Mathematical Analysis: An Overture I 數學分析入門 (一)
Nov 2014 - March 2015
Jointly offered with Hong Kong Academy of Gifted Education

Introduction
引言

Learning Mathematical Analysis is the best way to establish logical thinking and rigorous mathematics. For this reason, Mathematical Analysis is always a core subject for mathematics major students in most universities in the world. Seeing the importance of this topic, Hong Kong Academy of Gifted Education and EPYMT join hands to provide this deep course of exactitude for the members of the academy. In this course, students are required to perform abstract deduction and logical arguments. It builds the mathematics mastery of students as well as enhances their strength in thinking. It also allows the students to learn in the atmosphere of a higher education institute.

要接受真正的數學訓練，培養邏輯的思考方式，學習「數學分析」是絕佳的途徑。正是由於這樣，世界主流大學的數學系都會把「數學分析」訂為主修生的必修科目。有見及此，香港資優教育學苑與我們將推出「數學分析I」，向學苑的成員介紹這門準確精密，影響深遠的學科。本科要求嚴格的抽象推理和邏輯論証，不單可磨練學生的數學技巧，更可提升他們的思維能力，為學生締造一個高等學府的學習環境。

Course Code
課程編號

SAYT1054 (CUHK)
MATS3610 (HKAGE)

Course outline
內容簡介

Natural phenomena from quantum vibration of fundamental particles to the expanding universe, all demonstrate unceasing variation. Some changes are simple and regular such as sunrise, sunset, and seasonal cycles. Some others are intriguing and unpredictable such as financial fluctuation and epidemic. Our lives are inevitably surrounded by changes. The mathematical study of changes and variation begins in Calculus that students first encounter in high school.

每種自然現象，從基本粒子的量子振動到宇宙的不斷膨漲，都展示出變化。有些變化簡單而有規律，如日出日落、季節的循環往復；有些變化複雜而難料， 如金融市場的波動、疫症的突然爆發，各種變化都影響著我們的生活。研究變化的數學，就是中學課程裡開始接觸的微積分。

Every student serious in mathematics knows that to truly understand Calculus, one must get a grip on the its underlying theory, namely, Mathematical Analysis. It is a university basic course; yet it is also a crucial step onto the pinnacle of mathematics. While Newton and Leibniz were the founders of Calculus, their work were at the same time built on their forerunners and relied on the deepening and structuring of their successors. Without Mathematical Analysis, Calculus would have been simply a tool of rough estimate and speculation.

認真學習數學的同學都知道，要深入了解微積分，必須理解、掌握它背後的數學理論 ── 數學分析，這門大學程度的數學科目是步入高等數學殿堂的階梯。牛頓 (Newton)和尼布列玆 (Leibniz)雖然是微積分的奠基者，但他們的工作一方面承習前人的建樹，另一方面也有賴後人的深化與整理。沒有後來的數學分析，微積分就只停留在憑猜度的計算方法。

Admission Screening Test
入學試

It will be held on 15, Nov(Sat)2014 at Lecture Theatre 1, Lady Shaw Building, The Chinese University of Hong Kong.
Go to this link for details

入學試於2014年11月15日(星期六)於香港中文大學邵逸夫夫人樓, 1號演講廳舉行
詳情請參閱此網頁

Teaching Personnel
教學人員

To be announced
有待公佈

Credit recognition, fee, and scholarship
學分認可、學費、獎學金

This course is recognized by the Science Faculty of The Chinese University of Hong Kong. Any student who has passed this course will be granted one credit unit when he/she is enrolled as an undergraduate of the university. EPYMT will also provide references for students to apply for credit exemption in other universities. In addition, the performance of a student in this course may also be considered upon university admission. Merit certificates may be issued but there is no special scholarship for this course.

本科獲中文大學理學院認可，學生修畢本科，而將來入讀中文大學本科，可獲得豁免1學分；若升讀其他大學而以本科申請學分豁免，本課程亦會提供資歷證明。學生修讀本科的表現，亦將會作為大學入學取錄考慮因素之一。本科設有優異獎狀， 並不設有獎學金。

Admission and application
入學方法

This course only admits members of Hong Kong Academy of Gifted Education. Those who are interested in please contact the academy. Applicants must pass the Admission Screening Test arranged by the Enrichment Programme for Young Mathematics Talents (EPYMT)
Application details please click here


本科只為香港資優教育學苑成員而設，有興趣修讀者，請向該學苑申請。申請人必須通過數學英才精進課程安排的入學測驗。
申請詳情請參閱這裡

Venue
上課地點

Most of the classes will be held at Room G35, Lady Shaw Building, The Chinese University of Hong Kong. Some of them will be held at Room 401, William M. W. Mong Engineering Building,The Chinese University of Hong Kong .
大部分課堂將於香港中文大學邵逸夫夫人樓G35室進行, 有部分會在香港中文大學蒙民偉工程學大樓401室進行。

Arrival Instructions 交通路線

Campus Map 校園地圖

Time-table for Shuttle Bus Service 校車時間表


Time
時間

9:30 am – 12:00 nn

Programme Schedule
Session Date Venue Content
1 29/11/2014 LSB G35 Sets, logics, functions, induction and inequalities
2 13/12/2014 ERB 401 Review, exercises, discussion, hint and methods
3 10/01/2015 LSB G35 Rational, irrational and real numbers
4 17/01/2015 LSB G35 Review, exercises, discussion, hint and methods
5 24/01/2015 LSB G35 Preparation for test
6 31/01/2015 LSB LT1 Mid-course Assessment
7 07/02/2015 LSB G35 Countable, uncountable and sequences
8 14/02/2015 LSB G35 Review, exercises, discussion, hint and methods
9 28/02/2015 LSB G35 Bounds and completeness of real numbers
10 07/03/2015 LSB G35 Review, exercises, discussion, hint and methods
11 21/03/2015 LSB G35 Preparation for exam
12 28/03/2015 LSB LT6 Final Assessment

Enquiry
查詢

epymt@math.cuhk.edu.hk