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 Hours and days: T5T6T7 Classroom: 綜三 631 Teaching Assistants: TBA Prerequisite: 高等微積分

Office: 綜三 631 Phone Number: (03) 5715131 Ext: 33067 Office Hours: F5F6, or by appointments Email: kchen@math.nthu.edu.tw

 

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.