18.1002/18.100B  Real Analysis

Final exam scores posted; final grade cutoffs

I am very happy with the overall performance on the final exam. The class median was 145/180 (one point over 80 percent). The final grades are awarded as follows: A > 82 percent, B >67 percent), C >52 percent
(with + and - grades near the borderlines). Extra credit was added after the
cutoffs were computed so as to avoid influence.

Thanks for being such a good class. Have a very nice IAP break.
Your questions were excellent: If any of you have more questions, about your exam or about analysis in general, I invite you to visit me any time.

The one final exam problem that everyone had trouble with
was showing that the second term, the constant c_2 in the asymptotics of the sum n^{-\alpha} exists. The only mechanism to show that it exists is to show that it is represented by a convergent series, for example, a series of positive terms that is bounded above. We did not have time to practice with asymptotic expansions. In the second problem, with integration by parts,
many of you realized that an entire second integration by parts is needed to establish that the first term is present. In the sum n^{-\alpha}
problem, many of you found the O(1) bound and mistakenly thought
that this finishes the argument. This also led several of you to think you had computed c_2 when you did not have the correct value for it.

With best wishes,
David Jerison

Announced on 26 December 2016  4:03  p.m. by David Jerison

Muddy answers 15 posted

I answered a few questions about the exam on the last muddy card post. Notably, in the list of proofs 1, you should aim at the most direct proof that is as self-contained as possible. You are responsible for the practice problems for the hour tests, although the ones specifically prepared for
the final should be your highest priority. There's a misprint in the
Arzela-Ascoli theorem, it should be part of problem 8 so it's clear that K is compact (and we are using 8b that C(K) is complete, not 6b which does not exist).

Announced on 20 December 2016  11:15  p.m. by David Jerison

Corrections to asymptotics notes posted

Announced on 20 December 2016  3:51  p.m. by David Jerison

Office hrs; new asymptotics posting

My office hrs for this week are
Monday 6:30-8pm
Tues 1:30-3:30pm
Wed 1:30-3:30pm
I just posted notes on the asymptotics part of the final lecture along with the answers to the three practice exercises 1a, 2a and 3a and a few other related questions. I will answer muddy questions about exam problems in a later posting. I don't generally answer any direct questions of this type
in office hrs, except if they are (or will be) posted for the whole class.

Announced on 18 December 2016  8:48  p.m. by David Jerison

solutions to Exercise 0 (PS9 and PS11) just posted

discussion of asymptotics and a other commentary to follow late on Sunday.

Announced on 16 December 2016  10:11  p.m. by David Jerison