Abstract Algebra and Famous Impossibilities
By Patrick Wong, HKUST
Date: July 27, 2010. (Tuesday)
Time: 6:00pm-7:30pm
Venue: Room 4504 (near Lifts 25 & 26) , HKUST
Target Audience: Students with basic algebra background
Abstract: The famous problems of squaring the circle, doubling the cube, and trisecting the angle have not yielded to purely geometrical methods. It was, however, the development of abstract algebra in the nineteenth century which enabled mathematicians to conclude that these constructions are not possible. We are going to look at the way how algebra solve the geometric problems.
2010年7月23日 星期五
2010年7月19日 星期一
寫在高考放榜前（二）
其實要講的事也八八九九說完了。畢竟，既然大學就是開放，只要你敢走自己的路，也無謂多說其他。
今天，只想講一個小故事。
幾年前，一位後輩小學升中。她的成績在小學內一直很好，考試總是頭幾名。她的媽媽來找我，說想女兒升讀一間英文中學，但女兒總是想升讀一間中文中學。我被指派擔當「談判者」的角色。
談了一回，我知道了真正的原因，並認為這原因不成熟。那一刻，我起了一個可怕的念頭：甚麼也不要談了，直接跟她的媽媽說，逼她選一間英文中學。
最後我沒有這樣做——我慶幸自己沒有這樣做。儘管如此，幾年後回想，我仍然為自己曾經有過這樣的念頭而覺得可怕。
我回想自己短短的廿多載人生。是的，很多決定都是幼稚，甚至是錯的。但我慶幸我在人生眾多選擇中，決定權在自己手中——這要多謝我的父母。曾經享受著「高度自治」的人竟然起了這樣的一個念頭？這是何等可怕的事情？
幾年後的今天，我知道這位女兒在自己選擇的新學校中過得快樂。
******
現在，故事發生後的幾年，我讀過了《四代香港人》，亦讀了《三杯茶》裏主角Greg Mortenson的童年經歷，我更深刻的明白到父母與長輩的責任是要以身作則向子女提供良好的品德教育，在適當時候提供意見和輔導，而不是強逼甚至命令子女要做這要做那，令子女漸漸失去判斷力和走人生路的勇氣，變成自己的扯線公仔。
2010年7月9日 星期五
馬會可能通殺？買中了也輸錢？
世界盃是國際矚目的體育盛事，不少球迷一邊在電視前搖旗吶喊外，一邊下注，考考自己的眼光。投注項目五花八門，除了每場比賽的賽果外，亦有以世界盃為整體的專項，例如競猜小組首名、冠軍等。以上各種項目裏，只要你猜中了正確的結果（例如哪隊取得冠軍），便肯定獲得彩金，而彩金亦肯定比投注本金多。（如果猜對了也要輸，誰會下注？）可是這種想法未必一定正確。例如競猜誰是「神射手」（世界盃所有比賽裏入球最多的球員）便是一例。在某些情況下，猜錯了要輸掉本金，但猜對了也贏不了！
為甚麼會這樣荒謬呢？這是因為「神射手」與世界盃冠軍不同：冠軍只有一個，但「神射手」卻可以超過一個（見註）。簡單來說，假如有兩名球員都射入五球，而沒有人射得六球或以上，這兩名球員都是「神射手」。如果「神射手」多於一個，香港賽馬會如何計算彩金？原來在這種情況下，投注本金會先除以神射手的數量才計算彩金。這就是買中了也要賠錢的關鍵。看看以下的現實例子：
準決賽結束後，荷蘭的史奈達 (Wesley Sneijder) 和西班牙的韋拿 （David Villa) 暫時以五球領先。撰寫本文時，韋拿的「神射手」賠率為 1.85 倍。假設現在某人以 1000 元本金下注韋拿為「神射手」。如果決賽和季軍戰都沒有球員入球，史奈達和韋拿將同為「神射手」。雖然這位投注者買中了，但他可得的「彩金」卻只有 1000 ÷ 2 × 1.85 = 925 元，輸了 75 元。如果同射得五球的球員有三個或四個，他將更倒楣，輸得更多。
這就是賭博世界常用的併頭名次規則 (dead heat rules)，每當勝出者比預期多時便適用。「併頭名次」在足球世界裏極少發生，只會偶然在賽馬世界出現，難怪這規則不易為人所知。
註：上文提及的「神射手」併頭只在香港賽馬會的賭博規則出現，與國際足協 (FIFA) 的神射手獎 (Golden Boot Award) 的決定規則不同。假如兩名球員射入相同的球數，助攻 (assist) 較多者名次較高；若助攻次數亦相同，總出場時間較短者名次較高。
2010年7月7日 星期三
CMPC Student Seminar Series
A group of people from HKUST are holding a series of seminar in different area in undergraduate mathematics.
