非歐幾何賞析
課程編號: SAYT1214
上課日期: 6/8, 9/8, 10/8, 13/8, 14/8, 16/8, 17/8, 20/8, 21/8, 2018
考試日期: 24/8/2018
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703(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
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。
Understanding Non-Euclidean Geometry
Course code: SAYT1214
Date: 6/8, 9/8, 10/8, 13/8, 14/8, 16/8, 17/8, 20/8, 21/8, 2018
Examination Date: 24/8/2018
Time: 9:30am-12:00nn(Lecture), 1:00pm-4:15pm(Tutorial session)
Venue: Room 703, 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
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.
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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