| 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 |
|
|
| 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.10) |
| Week 2 |
1.2 Compact & Connected sets(Sep.17) |
| Week 3 |
1.3 Continuous functions(Sep.24) |
| Week 4 |
2.1-2 Measurability(Oct.01) |
| Week 5 |
2.3 Measure(Oct.08) |
| Week 6 |
2.4-5 Integration(Oct.15) |
| Week 7 |
2.6 Measure zero sets(Oct.22) |
| Week 8 |
Midterm(Oct.29) |
| Week 9 |
3.1 Vector space(Nov.5) |
| Week 10 |
3.2 Riesz representation Theorem(Nov.12) |
| Week 11 |
3.3 Borel measure(Nov.19) |
| Week 12 |
3.4-5 Lebesgue measure(Nov.26) |
| Week 13 |
4.L^p - space(Dec.3) |
| Week 14 |
4.L^p - space (Dec.10) |
| Week 15 |
Final (Dec.17) |
| Week 16 |
Discussion (Dec.24) |
self-directed
learning |
03.Preparing presentations or reports related to industry and academia.
|
|
| Evaluation |
Homework 40%
Midterm Exam 30%, Final Exam 30% |
| 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(Link URL) |
| include experience courses：N |
|