微分幾何初探
課程編號: SAYT1134
上課日期: 14/7, 17/7, 18/7, 20/7, 21/7, 24/7, 27/7, 28/7, 31/7, 2017
考試日期: 3/8/2017
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407或LT (基本課)，導修課地點會另行通知
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
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。
Towards Differential Geometry
Course code: SAYT1134
Date: 14/7, 17/7, 18/7, 20/7, 21/7, 24/7, 27/7, 28/7, 31/7, 2017
Examination Date: 3/8/2017
Time: 9:30am-12:00nn(Lecture), 1:00pm-4:15pm(Tutorial session)
Venue: 407 or LT, William M.W. Mong Engineering Building (Lecture), further
notifications for tutorial classrooms
Lecturer: Dr. Lau Chi Hin (CUHK)
University Recognition: 2 credits of CUHK
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.
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 「複數的幾何面貌」。
* Passed Geometric Perspectives of Complex Numbers before.
* 曾獲得以下任何一個學分科目取錄:「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 credit-bearing courses before: Number
Theory and Cryptography, Towards Differential Geometry, Mathematical
Analysis, and Understanding Non-Euclidean Geometry.
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