|
National Taiwan Normal University Course Outline Fall , 2025 |
|
@尊重智慧財產權,請同學勿隨意影印教科書 。 Please respect the intellectual property rights, and shall not copy the textbooks arbitrarily. |
|
| I.Course information |
| Serial No. | 2701 | Course Level | Undergraduate / Master |
| Course Code | MAC9020 | Chinese Course Name | 計算共形幾何（一） |
| Course Name | Computational Conformal Geometry (I) | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Sel. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | |||
| Comment | |||
| Course Description | |||
| Day & Class Period/Location | Fri. 6-8 Gongguan M310 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Develop mathematical expertise |
College: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic Master: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic |
||
| 2. Develop the ability to solve problems with mathematics |
College: 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity Master: 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity |
||
| 3. Improve abstract thinking |
College: 3-4 Having insights, intuitions, and senses of mathematics Master: 3-4 Having insights, intuitions, and senses of mathematics |
||
| 4. Interpret the connections between mathematics and other disciplines from a higher perspective |
College: 1-5 Being able to use mathematics as tools to learn other subjects 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 2-1 Being able to communicate and express mathematically 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning Master: 1-5 Being able to use mathematics as tools to learn other subjects 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 2-1 Being able to communicate and express mathematically 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning |
||
| II. General Syllabus |
| Instructor(s) | YUEH, Mei-Heng/ 樂美亨 | ||
| Schedule | |||
1. Background and Recent Development of Computational Conformal Geometry (2 weeks) 2. Homotopy Groups (2 weeks) 3. Simplicial Homology and Cohomology (2 weeks) 4. Topological Algorithms (2 weeks) 5. Harmonic Mappings (2 weeks) 6. Students' Midterm Reports (1 week) 7. Conformal Mappings (2 weeks) 8. Surface Registration and Morphing (2 weeks) 9. Students' Final Reports (1 week) |
|||
| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | Deliver course. | ||
| Lab/Studio | Deliver step-by-step programming and have students practice simultaneously. | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Class discussion involvement | 60 % | ||
| Presentation | 40 % | Read related books and study related classical and recent papers. | |
| Required and Recommended Texts/Readings with References | 1. Xianfeng David Gu, Shing-Tung Yau, Computational Conformal Geometry, Higher Education Press, 2008. |
||