非歐幾何賞析
課程編號: SAYT1214
上課日期: 4/8, 7/8, 10/8, 11/8, 14/8, 15/8, 17/8, 18/8, 21/8, 2017
考試日期: 25/8/2017
上課時間: 9:30am-12:00nn(基本課)，1:00pm-4:15pm(導修課)
上課地點: 蒙民偉工程學大樓405(基本課)，導修課地點會另行通知
任教教授: 溫有恒教授 (香港中文大學)
大學認可: 中文大學2學分
對象: 曾修讀本課程或特別優秀的高中學生，學員須具備大學初等數學的知識。
內容簡介:
本科以複平面的特殊幾何結構為起點，討論複數變換的對稱性和保圓性，並介紹複平面與球面的對應，以及學習莫比烏斯變換。掌握這些知識後，同學便可從現代的幾何觀點，理解「非歐幾何」各種異常有趣的性質，包括：平行與超平行、非歐距離、常曲率空間和非歐三角學等。
Understanding Non-Euclidean Geometry
Course code: SAYT1214
Date: 4/8, 7/8, 10/8, 11/8, 14/8, 15/8, 17/8, 18/8, 21/8, 2017
Examination Date: 25/8/2017
Time: 9:30am-12:00nn(Lecture),
1:00pm-4:15pm(Tutorial session)
Venue: 405, William M.W. Mong Engineering Building (Lecture), further
notifications for tutorial classrooms
Lecturer: Prof. Wan Yau Heng Tom (CUHK)
University Recognition: 2 credits of CUHK
Expected applicants: Senior form students who have distinguished mathematical performance or have taken any previous EPYMT course.
Students are expected to have exposure to beginning knowledge of tertiary
mathematics.
Introduction: Starting with special geometric structures of complex plane, students will learn symmetry and conformality on complex transformations; the intriguing correspondence between the complex plane and a sphere; and Mobiüs transformation. Then students would be introduced to a number of amazing properties of Non-Euclidean Geometry from a modern point of view, including hyper-parallelism, non-Euclidean distance, constant curvature, and hyperbolic trigonometry.
網上報名(Online application)
入學試免試條款 Conditions for Admission Screening Test Exemption
凡符合以下其中一項條款的申請人，可免除入學試而獲本科直接取錄。曾修讀「數學啟導修習I或II」的學生，仍須參加入學試，但可獲優先考慮。
Applicants who satisfy either one of the following condition may be exempted from Admission Screening Test and will be directly admitted into this course. Those who had taken "Enrichment Mentoring Mathematics I or II" still need to sit the Test, but will be considered with priority.
* 曾修讀並及格完成以下任何一個學分科目:「數論與密碼學」、「數學分析入門」、「微分幾何初探」。
* Passed in one of the following credit-bearing courses before: Number
Theory and Cryptography, Mathematical Analysis, and Towards Differential
Geometry.
* 曾獲得本科「非歐幾何賞析」取錄 。
* Being admitted into Understanding Non-Euclidean Geometry before.
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