國立清華大學數學系
實變數函數論一
Math 5130-00 (Fall 2011)
Real
Analysis I
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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 first semester we will introduce Lebesgue’s
theory of measure and integration. Topics to be covered include:
1. Preliminaries on set theory
2. Lebesgue measure
3. Lebesgue integral
4. Differentiation and integration
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 (25%): Selected exercises from Chapter 1~3
in Stein-Shakarchi’s book 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 (75%): Each exam worth 25% of the course grade. Dates of tests are
on Fridays, October 28, December 2, and January 6.
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.