國立清華大學數學系
實變數函數論二
Math 5131-00 (Spring 2024) Real Analysis II
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Instructor: 陳國璋 Kuo-Chang Chen |
Office: 綜三 609 |
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
For the first topic, I will use my lecture notes, together with materials from Wheeden-Zygmund’s book (section 5.4, Chap 8, 9). We follow Stein-Shakarchi’s book for other topics.
Syllabus
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HERE for details. Note that this is a 3-credit course, so in average there will be
3 hours of classes every week. Among the 4 scheduled class hours (M5M6R5R6), one is reserved for
recitations (problem sessions), instructed by teaching assistants.
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: Selected exercises from lecture notes and Chapters 4~7 in textbook will be assigned. Some of them will be collected and graded.
Click here for details.
Further details will be available during the first week of classes. 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).
Two exams (80%): Each exam worth 40% of the course grade. Dates of tests are on April 18 (Thursday) and June 17 (Monday).