Math 335 - Differential Geometry
Fall 2023
Emily Proctor




Please read the syllabus to learn all the details about the course.

Here is a chronological list of the videos and notes for the semester.




Homework

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Week beginning September 11:

• Read Sections 1.1, 1.2, and 1.3 of Woodward and Bolton.


• Watch the following.

  For Wednesday, September 13: watch Section 1.1 videos Part 1/notes, Part 2/notes, and Part 3/notes.

  
  

  For Friday, September 15: watch Section 1.2 videos Part 1/notes and Part 2/notes, and Section 1.3 video Part 1/notes.



• Complete Assignment 1, due Monday, September 18.
  

  For Wednesday, September 13: be prepared to discuss Problems 1 and 4 in class.

  
  

  For Friday, September 15: be prepared to discuss Problems 3 and 6 in class.

  
  

  For Monday, September 18: be prepared to discuss Problem 7 in class.

  
  

Week beginning September 18:

• Read Section 1.5 of Woodward and Bolton. For more information on the definition of the derivative, see p.43 of Woodward and Bolton. I will also email out another source on this in case it would help you to see more.


• Watch the following.

For Monday, September 18: watch Section 1.5 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Wednesday, September 20: watch Section 1.5 videos Part 4/notes, and Part 5/notes.




For Friday, September 22: watch Section 2.1/Background videos Part 1/notes, Part 2/notes, and Part 3/notes.



• Complete Assignment 2, due Monday, September 25.
  

  For Wednesday, September 20: be prepared to discuss Problems 2 and 3 in class.

  
  

  For Friday, September 22: be prepared to discuss Problems 4 and 5 in class. We will also talk more about the definition of the derivative in class.

  
  

Week beginning September 25:

• Read Sections 2.1-2.4, and 3.1 of Woodward and Bolton.


• Watch the following.

For Monday, September 25: watch Section 2.1 videos Part 4/notes, Part 5/notes, and Part 6/notes.




For Wednesday, September 27: watch Section 2.2-2.4 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Friday, September 29: watch Section 3.1 videos Part 1/notes, Part 2/notes, and Part 3/notes.



• Complete Assignment 3, due Monday, October 2.
  

  For Monday, September 25: be prepared to discuss Problems 1 and 6 in class.

  
  

  For Wednesday, September 27: be prepared to discuss Problems 2, 3, and 5 in class.

  
  

  For Friday, September 29: be prepared to discuss Problems 7 and 8 in class.

  
  

Week beginning October 2:

• Read Sections 3.2, 3.3, 3.4, and 3.8 of Woodward and Bolton.


• Watch the following.

For Monday, October 2: watch Section 3.1 videos Part 4/notes and Part 5/notes.




For Wednesday, October 4: watch Section 3.2, 3.3, and 3.4 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Friday, October 6: watch Section 3.8 videos Part 1/notes, Part 2/notes, and Part 3/notes.



• Complete Assignment 4, due Monday, October 9.
  

  For Monday, October 2: be prepared to discuss Problems 1 and 4 in class.

  
  

  For Wednesday, October 4: be prepared to discuss Problem 7 in class.

  
  

  For Friday, October 6: be prepared to discuss Problems 2 and 6 in class.

  
  

Week beginning October 9:

• Read Section 4.1 of Woodward and Bolton.


• Watch the following.

For Monday, October 9: watch Section 4.1 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Wednesday, October 11: watch Section 4.1 videos Part 4/notes and Part 5/notes.



• Complete Assignment 5, due Monday, October 16.
  

  For Monday, October 9: be prepared to discuss Problems 2, 3, and 4 in class.

  
  

  For Wednesday, October 11: be prepared to discuss Problems 5 and 6 in class.

  
  

Week beginning October 16:

• Read Sections 4.2 and 4.3 of Woodward and Bolton.


• Watch the following.

For Monday, October 16: watch Section 4.2 videos Part 1/notes and Part 2/notes.




For Wednesday, October 18: watch Section 4.2 videos Part 3/notes and Part 4/notes.




For Friday, October 20: watch Section 4.3 videos Part 1/notes, Part 2/notes, and Part 3/notes.



• Complete Assignment 6, due Monday, October 30.
  

  For Monday, October 16: be prepared to discuss Problems 1 and 3 in class.

  
  

  For Wednesday, October 18: be prepared to discuss Problem 2 in class.

  
  

  For Friday, October 20: be prepared to discuss Problems 5 and 6.

  
  

Week beginning October 23:

• For Monday, October 23: Consider the following questions, designed to help you develop an overview of the material we've covered so far, and to help prepare you for the oral component of the midterm. We can discuss the questions together in class on Monday. The questions for the written portion of our exam will be available at end of class on Monday.


