Math 132: Smooth Manifolds, Spring 2017MWF 1-2pm, Science Center *309*Instructor: George Melvingmelvin@math.harvard.edu
Office Hours: M 11am-12pm, Th 4.30-5.30pm |
 Source: wikipedia.org |
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Announcements
- April 21
- Please sign-up here if you'd like to receive feedback on a draft of Project II.
- April 18
- HOMEWORK 11 CORRECTION: Problem 3.3.6 should have a minus sign in the exponent. Apologies for the confusion!
- April 13
- Homework 11 has been posted.
- April 10
- Project II topics have been posted. Note the deadlines!
- HOMEWORK 10 CORRECTION: You should assume that the manifold has empty boundary (this is also an implicit assumption in the statement of Jordan-Brouwer).
- Homework 5 and 6 solutions have been posted. Solutions to Homework 7,8,9 will be posted over the next few days.
- April 6
- Homework 9 & Homework 10 have been posted.
- Homework 10 is due Wednesday April 12.
- HOMEWORK 9 UPDATE: Please omit 3.2.4 and part (b) of the last problem (3.2.8).
- HOMEWORK 10 UPDATE: The omitted problems from Homework 9 have been added to Homework 10.
- March 28
- I have posted the gradesheet for Project I.
- HOMEWORK 8 CORRECTION: I have updated the statement of Problem 2 - we require the continuous extension of Borsuk-Ulam.
- March 24
- There is an upcoming conference in mathematics, with a focus on gender inclusivity, taking place at Harvard on Saturday April 1st. More information can be found here. It looks like it will be a lot of fun! Let me know if you have any questions.
- Homework 8 has been posted online and is due Friday 3/31.
- March 21
- No class Wednesday 3/22 - I will be out of town. I will look to reschedule a make-up class at some point in the future.
- Homework 7 has been posted online and is due Monday 3/27.
- Homework 8 will be due Friday 3/31.
- Summary of lectures from weeks 6 and 7 have been posted. Let me know if you find any mistakes or have any questions.
- OFFICE HOURS UPDATE: I will not hold office hours this Thursday 3/23. I will hold office hours on Friday 3-4pm, SC209. As always, if you would liketo schedule a chat at a different time then just let me know.
- March 3
- Please fill out this poll if you would like to schedule an appointment to discuss your Project I Draft. Please select a single time slot that hasn't already been taken.
- March 1
- Homework 6 has been posted online. Let me know if you find any typos!
- February 27
- Please let me know your thoughts on what you think about homework so far in the course. Suggestions/feedback are very much appreciated and allow me to ensure we are on the same page regarding reasonable homework expectations.
- GUILLEMIN-POLLACK ERRATA: can be found here.
- HOMEWORK 5, 1.8.11: the hint in Problem 1.8.11 is confusing (to me at least!). Look in the Guillemin-Pollack errata above to see a more helpful hint.
- Solutions to Homework 4 have been posted.
- February 26
- Summary of lectures from Weeks 4 and 5 have been posted online. Let me know if you find any mistakes or have any questions.
- Homework 5 typos fixed. Updated Homework is posted online.
- February 22
- February 21
- Homework 4 typo: in problem 1.1.18(d), it should say "... smooth real-valued function r(x), x in R^k..."
- February 18
- February 15
- February 14
- Homework 3 update: You may use the following results: 1) the notion of homotopy is an equivalence relation, 2) the Stability Theorem of Section 1.6 in Gullemin-Pollack.
- Homework 3 typos: Problem 1.6.4 should read '...only if all smooth maps from any arbitrary manifold Y into X are homotopic.' Apologies for the confusion.
- February 11
- I have posted a summary of the material covered in week 3. Let me know if you have any questions and/or find any mistakes!
- I have posted some solutions to Test Yourself quizzes.
- February 8
- Homework 3 has been posted online.
- I've posted a proof of the Local Submersion Theorem. Let me know if you find any mistakes.
- We will have a Diagnostic Quiz during class on Wednesday, February 15. This will be a 20-30 minute quiz intended to check yor ability to do basic computations and to test your knowledge on the basic ideas we have seen so far; there will be no proofs. Here is some further information about the Quiz.
- February 7
- Homework 2 TYPO: someone has caught a typo in the definition of the function in problem 1d). It should read, f(x,u1,u2,u3) = (x,u1ix+u2jx+u3kx). Thanks to Kyle for spotting that!
- February 6
- Here is a really interesting article discussing teacher/student expectations in upper-level college mathematics courses by Prof. K. Weber of Rutgers University.
- February 5
- Homework 2 Update:You are not required to submit Problem 1.4.4 with Homework 2.
- I have posted some old notes of Prof. Taubes outlining a proof of the Inverse Function Theorem.
- February 4
- Lecture notes from Week 2 have been posted. Let me know if you find any mistakes or have any questions!
- I have posted some further exercises and a Test Yourself quiz.
- Initial feedback: (CLOSED) Please provide some feedback on how you think the course is going so far. It's great to learn from you what things you think could be improved and/or what things you think are going well.
- February 3
- I realised that the linear algebra exercise I mentioned in class is not quite correct! I've given the correct statement on the Local Immersion Theorem handout. As a result, note that this handout is slightly different from the one given in class. Let me know if you find any further mistakes!
- February 2
- Update on office hours: my office hours will be held in SC229 for the remainder of the semester.
- The Late Days Policy has been outlined here. Please read this if you considering using the Late Days Policy.
- February 1
- Update on homework policy: the lowest homework grade will be dropped.
- January 31
- I've been advised that there is a typo in Problem 1.1.4 in the textbook (and first problem on Homework 1). The problem should read "... B_a be the open ball {x : |x|< a }...". Apologies for any confusion, and thanks to Leo for spotting the mistake.
- I have posted a LaTeX template online in the 'homework' section. I will make sure to post a similar template each week.
- Homework 2 has been posted online.
- January 30
- Please RSVP if you would like to get dinner with myself and some of your classmates through the College's Classroom to Table program.
- I have updated the definition of connected in Homework 0.
- I have updated the notes from Week 1. Let me know if you find any mistakes.
- I have added some notes in the misc section that provide a description of an exotic 7-sphere.
- January 28
- I have posted some notes and supplementary (non-compulsory) exercises in the 'notes' section.
- January 27
- As we have not yet discussed the material, Problem 2.1.7 from Homework 1 need not be submitted.
- Each weekend I will post the following:
- a summary of what we covered in class, including any additional results I didn't have time to cover,
- a list of problems/exercises pertaining to that weeks material (not be submitted),
- a short (non-compulsory) quiz for you test what you learned the preceding week.
- January 25
- Julian will be holding discussion section each Friday at 3-4pm in SC104, although this time/location may be subject to change. In addition, you will be able to find Julian at Math Night, 8-9pm, in Leverett Dining Hall for his 'office' hours.
- January 24
- There has been a room change - class will now meet MWF 1-2pm in SC309.
- Homework 1 is posted. Some additional problems have been added - these are not required to be submitted.