非歐幾何賞析
課程編號: SAYT1214
上課日期: 19/9, 26/9, 3/10, 10/10, 17/10, 24/10, 31/10, 7/11, 14/11, 2020 (Sat)
考試日期: 21/11/2020 (Sat) ; 後備考試日期: 28/11/2020 (Sat)
上課時間: 10:30am – 5:15pm
上課地點: [中文大學, 詳情有待公佈] *
任教教授: 鄭文銓博士 (香港中文大學)
大學認可: 中文大學2學分
教學語言：粵語為主，附以英文教材
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。
學費: 港幣 3,970元正 (已包含港幣20元申請費用)**
備註
*此課程暫定於中文大學內授課，或有可能轉為線上授課，視乎實際情況而定。
**如課程最終轉為線上授課，學費將會調整為港幣 3,020元正 (已包含港幣20元申請費用) 。
Understanding Non-Euclidean Geometry/font>
Course code: SAYT1214
Date: 19/9, 26/9, 3/10, 10/10, 17/10, 24/10, 31/10, 7/11, 14/11, 2020 (Sat)
Examination Date: 21/11/2020 ; Reserved Date: 28/11/2020 (Sat)
Time: 10:30am – 5:15pm
Venue: [CUHK. Details to be announced]*
Lecturer: Dr. CHENG Man Chuen (CUHK)
University Recognition: 2 credits of CUHK
Medium of Instruction: mainly in Cantonese with English course materials
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 Mobius 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.
Tuition fee: HK$3,970 (with $20 application fee included)**
Remark:
*This course is offered face-to-face lessons at CUHK campus. It may switch to online teaching, subject to the actual situation.
**The tuition fee will be adjusted to HK$3,020 (with $20 application fee included) if the course finally switches to online teaching.
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。（參考附註）
Applicants who satisfy either one of the following condition may be exempted from Admission Screening Test and will be directly admitted into this course. (refer to note below)
- 曾修讀並及格完成以下任何一個科目取錄: 「複數的幾何面貌」、「複數與解析幾何」、「近世代數初探」。
Passed in any of the following courses before: Geometric Perspectives of Complex Numbers, Complex Number and Analytical Geometry, and Towards Modern Algebra.
- 曾獲得以下任何一個科目取錄:「數論與密碼學」、「微分幾何初探」、「數學分析入門」、「非歐幾何賞析」。
Being admitted in one of the following courses before: Number Theory and Cryptography, Towards Differential Geometry, Mathematical Analysis, and Understanding Non-Euclidean Geometry.
（參考附註 note）
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。
Those who had taken "Enrichment Mentoring Mathematics I or II" still need to sit the Test, but will be considered with priority.
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