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National Taiwan Normal University Course Outline Fall , 2026 |
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| I.Course information |
| Serial No. | 2671 | Course Level | Master / PhD |
| Course Code | MAC8040 | Chinese Course Name | 計算幾何變分建模專題 |
| Course Name | Topics in Variational Modeling for Computational Geometry | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Sel. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Teach in English | Y | Teach in National Languages | |
| Prerequisite Course | ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students. | ||
| Comment | |||
| Course Description | |||
| Day & Class Period/Location | Fri. 6-8 Gongguan M311 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. To formulate and analyze geometric problems through rigorous variational modeling and energy-based frameworks. |
Master: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic 1-4 Possessing the abilities to propose and solve questions in advanced mathematics Doctor: 1-1 Equipped with professional mathematics competences 1-2 Being able to reason and induct with mathematical logic 1-4 Possessing the abilities to propose and solve questions in advanced mathematics |
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| 2. To develop a deep understanding of continuous and discrete geometric structures, and to derive their associated differential and variational formulations. |
Master: 1-1 Equipped with professional mathematics competences 1-3 Being able to think mathematically and critically 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 3-4 Having insights, intuitions, and senses of mathematics Doctor: 1-1 Equipped with professional mathematics competences 1-3 Being able to think mathematically and critically 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 3-4 Having insights, intuitions, and senses of mathematics |
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| 3. To design, implement, and theoretically analyze structure-preserving numerical methods for geometric variational problems. |
Master: 1-2 Being able to reason and induct with mathematical logic 1-4 Possessing the abilities to propose and solve questions in advanced mathematics 3-2 Possessing the abilities to think independently, criticize, and reflect 4-1 Being knowledgeable and being able to self-develop in the profession Doctor: 1-2 Being able to reason and induct with mathematical logic 1-4 Possessing the abilities to propose and solve questions in advanced mathematics 3-2 Possessing the abilities to think independently, criticize, and reflect 4-1 Being knowledgeable and being able to self-develop in the profession |
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| 4. To cultivate independent research competence through critical literature study, mathematical communication, and project-based investigation in computational geometry. |
Master: 2-1 Being able to communicate and express mathematically 2-4 Possessing the competences of lifelong learning 3-2 Possessing the abilities to think independently, criticize, and reflect 4-2 Possessing a consistent and firm attitude toward pursuing truths Doctor: 2-1 Being able to communicate and express mathematically 2-4 Possessing the competences of lifelong learning 3-2 Possessing the abilities to think independently, criticize, and reflect 4-2 Possessing a consistent and firm attitude toward pursuing truths |
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| II. General Syllabus |
| Instructor(s) | YUEH, Mei-Heng/ 樂美亨 | ||
| Schedule | |||
1. Variational principles and geometric energy functionals (3 weeks) 2. Smooth and discrete geometric structures (2 weeks) 3. Consistency and structure-preserving discretization (2 weeks) 4. Students' midterm reports (1 week) 5. Numerical optimization on geometric and manifold settings (2 weeks) 6. Convergence theory and stability analysis (2 weeks) 7. Advanced topics in geometric variational modeling (3 weeks) 8. Students' final reports (1 week) |
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| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | 講授課程。 Deliver course. | ||
| Problem-based learning | 以問題導向進行建模與分析。 Problem-based modeling and analysis. | ||
| Case studies | 文獻回顧與研討。 Literature review and discussion. | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Class discussion involvement | 20 % | 參與討論並對同儕報告提供回饋。 Participation in discussions and peer feedback. | |
| Presentation | 40 % | 口頭簡報。 Oral report for the topic research. | |
| Case study reports | 40 % | 專題研究書面報告。 Written report for the topic research. | |
| Adjustment methods for students | |||
| Required and Recommended Texts/Readings with References | 1. Classical and Discrete Differential Geometry: Theory, Applications and Algorithms, David Xianfeng Gu and Emil Saucan, CRC Press (2023).
2. Numerical Optimization, Jorge Nocedal and Stephen J. Wright, Springer (2006).
3. Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry, Gary P. T. Choi and Lok Ming Lui, Springer (2022).
4. Computational Conformal Geometric Methods for Vision, Na Lei, Feng Luo, Shing-Tung Yau, and Xianfeng Gu, Springer (2023). |
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