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
Grader: Catalin Carstea


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.)


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.