國立清華大學數學系
實變數函數論一
Math 5130-00 (Fall 2023) Real Analysis I
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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 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
Syllabus
Click
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
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/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. 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.
Three exams (75%): Each exam worth 25% of the course grade. Dates of tests are on October 30 (Monday), November 30 (Thursday), and January 8 (Monday).