Midterm I (February 25 - March 1, 2019)

Material

1/23: Introduction to differentiable manifolds

1/25 - 2/18: More examples of 3-manifolds and 4-manifolds

2/20: Inverse function theorem and implicit function theorem

2/22: A locally level set, a locally graph, and a locally patch of differentiable manifolds

2/25: The tangent space to manifolds

2/27: The tangent bundle of manifolds

Here is my lecture note before midterm 1

Exam

Here is my written exam (available after March 4)