Analysis II: 18.101 (Fall 2020)

• The Plan

  Here (as of 11 August) is what I (Richard Melrose) plan to do. Things might change but probably not significantly.
  • The class will meet as advertised, Tuesday and Thursdays 11-12:30 EDT but there is no in-person component.
  • The assigned texts are Spivak's "Calculus on Manifolds" and Munkres' "Analysis on Manifolds"; they both have their faults. I also hope to make use of some additional notes later in the course.
  • I would like to speak to each (prospective) student by zoom before the beginning of class, or at least during the first week, and again around the time of the test. I will contact you by email.
  • Each `class' will have a short recorded lecture which should be viewed in advance -- I think around 15-20 mins -- which gives a short overview. I hope to record these in my office using the blackboards there. My first effort (of a preparatory lecture on metric spaces) was not a great success so I will have to make some changes! Suggestions are welcome, my next recording efforts will be Aug 17/18.
  • The classes themselves will be zoom interactive, recorded. I plan to have at least one additional time slot for interactive discussion(s) to allow easier access from other time zones; requests are encouraged.
  • Homework will be roughtly weekly, 9 or 10 assignments in all.
  • There will be one `in-class test' on or around October 22, with at least one alternative time. You will be required to log into zoom at the beginning and sign off at the end after submitting your test electronically.
  • There will be a final exam, conditions similar to the test.
  • Grading: There will be two grading schemes the `morally approved' progressive schem based on homework (60pc) test (20pc) and final (20pc). The second `potentially disasterous' scheme is 100pc on the final. You will receive the higher of the grades computed by these two methods. The idea is that the final should serve largely as a self-assessment guide for you.
  • Office hours. The grader will hold some, to be decided.
  • Questions by email/zoom. You are encouraged to contact me by email or zoom (and maybe by text message) if you have questions and I will endeavor to respond to these reasonably promptly.

  Lecture outline, homework schedule etc to follow soon(ish).