國立清華大學數學系
實變數函數論二
Math 5131-00 (Spring 2018) Real
Analysis II
|
Office: 綜三 609 |
Textbook
E. M. Stein and R. Shakarchi: Real
Analysis,
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.