• For Wednesday, October 25: We will have our oral exams in place of class. The oral exams will take place in my office.


• For Friday, October 27: Complete the written portion of the exam. Submit your final write-up to me at the beginning of class on Friday. Please note that this deadline is firm.


• For Friday, October 27: Read Section 5.1 of Woodward and Bolton.


• Watch the following.

For Friday, October 27: watch Section 5.1 videos Part 1/notes and Part 2/notes.



• Complete Assignment 6, due Monday, October 30.
  

  For Friday, October 27: be prepared to discuss Problem 4 in class.

  
  

Week beginning October 30:

• Read Sections 5.2 and 5.7 of Woodward and Bolton.


• Watch the following.

For Monday, October 30: watch Section 5.1 videos Part 3/notes and Part 4/notes.




For Wednesday, November 1: watch Sections 5.2 and 5.7 videos Part 1/notes and Part 2/notes.




For Friday, November 3: watch Sections 5.2 and 5.7 videos Part 3/notes and Part 4/notes.



• Complete Assignment 7, due Monday, November 6.
  

  For Monday, October 30: be prepared to discuss Problems 1 and 2 in class.

  
  

  For Wednesday, November 1: be prepared to discuss Problems 3 and 5 in class.

  
  

  For Friday, November 3: be prepared to discuss Problems 4 and 6 in class.

  
  

Week beginning November 6:

• Read Sections 5.4, 5.9, 5.10, and 5.3 of Woodward and Bolton.


• Watch the following.

For Monday, November 6: watch Section 5.4, 5.9, and 5.10 video Part 1/notes.




For Wednesday, November 8: watch Section 5.3 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Friday, November 10: watch Section 5.3 videos Part 4/notes, Part 5/notes, and Part 6/notes.



• Complete Assignment 8, due Monday, November 13.
  

  For Monday, November 6: be prepared to discuss Problems 1 and 6 in class.

  
  

  For Wednesday, November 8: be prepared to discuss Problems 3 and 5 in class.

  
  

  For Friday, November 10: be prepared to discuss Problems 2 and 4 in class.

  
  

Week beginning November 13:

• Read Section 6.1, 6.2, and 7.1 of Woodward and Bolton.


• Watch the following.

For Monday, November 13: watch Section 6.1 videos Part 1/notes and Part 2/notes.




For Wednesday, November 15: watch Section 6.2 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Friday, November 17: watch Section 7.1 videos Part 1/notes, Part 2/notes, and Part 3/notes.



• Complete Assignment 9, due Monday, November 27.
  

  For Monday, November 13: be prepared to discuss Problems 1 and 3 in class.

  
  

  For Wednesday, November 15: be prepared to discuss Problems 2 and 4 in class.

  
  

  For Friday, November 17: be prepared to discuss Problem 5 in class.

  
  

Week beginning November 20: Happy Thanksgiving!

Week beginning November 27:

• Read Sections 7.2, 7.3, 7.4, 8.2, and 8.3 of Woodward and Bolton.


• Watch the following.

For Monday, November 27: watch Section 7.2 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Wednesday, November 29: watch Sections 7.3 and 7.4 videos Part 1/notes and Part 2/notes.




For Friday, December 1: watch Sections 8.2 and 8.3 videos Part 1/notes, Part 2/notes, Part 3/notes, and Part 4/notes.



• Complete Assignment 10, due Friday, December 8.
  

  For Monday, November 27: be prepared to discuss Problem 1 in class.

  
  

  For Wednesday, November 29: be prepared to discuss Problem 6 in class.

  
  

  For Friday, December 1: be prepared to discuss Problems 2 and 3 in class.

  
  

• For your calendar: the take-home portion of our final exam will be Monday, December 11 until Thursday, December 14, 2pm. The oral component of the exam will be Monday, December 11.

Week beginning December 4:

• Read Sections 8.3, 8.4, and 8.5 of Woodward and Bolton.


• Watch the following.

For Monday, December 4: watch Section 8.3 videos Part 1/notes, Part 2/notes, and Part 3/notes.




For Wednesday, December 6: watch Section 8.4 videos Part 1/notes and Part 2/notes.




For Friday, December 8: watch Section 8.5 videos Part 1/notes and Part 2/notes.



• Complete Assignment 10, due at class time Friday, December 8.
  

  For Monday, December 4: be prepared to discuss Problems 4 and 5 in class.

  
  

  For Wednesday, December 6: be prepared to discuss Problem 7 in class.

  
  

  For Friday, December 8: we will wrap up our discussion of the Gauss-Bonnet theorem, and the class! We can also use the time to discuss these questions, designed to help you solidify your big picture understanding of the course, and prepare for our oral exam. Please submit your finished write-up of Assignment 10 by the end of class time.