Spring 2024 MATH 5400
Undergraduate Geometry, 大學部幾何學

2/20/2024(星期二): Course introduction.

2/22/2024(星期四): Parametrized and regular curves.

2/27/2024(星期二): Curvature, torsion, and Frenet equations.

2/29/2024(星期四): Fundamental Theorem of local curves.

3/5/2024(星期二): Isoperimetric inequalities.

3/7/2024(星期四): Winding numbers and curvature.

3/12/2024(星期二): The four vertex theorem.

3/14/2024(星期四): Introduction to regular surfaces, local coordinates.

3/19/2024(星期二): Local coordinates, regular level sets.

3/21/2024(星期四): Change of parameters.

3/26/2024(星期二): More on change of coordinates.

3/28/2024(星期四): Smooth maps on regular surfaces, surface of revolution.

4/2/2024(星期二): Midterm Exam 1.

4/4/2024(星期四): No Class (兒童節).

4/9/2024(星期二): No Class (春假).

4/11/2024(星期四): Introdicton to tangent spaces.

4/16/2024(星期二): Differential of maps.

4/18/2024(星期四): Discussion of midterm 1.

4/23/2024(星期二): First fundamental forms.

4/25/2024(星期四): Computations of first fundamental forms and area.

4/30/2024(星期二): Orientability and Gauss maps.

5/2/2024(星期四): Gauss maps and its derivative.

Homework 1 (截止日 3/7/2024 In class):
Section 1.2: 2, 5.
Section 1.3: 2, 4, 7, 8, 9, 10.
Section 1.4: 1, 2, 3, 6.

Homework 2 (截止日 3/21/2024 In class):
Section 1.5: 1, 2, 3, 6, 9, 11, 17,
Section 1.7: 3, 4, 6, 8, 11.
Section 2.2: 3, 6, 7, 8.

Homework 3 (截止日 4/2/2024 In class):
Section 2.2: 12, 17.
Section 2.3: 2, 3, 6, 9, 14, 16.

Homework 4 (截止日 4/30/2024 In class):
Section 2.4: 3, 5, 10, 13b, 15, 18, 20.
Section 2.5: 1, 3, 7, 8, 11, 14.

Homework 5 (截止日 5/16/2024 In class):
Section 3.2: 2, 3, 5, 6, 11, 18.
Section 3.3: 1, 5, 6, 20, 22.