Math 518, Fall 2021

Math 518, Differential Manifolds 1, Fall 2021

The syllabus sheet with other course information. This includes office hours and other contact information

The detailed course diary which describes all assignments will include links to homework, handouts,, etc.

Here is the detailed plan for the semester:

Chapter 1: We will omit "Fundamental groups of manifolds" but cover the remainder of this chapter: pages 1-9 and 10-29.
Chapter 2: We will cover this chapter entirely: pages 32-47.
Chapter 3: We will cover this chapter entirely: pages 50-75.
Chapter 4: We will omit "Smooth covering maps" but cover the remainder of the chapter: pages 77-91.
Chapter 5: We will cover this chapter entirely: pages 98-122.
Chapter 6: We will omit this chapter.
Chapter 7: We will omit "The Universal Covering Group" but cover the rest of the chapter, pages 150-154 and 156-171.
Chapter 8: We will cover this chapter entirely: pages 174-199.
Chapter 9: We will omit "Flows and Flowouts on Manifolds with Boundary", "Commuting Vector Fields", "Time-Dependent Vector Fields", and "First-Order Partial Differential Equations," but cover the remainder of the chapter: pages 205-222 and 227-231.
Chapter 10: We will cover this chapter entirely: pages 249 - 268.
Chapter 11: We will cover this chapter entirely: pages 272-298.
Chapter 12: We will cover this chapter entirely: pages 304- 324.
Chapter 13: We omit this chapter.
Chapter 14: We will cover this chapter entirely: pages 349-373.
Chapter 15: We will omit "The Riemannian Volume Form" and "Orientations and Covering Maps" but cover the remainder of the chapter: pages 377-388.
Chapter 16: We will omit "Manifolds with Corners," "Integration on Riemannian Manifolds," and "Densities", but cover the remainder of the chapter: pages 400-415.
Chapter 17: Time permitting, we will cover this chapter entirely: pages 440-464.
Appendix A: We will omit "Homotopy and the Fundamental Group" and "Covering Maps" by cover the rest of the appendix: pages 596-612.
Appendix B, C, D: We need the statements from these sections, but will not cover the proofs.

Note: The total pages in chapter 1-9 is 182 (20 days) and in chapters 10-17 is 146 (22 days).

Midterm

The test will be Wednesday, October 13.
The test will be available on Canvas from 9am to 10pm. However, each student needs to choose a consecutive two-hour interval to take the exam. I suggest 9-11AM, 10AM-noon, or 7-9PM so that I am available. You may choose a different time, but must finish by 10pm.
You may use the book, my notes, your notes, and your graded material. However, you may not use any other material. Moreover, once you have seen the exam you may not discuss it's contents with anyone until after 10pm.
I will be available by phone from 9am to 12am and from 7pm to 9pm, and may be available at other times. My number is 650-200-6348. You may also email me, but I suggest phoning if you need an immediate response.
The midterm will cover the material through Monday, October 4. This includes all the material in the Appendices and Chapter 1-8 described above, plus pages 205-217.
There will be no lecture and no homework due on Wednesday, October 13. The next homework will be due on Wednesday, October 20.

Practice exams

You can find old comp exams at Study for Comp Exams. You can look at any old exam, but please remember that we are only halfway through the semester, so won't have covered all the material. Additionally, most of these tests were not open book. Here are three specific practice exams:

Problems 1, 4, 5 from 2021
Problems 1c, 2, 3 -- but omit the word "orientable" -- from 2020
Problems 1bc, 2 from 2018