國立清華大學數學系
實變數函數論二
Math 5131-00 (Spring 2018)  Real Analysis II

Instructor: 陳國璋 Kuo-Chang Chen
Hours and days: F3F4F6
Classroom: 綜三 631
Teaching Assistant:張格銘
Prerequisite: 高等微積分, 實變數函數論一

Office: 綜三 609
Phone Number: (03) 5715131 Ext: 33067
Office Hours: T5T6, 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 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 (25%): Selected exercises in Stein-Shakarchi’s book, plus some additional exercises from my lecture notes will be assigned. Click here for details. Quizzes will be based on homework assignments. Further details will be available during the first week of classes.
Three exams (75%): There will be three exams, each worth 25% of the course grade. Dates of these exams are (Fridays) April 13, May 18, June 22.

 

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 either weighted to other exams or a make-up exam will be arranged.