國立清華大學數學系
實變數函數論二
Math 5131-00 (Spring 2012)
Real
Analysis II
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Office: 綜三 609 |
Textbook
E. M. Stein and R. Shakarchi: Real Analysis,
References
H.L. Royden: Real Analysis, Macmillian, 1988.
R. L. Wheeden and A. Zygmund:
Measure and Integral - An introduction to
Real Analysis, Marcel Dekker, 1977.
Course
Description
This course is an introduction to the theory of measure and
integration.
In the second semester we will introduce some elements of functional analysis,
abstract measure and integration. Topics
to be covered include:
1. Introduction to Banach spaces
and Lp
2. Introduction to Hilbert spaces and L2
3. Abstract measure and integration
4. Hausdorff measure and fractals
Attendance
Students are expected to attend every scheduled class. It is
the student's responsibility to keep informed of any announcements, syllabus
adjustments or policy changes made during scheduled classes.
Grading
Homework/Quizzes (20%): Selected exercises from Chapter 4~7
in Stein-Shakarchi’s book, plus some additional
exercises from my lecture notes will be assigned. Click here for
details. Some of them will be collected and graded. Quizzes will be based on
homework assignments. Further details will be available during the first week
of classes.
Three exams (80%): There will be three exams, midterm exams will worth 60% of
the course grade. Dates of two midterm exams are on Fridays, April 6, and May
18. The final exam will be an oral test accompanied with a finial report, taken
place on June 20.
Absence
from exams
You
should miss an exam only for the most compelling reasons and you should obtain
permission in advance (except in some extraordinary circumstances). If you miss
an exam for legitimate reasons, then it will be weighted to other exams. There
will be no make-up exam.