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2009年7月21日 星期二

IMO Q6 2009

There is this collaborative project of solving IMO Q6 2009: http://terrytao.wordpress.com/2009/07/20/imo-2009-q6-as-a-mini-polymath-project/. Perhaps some of you will be interested in thinking about the problem together (with all the other math people around the world)? I saw Tim Gowers (a Field's medalist) constantly making comments on the various approaches that people suggest, so it might be interesting to read the comments as people make progress even if you are not actively thinking about it.

2009年7月17日 星期五

Video lectures online

I was just brought into notice that seven videotaped lectures from 1964 by the renowned physicist Richard Feynman, on "The Character of Physical Law", have been put online for public use. (I learned this from this post by Terry Tao, and if you're interested in these lectures by Feynman you'll also probably be interested in the following more advanced lectures that he gave.) I hope it's not too out of place to put this piece of news here, but having heard this triggered me to look online for some good math lectures as well. I found the following site, which has some good undergraduate level mathematics lectures (probably accessible to some F.6 or F.7 students too):

http://ocw.mit.edu/OcwWeb/web/courses/av/index.htm#Mathematics

In fact I think the first course, on single variable calculus, should be good for students studying Additional mathematics. These are very good learning materials, and hopefully some of you will find it useful.

2009年7月2日 星期四

充滿數學哲理的名言（二）

８　２　６

４　１　３

５　７　９

「1 應該放在中間」是很自然的想法，這源自我們「對數學的感覺」。這份「數學感」是很重要的，因為解決數學問題時我們很多事不會預知結果，而是要找出結果再作證明，過程中這份「感覺」往往可以指導我們作出合理的猜測，此乃「大膽假設」。在「有感覺」的前提下，我們的假設不妨大膽一點（注意「大膽假設」異於「隨意猜測」，前者是基於理性的「數學感」的），事實上數學的發展是很靠創意和想像力的，而作出假設也可以給我們清晰的目標。