Math563-syllabus.docx
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Math563H Spring 2019 Differential Geometry Instructor: Belgin Korkmaz Office:
1124 LGRT (413-545-7677)
Office hours: Monday 15:00-16:30, Tuesday 10:00-12:00, Thursday 10:30-12:00 or by appointment e-mail:
[email protected]
The course covers standard materials in the theory of curves in the plane and the space, and the theory of surfaces in the space. We will develop their local invariants (curvature and torsion for curves, fundamental forms and curvature for surfaces.) We will also explore the interplay between local and global properties. Textbook is Differential Geometry of Curves and Surfaces (2nd edition) by Manfredo P. Do Carmo. Homework: There will be written homework weekly. When working on homework problems you may collaborate with fellow students but you should write down your own version of the solution. DO NOT COPY from others. Homeworks will be due in class before the class begins. No late homeworks will be accepted. Grading Mid-term exam 35% Final Exam 35 % Homework 30% Tentative Schedule Week 1 January 2225 2 Janıary 28Feb. 1 3 Feb. 4-8 4 Feb. 11-15 5 Feb. 19-22 6 Feb. 25March 1 7 March 4-8
Section(s) to be covered Parametrized Curves, Regular Curves (1.2, 1.3) Local Theory of Curves (1.3, 1.5)
Comments
Isoperimetric Inequality, Regular Surfaces (1.7, 2.2) Inverse Images of Regular Values, Change of Parameters (2.2, 2.3) Differentiable Functions on Surfaces, Tangent Plane (2.3, 2.4) Differential of a Map, First Fundamental Form (2.4, 2.5) Area, Orientation (2.5, 2.6)
Feb. 4 Last day to drop with no record
Presidents’ Day, Monday Feb. 18 Monday schedule on Tuesday
Midterm Exam Wednesday March 6
March 11-15 SPRING RECESS 8 March 18-22 Gauss Map (3.2) 9 March 25-29 Gauss Map in Local Coordinates (3.3) 10 April 1-5 Vector Fields (3.4) 11 April 8-12 Isometries (4.2) 12 April 16-19 Gauss Theorem (4.3)
13 April 22-26 14 April 29May 1 May 8, Wednesday
Parallel Transport, Geodesics (4.4) Gauss-Bonnet Theorem (4.5) Final Exam
March 19 Last day to drop with “W”
Patriot’s Day, Monday April 15 Monday schedule on Wednesday Midterm Exam 2 Wednesday April 17 Wednesday, May 1 Last day of classes Exam room: LDRT 147 8:00-10:00
1124 LGRT (413-545-7677)
Office hours: Monday 15:00-16:30, Tuesday 10:00-12:00, Thursday 10:30-12:00 or by appointment e-mail:
[email protected]
The course covers standard materials in the theory of curves in the plane and the space, and the theory of surfaces in the space. We will develop their local invariants (curvature and torsion for curves, fundamental forms and curvature for surfaces.) We will also explore the interplay between local and global properties. Textbook is Differential Geometry of Curves and Surfaces (2nd edition) by Manfredo P. Do Carmo. Homework: There will be written homework weekly. When working on homework problems you may collaborate with fellow students but you should write down your own version of the solution. DO NOT COPY from others. Homeworks will be due in class before the class begins. No late homeworks will be accepted. Grading Mid-term exam 35% Final Exam 35 % Homework 30% Tentative Schedule Week 1 January 2225 2 Janıary 28Feb. 1 3 Feb. 4-8 4 Feb. 11-15 5 Feb. 19-22 6 Feb. 25March 1 7 March 4-8
Section(s) to be covered Parametrized Curves, Regular Curves (1.2, 1.3) Local Theory of Curves (1.3, 1.5)
Comments
Isoperimetric Inequality, Regular Surfaces (1.7, 2.2) Inverse Images of Regular Values, Change of Parameters (2.2, 2.3) Differentiable Functions on Surfaces, Tangent Plane (2.3, 2.4) Differential of a Map, First Fundamental Form (2.4, 2.5) Area, Orientation (2.5, 2.6)
Feb. 4 Last day to drop with no record
Presidents’ Day, Monday Feb. 18 Monday schedule on Tuesday
Midterm Exam Wednesday March 6
March 11-15 SPRING RECESS 8 March 18-22 Gauss Map (3.2) 9 March 25-29 Gauss Map in Local Coordinates (3.3) 10 April 1-5 Vector Fields (3.4) 11 April 8-12 Isometries (4.2) 12 April 16-19 Gauss Theorem (4.3)
13 April 22-26 14 April 29May 1 May 8, Wednesday
Parallel Transport, Geodesics (4.4) Gauss-Bonnet Theorem (4.5) Final Exam
March 19 Last day to drop with “W”
Patriot’s Day, Monday April 15 Monday schedule on Wednesday Midterm Exam 2 Wednesday April 17 Wednesday, May 1 Last day of classes Exam room: LDRT 147 8:00-10:00
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