| 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.9) |
| Week 2 |
Attend the symposium(理學院2026國際前瞻永續科技研討會)(Sep.16) |
| Week 3 |
1.2 Compact & Connected sets/1.3 Continuous functions(Sep.23) |
| Week 4 |
2.1-2 Measurability(Sep.30) |
| Week 5 |
2.3 Measure(Oct.07) |
| Week 6 |
2.4-5 Integration(Oct.14) |
| Week 7 |
2.6 Measure zero sets(Oct.21) |
| Week 8 |
Midterm(Oct.28) |
| Week 9 |
3.1 Vector space(Nov.04) |
| Week 10 |
3.2 Riesz representation Theorem(Nov.11) |
| Week 11 |
3.3 Borel measure(Nov.18) |
| Week 12 |
3.4-5 Lebesgue measure(Nov.25) |
| Week 13 |
4.L^p - space(Dec.02) |
| Week 14 |
4.L^p - space (Dec.09) |
| Week 15 |
Final (Dec.16) |
| Week 16 |
Discussion (Dec.23)
|
self-directed
learning |
03.Preparing presentations or reports related to industry and academia.
After class, students should review the lecture materials, solve related practice problems, and engage in independent study on topics related to the class to improve their mathematical reasoning and communication skills. |
|
| Evaluation |
Homework 40%(4times, each 10%)
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 |
|