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MAT 544: Analysis

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Department of Mathematics

SUNY at Stony Brook

New graduate students who feel that they do not need to take this
course must get a waiver from the graduate director or course
professor. Waivers
will not be unreasonably denied.

**Text:** A First Graduate Course in Real Analysis,
by Daryl Geller, available only in the Graduate Math Office.

**Professor:** Prof. Daryl Geller, Math Tower 4-100B

Phone: 632-8327 email: *daryl@math.sunysb.edu*

**Office hours: ** Tuesdays and Thursdays, 12:50-2:20.

**Homework:** Homework will be assigned each week, and will
count for 15% of your grade in the course. Please hand it in, in class,
on Thursdays`.

**Grader:** Ritwik Mukherjee, 2-117 Math.

** Office hours: ** Thursdays 2:30-3:30 at MLC, Fridays 10:30-11:30
at 2-117, and Fridays 11:30-12:30 at MLC.

**Examinations:** There will be two tests during the semester
(dates to be negotiated). Together, they will count for 50%
of
the grade in the course. The final examination will count for 35%
of the grade in the course.

**Final Exam** -- Tuesday, December 14, 2:15 - 4:45 p.m.

Homework (due in class, Tuesday 9/14), is: Exercises 1.1.4, 1.1.23,
1.1.24, 1.1.28, 1.2.10, 1.2.13, 1.3.9, 1.3.11.

Homework (due in class, Thursday 9/16), is: Exercises 1.3.30, (1.4.6,
1.4.7, 1.4.8) -- (this is basically one problem), 1.4.9, 1.5.8, 1.5.9.

Homework (due in class, Thursday 9/23), is: Exercises 2.1.1, 2.1.6, 2.1.7,
2.1.8, 2.1.10, 2.2.11, 2.2.12.

Homework (due in class, Thursday 9/30), is: Exercises 2.2.18, 2.2.19,
2.2.21, 2.3.11, 2.3.14, (2.3.25, 2.3.26) -- (this is basically one
problem), 3.1.9, 3.1.10

Homework (due in class, Thursday 10/7), is: Exercises 3.2.9, 3.3.7,
3.3.9, 3.5.3, 3.5.8, 3.6.3.

Homework (due in class, Thursday 10/21), is: Exercises 3.6.10, 3.6.12,
3.6.15, 3.6.16. 3.6.20, 3.6.21.

Homework (due in class, Thursday 10/28), is: Exercises 3.8.3, 3.8.4,
3.8.5, 3.8.6, 3.8.7, 3.8.8, 3.8.10.

**Midterm** in class on Tuesday, 10/26, covering chapters 1-3.

Homework (due in class, Thursday 10/4) is:
Exercises 4.1.14, 4.1.20,
Exercises 4.2.6 (in (a), prove more
generally that if V is any open set contained in [0,1], with m(V)=1,
then the characteristic function of V is Riemann integrable), 4.3.14,
4.3.15, 4.3.16, 4.3.17, and the following additional exercise:

Define a function f, mapping the reals to the reals, by the rule
f(x) = 3x for x less than 1/2, f(x) = 3(1-x) for x greater than or equal to 1/2.
Find the (filled-in) Julia set of f (that is, the set of real numbers whose
iterates under f don't approach plus or minus infinity). (Hint: use
Exercise 4.2.6 (b).)

Homework (due in class, Thursday 10/11) is:
Exercises 4.5.6, 4.5.7, 4.5.8, 4.5.10, 4.6.5, 4.6.13, 4.7.3.

**Midterm** in class on Thursday, 11/18, on Chapter 4.

Also please do Exercises 4.7.4, 4.7.5, 4.7.6 for Thursday 11/18.

Homework (due in class, ** Tuesday 11/23 **) is:
Exercises 5.1.6, 5.2.6, 5.2.14, 5.2.21.

Homework (due in class, Thursday 12/2) is:
Exercises 5.3.9, 5.3.13, 5.3.14; also read pages 276-280, and do
Exercises 6.2.3, 6.2.4 (hint for part (b): the answer is NO), 6.2.6,
6.2.7, 6.2.8, 6.2.9.

Homework (due in class, Thursday 12/9) is:
5.5.8, 5.6.5, 5.6.7, 5.7.10, 5.7.11, 5.7.12, 5.7.13, 5.7.14.

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*DSS advisory.* If you have
a physical, psychiatric, medical, or learning disability that may affect
your ability to carry out the assigned course work, please contact the
office of Disabled Student Services (DSS), Humanities Building, room 133,
telephone 632-6748/TDD. DSS will review your concerns and determine
what accommodations may be necessary and appropriate. All information and
documentation of disability is confidential.