## 2011年11月19日 星期六

### 錯誤

Wolfram Alpha 奇景一攝：

## 2011年10月26日 星期三

### 小四題目被批太難

--- A B 兩自然數作相乘，如果A十位的"1"看成"7"，結果多了 4140，把B十位的"6"看成"4"，結果少了2240。---

1. 首先逐步拆解，也就前一半後一半來看，別想得太複雜，也別老想著一步完成。

2. 其次要對十位有一個良好概念，把"1"看成"7"，就應該想到A 這數字的十位多了"6"， 也就是總共多了"60"。

3. 再者就可以把乘法形象化，原本有一堆蘋果(A乘以B)或(B乘以A)，把A看成箱子，現在A多了60箱，總共多了 4140個蘋果。

4. 用除法4140/60求得一箱有多少蘋果，即B。同樣想法做後半，得A。

IT助理

## 2011年7月3日 星期日

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Recently, there has been much controversy over a proposed change to the by-election system of the Legislative Council of Hong Kong. In this seminar, we shall take a look at some mathematical and non-mathematical issues of electoral systems, and try to explore the best by-election system under different electoral systems, especially for proportional representation, the system currently used in the geographical constituencies in the Legislative Council of Hong Kong.

## 2011年5月25日 星期三

### 捨去（rejected）

(1) 「由於解題過程中曾經兩邊取平方」是老師或課本經常給出的解釋，但這不是正確，或至少不是完滿的解釋，至少我們知道「需要驗算」的情況不止這一種。這個有機會另文再談。

(2) 這個牽涉一些複數的理論。對於實數的「開方」，我們取非負的平方根，例如 $\dpi{100} \sqrt{{9}$ 是 3 而不是 -3。對於負數及一般複數的「開方」，我們也會選一個「主值」（principal value，詳見這裡）。

(3) 「在處理實數的過程中離開了實數的世界」在數學上並不罕見，例如我們可以利用複分析（complex analysis）的技巧計算這個看來和複數毫無關係的積分：

## 2011年5月15日 星期日

### EPYMT2011

The Department of Mathematics, CUHK is offering 4 courses of a summer outreach programme "Enrichment Programme for Young Mathematics Talents" (EPYMT), for secondary school students. These courses include:

Geometric Perspectives of Complex Numbers (suits F.3-F.4 students) and
Understanding Non-Euclidean Geometry (suits F.6-F.7 students).

Junior form students who perform particularly well in mathematics may also be admitted. The students who join the course(s) of EPYMT can learn advanced mathematics during summer and get well equipped for New Senior Secondary Mathematics Curriculum. Besides, admitted students may also get admission consideration and/or two credits at CUHK.

All of the courses will be held at CUHK campus and be taught by the professors or lecturers of our department.

Online Registration and deadline: Midnight 18 May, 2011
Admission Screening Test: 21 May, 2011
Please kindly visit here for the details of each course.

## 2011年4月12日 星期二

### 約定俗成

「曼聯戰敗了阿仙奴獲得了冠軍」
• 曼聯戰敗了（輸了），阿仙奴獲得冠軍？
• 曼聯戰敗了阿仙奴（曼聯擊敗阿仙奴），所以曼聯獲得冠軍？
「Someone who knows Alan or Billy is here.」
• Someone who knows (one of Alan and Billy) is here?
• (Someone who knows Alan) or (Billy himself) is here?

• ab2 是指 a(b2) 而非 (ab)2，但 cm2 卻是指 (cm)2，即 1 cm2 = (0.01 m)2 而不是 0.01(m2)。

• sin 2 a 是指 (sin 2) a 還是 sin(2a)？絕大多數人接受是 sin(2a)，但 sin a cos b 是指 (sin a)(cos b) 還是 sin (a cos b) 呢？絕大多數人會認為是 (sin a)(cos b)。兩者看來是有點矛盾的，但這是「俗成」了。

## 2011年4月2日 星期六

### 第十屆培正數學邀請賽決賽題目及答案

http://www.mathdb.org/resource_sharing/others/s_puiching10_F1.pdf

http://www.mathdb.org/resource_sharing/others/s_puiching10_F2.pdf

http://www.mathdb.org/resource_sharing/others/s_puiching10_F3.pdf

http://www.mathdb.org/resource_sharing/others/s_puiching10_F4.pdf

http://www.mathdb.org/resource_sharing/others/s_puiching10_F5.pdf

http://www.mathdb.org/resource_sharing/others/s_puiching10_FA.pdf

## 2011年3月1日 星期二

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Any other special angles? Algebra knows.

Since we were in junior secondary school, we have already learnt about the trigonometric functions sin, cos and tan, and their values at the special angles 30°, 45° and 60°, for example, cos60°=1/2.

In this seminar, we investigate the possibility for a trigonometric ratio cos(360°/p) to be expressed in terms of distinct radicals and rational numbers, where p is a prime. It turns out that the only two possibilities are p=3 and p=5.

We will use the Galois Theory in abstract algebra to prove this result.

### 數學資料庫生日會

3 月 13 日（星期日）是數學資料庫的生日的前一天！如此大日子，我們安排了一連串的活動，大家萬勿錯過！

• 當天晚上是數學資料庫的週年晚宴暨生日會，安排如下：

其他　 -- 100 元

* 需於 3 月 6 日（星期日）下午 8 時前連同姓名、人數（中學生和非中學生人數）和聯絡電話電郵至 mathdb.fomd@gmail.com，我們將以電話回覆作實。

## 2011年2月15日 星期二

### 香港中文大學公開講座

• 講者：鍾子信教授
• 日期：2011 年 2月26日 (星期六)
• 時間：上午 10:30 至 中午 12:00
• 地點：香港中文大學邵逸夫堂
• 語言：粵語

http://www.math.cuhk.edu.hk/publect/lecture20/lecture20.html

## 2011年1月6日 星期四

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Combinatorics - A Bit More Than Counting

Among Mathematics graduate students, some of them have never heard the word "Combinatorics". Even in a graduate class of Combinatorics, the professor, a star in the area, said that he could not really define what is Combinatorics. Field Medalist Terrence Tao claimed that Combinatorics may be the only exceptional area in modern Mathematics research. There are many areas in Mathematics related to Combinatorics, e.g. algebraic combinatorics, analytic combinatorics, probabilistic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial algorithms, combinatorial design.
These facts seem contradicting as the subject of huge coverage is unaware by some of the reasearchers in Mathematics. That is Combinatorics. Not until recently Combinatorics is not covered in Hong Kong public examination syllabus, while it includes concepts like permutations and combinations in the core syllabus. I am going to talk about the interesting side of Combinatorics in this seminar.

## 2011年1月5日 星期三

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Combinatorics - A Bit More Than Counting

Among Mathematics graduate students, some of them have never heard the word "Combinatorics". Even in a graduate class of Combinatorics, the professor, a star in the area, said that he could not really define what is Combinatorics. Fields Medalist Terrence Tao claimed that Combinatorics may be the only exceptional area in modern Mathematics research. There are many areas in Mathematics related to Combinatorics, e.g. algebraic combinatorics, analytic combinatorics, probabilistic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial algorithms, combinatorial design.

These facts seem contradicting as the subject of huge coverage is unaware by some of the researchers in Mathematics. That is Combinatorics. Not until recently Combinatorics is not covered in Hong Kong public examination syllabus, while it includes concepts like permutations and combinations in the core syllabus. I am going to talk about the interesting side of Combinatorics in this seminar.