NCHU Course Outline
Course Name (中) 分析學(6594)
(Eng.) Analysis
Offering Dept Department of Applied Mathematics
Course Type Elective Credits 3 Teacher Kyung-Youn Kim
Department Department of Applied Mathematics/Graduate Language English Semester 2024-FALL
Course Description Under the background of knowledge of basic topology and continuity, introduce the measure theory, L^p - space and Product spaces.
Prerequisites
self-directed learning in the course N
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
For the students to develop a strong foundation in Real Analysis and the theory of integration and measure theory.
1.Mathematical Thinking and Logic
2.Professional Knowledge in Mathematical Analysis
50
50
topic Discussion/Production
Discussion
Lecturing
Exercises
Written Presentation
Study Outcome
Assignment
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 1.1 Metric space(Sep.11)
Week 2 1.1 Metric space 1.2 Compact & Connected sets(Sep.18)
Week 3 1.3 Continuous functions(Sep.25)
Week 4 2.1-2 Measurability(Oct.02)
Week 5 2.3 Measure(Online class)(Oct.09)
Week 6 2.4-5 Integration(Oct.16)
Week 7 2.6 Measure zero sets(Oct.23)
Week 8 Midterm(Oct.30)
Week 9 3.1 Vector space(Nov.6)
Week 10 3.2 Riesz representation Theorem(Nov.13)
Week 11 3.3 Borel measure(Nov.20)
Week 12 3.4-5 Lebesgue measure(Nov.27)
Week 13 4.L^p - space(Dec.4)
Week 14 4.L^p - space(Dec.11)
Week 15 4.L^p - space(Dec.18)
Week 16 Final(Dec.25)
Week 17 Holiday(Jan.01)
Week 18 Discussion(Jan.08)
Evaluation
Homework 50%,Attendance 10%
Midterm Exam 20%, Final Exam 20%
Textbook & other References
Textbook:
Principles of Mathematical Analysis, Rudin, Walter, 3rd ed., McGraw-Hill, 1976;
Real and Complex Analysis, Rudin, Walter, 3rd ed., McGraw-Hill, 1986;
Real Analysis, Royden and Fitzpatrick, 4th ed., Prentice Hall, 2009.

References:
A Second Course in Mathematical Analysis, Burkill and Burkill, 3rd ed., Cambridge University Press, 2002;
Real Analysis, Stein and Shakarchi, Princeton University Press, 2005.
Teaching Aids & Teacher's Website
Lecture note will be distributed in ilearning 3.
Office Hours
Wednesday: 16:00-17:00
Thursday: 16:00-17:00
Sustainable Development Goals, SDGs
include experience courses:N
Please respect the intellectual property rights and use the materials legally.Please repsect gender equality.
Update Date, year/month/day:2024/09/18 12:11:25 Printed Date, year/month/day:2024 / 10 / 13
The second-hand book website:http://www.myub.com.tw/