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MATH 312---Autumn, 2009

Analysis I: Measure, Integration, and Probability

MWF 11:30 -- 12:20, 206 Eckhart

Greg Lawler , 415 Eckhart,

e-mail: lawler at math.uchicago.edu

Grader: Catalin Carstea

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Rudin, Real and Complex Analysis

Notes on Probability,

This is the first quarter of a three-quarter sequence on
real and complex analysis intended primarily for first-year
graduate students in the department of mathematics (but is open to
all students with the appropriate background and mathematical
maturity). Lectures on Mondays and Wednesdays
will cover the material in the
first half of Rudin's book and Friday lectures will be on
probability.

There will be weekly homework exercises due on Wednesdays. That
assignment will cover material from the lectures of the previous
week. There will also be a large problem set at the end of
the semester that will serve as a final exam. The final problem
set will
be due Wednesday, December 9 at noon.
Students may work together on homework exercises EXCEPT FOR THE FINAL
PROBLEM SET WHICH MUST BE INDIVIDUAL
WORK, but must write-up their work separately.

IMPORTANT NOTE: As mentioned in class,
there will be no class the week of November 2. However,
there is an assignment due for the week.

Problems sets will be posted when available.

Problem Set 1 (due Oct 7)

Problem Set 2 (due Oct 14)

Problem Set 3 (due Oct 21)

Problem Set 4 (due Oct 28)

Problem Set 5 (due Nov 4)

Problem Set 6 (due Nov 11)

Problem Set 7 (due Nov 18)

Problem Set 8 (due Nov 25)

Problem Set 9 (due Dec 2)

The
FINAL PROBLEM SET will not be posted here. It was handed out
on class on Monday, Nov. 30. Additional copies can be obtained
from me. They are due at 12:00 noon on December 9 --- I will
collect them in the first year office in the basement of
Eckhart.

NOTE: The due time has been extend to 4:30pm on December 9. The
pizza will be served then rather than at noon as previously
announced. (This change was announced in class on Friday.)

CORRECTIONS TO FINAL PROBLEM SET

On Problem 20, f and g are assumed to be L^1 on [0,2\pi]
and extended periodically. (As pointed out by somebody, there are not
many L^1 functions on R that have period 2\pi !)

There is a typo on problem 12. As stated the problem is very
easy and the hint is ridiculous. The intended problem replaces
e^j inside the sum with n^j. Extra credit for finding this correction
and doing the intended problem.