6.5) HW4 (Due 10/14) Solutions 7 10/11, 10/13 Genuine Differential Geometry Starts Here: L10--11: The second fundamental form 7.1, 7.2, 7.3 HW5 (Due 10/21) Solutions 8 10/18, 10/20 L12--13: Curvatures for surfaces 8.1, 8.2 (8.3, 8.4, 8.5, 8.6, 12.1,12.2,12.3,12.4,12.5) HW6 (Due 10/28) Solutions 9 10/25, 10/27 L14--15: Parallel transport and geodesics 7.4, 9.1, 9.2, 9.3, 9.4 (9.5) HW7 (Due 11/7) Solutions 10 11/1 11/3 Review for Midterm 2 Midterm 2 (Solutions) 11 Fall Reading Week 12 11/15, 11/17 Review of Midterm 2 L16--17: Gauss' Theorema Egregium 10.1, 10.2 (10.3, 10.4) HW8 (Due 11/25) Solutions 13 11/22, 11/24 L18--19: The Gauss-Bonnet Theorem 13.1 (13.2, 13.3, 13.4, 13.5, 13.6, 13.7, 13.8) HW9 (Due 12/2) Solutions 14 11/29, 12/1 L20-21: Generalizations to hypersurfaces Go through the textbook and previous lecture notes. 15 12/6 Review for Final Go through the textbook and previous lecture notes.