The topics are mainly from undergraduate,
students who are interested in are welcome.
The first two seminars will start on the next week.
The location are taken place at the Hong Kong University of Science and Technology.
One can go to the HKUST by minibus at Choi Hung MTR Station (Exit C)
Symmetry, Group Theory and Art
By Hoi Luk, (HKU Space)
Date: July 14, 2010. (Wednesday)
Time: 6:00pm-7:30pm
Venue: Room 4504 (near Lifts 25 & 26) , HKUST
Target Audience: Undergraduate who is interested in exploring more about Abstract Algebra
Abstract: This is an introductory talk on Abstract Algebra. Group is a central concept in Abstract Algebra and it plays important roles in Geometry, Topology, ODE and etc. The talk will include the mathematical concept of symmetry, the use of Group in studying symmetry and Wallpaper Groups in Art. It is designed for undergraduate students who are interested in exploring more about Abstract Algebra and it may serve as the motif for those going to take MATH 311 (Algebra I).
Financial Mathematics - The Art of Compromise
By Jeff Tam, (Tokyo Metropolitan University)
Date: July 15, 2010. (Thursday)
Time: 6:30pm-8:00pm
Venue: Room 4504 (near Lifts 25 & 26) , HKUST
Target Audience: Undergraduate with basic quantitative background who is interested in financial mathematics
Abstract: Financial Mathematics has taken the world by storm since its inception during the 80s. In light of the recent financial crisis, the purpose of this talk is to unveil financial mathematics, divulging vital information such as its theoretical foundation, industrial practice, research frontier, etc. Most importantly, where does the "model world" and "reality" meet? What kind of compromise can bring these two together while (hopefully) not sacrificing too much reliability.
For more details on the coming seminars,
please visit http://ihome.ust.hk/~delamath/CMPC/CMPCSem.htm
The topics are mainly from undergraduate,
students who are interested in are welcome.
The first two seminars will start on the next week.
The location are taken place at the Hong Kong University of Science and Technology.
One can go to the HKUST by minibus at Choi Hung MTR Station (Exit C)
Symmetry, Group Theory and Art
By Hoi Luk, (HKU Space)
Date: July 14, 2010. (Wednesday)
Time: 6:00pm-7:30pm
Venue: Room 4504 (near Lifts 25 & 26) , HKUST
Target Audience: Undergraduate who is interested in exploring more about Abstract Algebra
Abstract: This is an introductory talk on Abstract Algebra. Group is a central concept in Abstract Algebra and it plays important roles in Geometry, Topology, ODE and etc. The talk will include the mathematical concept of symmetry, the use of Group in studying symmetry and Wallpaper Groups in Art. It is designed for undergraduate students who are interested in exploring more about Abstract Algebra and it may serve as the motif for those going to take MATH 311 (Algebra I).
Financial Mathematics - The Art of Compromise
By Jeff Tam, (Tokyo Metropolitan University)
Date: July 15, 2010. (Thursday)
Time: 6:30pm-8:00pm
Venue: Room 4504 (near Lifts 25 & 26) , HKUST
Target Audience: Undergraduate with basic quantitative background who is interested in financial mathematics
Abstract: Financial Mathematics has taken the world by storm since its inception during the 80s. In light of the recent financial crisis, the purpose of this talk is to unveil financial mathematics, divulging vital information such as its theoretical foundation, industrial practice, research frontier, etc. Most importantly, where does the "model world" and "reality" meet? What kind of compromise can bring these two together while (hopefully) not sacrificing too much reliability.
For more details on the coming seminars,
please visit http://ihome.ust.hk/~delamath/CMPC/CMPCSem.htm
2010年7月6日 星期二
Solving IMO Q6 collaboaratively
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