微分幾何初探
課程編號: SAYT1134
上課日期: 15/7, 16/7, 19/7, 20/7, 22/7, 23/7, 26/7, 27/7, 28/7, 2021
上課時間: 10:30am – 5:15pm
考試日期: 30/7/2021 (10:30am-1:30pm)
後備課堂日期: 21/7, 29/7, 31/7, 2021 (10:30am-5:15pm)
上課地點: [中文大學, 詳情有待公佈]*
任教導師: 劉智軒博士 (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: 準備升上中五或中六的同學，學員須具備良好的微積分與幾何知識，具物理知識則更好。
內容簡介: 本科將微積分與幾何直觀緊密結合起來，引領同學跳出直線、平面和圓錐曲線的桎梏，進入多姿多釆的曲線與曲面的天地。同學會運用微積分，包括偏微分來描述空間的曲線與曲面，計算曲線的切向量、法向量與曲率、曲面的切平面、測地線與高斯曲率，並進一步認識如高斯-博內定理等重要的幾何定理。
學費: 港幣 3,990元正 (已包含港幣40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 3,040元正 (已包含港幣40元申請費用) 。
Towards Differential Geometry
Course code: SAYT1134
Date: 15/7, 16/7, 19/7, 20/7, 22/7, 23/7, 26/7, 27/7, 28/7, 2021
Time: 10:30am – 5:15pm
Examination Date: 30/7/2021 (10:30am-1:30pm)
Reserved Date: 21/7, 29/7, 31/7, 2021 (10:30am-5:15pm)
Venue: [CUHK. Detail to be announced]*
Lecturer: Dr. Lau Chi Hin (CUHK)
University Recognition: 2 credits of CUHK
Medium of Instruction: mainly in Cantonese with English course materials
Expected applicants: Students advancing to Secondary 5 or 6, and have good knowledge of calculus and geometry. An exposure to physics will be helpful.
Introduction: This course, combining the knowledge of calculus and geometric intuition, leads students to explore the fruitful variety of curves and surfaces beyond lines, planes, and conics. Students will use calculus up to partial differentiation to describe curves and surfaces, to calculate the tangent vector, normal vector and curvature, tangent plane, geodesic and Gaussian curvature. Other essential geometric theorems, such as Gauss-Bonnet, will be introduced.
Tuition fee: HK$3,990 (with $40 application fee included)**
Remark:
*This course offers face-to-face lessons on CUHK campus. It may switch to online teaching, subject to the actual situation.
**The tuition fee will be adjusted to HK$3,040 (with $40 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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