國立清華大學數學系
實變數函數論一
Math
5130-00 (Fall 2017) Real Analysis I
Instructor:
陳國璋 Kuo-Chang Chen |
Office:
綜三 631 |
Textbook
E. M. Stein and R. Shakarchi: Real Analysis, Princeton University Press, 2005.
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
(30%): 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.
Two exams (70%): Each
exam worth 35% of the course grade. Dates of tests are on Tuesdays, November
14, and January 9.
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.