Category Archives: Miscellaneous

A discussion forum

Posted on 20/10/2015 by KKK

In order to facilitate discussion, I have set up a discussion forum here: http://cuhkmath.606h.net/phpBB3/viewforum.php?f=2 One of the most effective way of learning mathematics is by discussion. While there are excellent sites like MathOverflow or StackExchange where you may even find … Continue reading →

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Why does a mirror reverse left and right, but not top and bottom?

Posted on 04/06/2015 by KKK

If you stand in front of a mirror and raise your right hand, it appears in the mirror that you raise your left hand. Why does a mirror reverse left and right, but not top and bottom? For some of … Continue reading →

Posted in Geometry, Linear Algebra, Miscellaneous | Leave a comment

The 10th Taiwan Geometry Symposium

Posted on 07/04/2015 by KKK

This is not really a “mathematical” post. Since this is the first symposium I’ve ever co-organized, I am supposed to advertise it (a bit). So if you happen to be in Taiwan, and are interested in geometry (OK, I know … Continue reading →

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High degree polynomial with few real roots

Posted on 08/12/2014 by HL

There are univariate polyomials that the number of non-real roots is significantly larger than that of real roots. The simplest example is where is odd. It has one real root and non-real roots. In this post we show an example … Continue reading →

Posted in Algebra, Calculus, Miscellaneous | Leave a comment

Two little remarks on sphere

Posted on 15/04/2014 by michaelngelo

1. “Take a sphere of radius in dimensions, large; then most points inside the sphere are in fact very close to the surface.” David Ruelle Let and . Let The fraction of the volume of to the volume of is … Continue reading →

Posted in Geometry, Miscellaneous, Probability | Tagged , , | Leave a comment

Mathematics behind JPEG

Posted on 06/10/2012 by lamwk

Many of you should have this experience: when you save a picture with many words in Paint(小畫家) as .jpg file, some ugly artifacts appear. Then you may think why is such a low quality image format so common? At the … Continue reading →

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On integrating products of dot products

Posted on 17/06/2011 by leonardwong

Today KKK showed me the following formula: There exists a constant such that for all . Here the integral is either over the unit sphere or over the ball (of course the corresponding constants are different). In this note we … Continue reading →

Posted in Miscellaneous | 4 Comments

Interesting books and survey articles

Posted on 19/12/2010 by Mathematics@CUHK

It may be nice to collect in a post introductory books and survey articles in various areas in mathematics, so that all of us may take a look. This post is supposed to be edited by anyone. Analysis 1. Complex Analysis … Continue reading →

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Estimating the probability of grad school admission

Posted on 05/12/2010 by leonardwong

We start with a naive model of the situation. Model 1. Suppose that I apply for schools , , …, . I estimate that I will be admitted to school  with probability . Thus, if denotes the event that I am admitted … Continue reading →

Posted in Miscellaneous, Probability | 2 Comments

An exercise in combinatorics

Posted on 05/11/2010 by leonardwong

We answer the following question: Let and be positive integers with . What is the number of surjective maps from to ?

Posted in Miscellaneous, Probability | 1 Comment

A notice

Posted on 12/10/2010 by KKK

After running the blog for a while, I’ve noticed a few minor problems. I think the following ways may help improve this blog. 1. I found that some of you have updated the post. This is good. However, because of … Continue reading →

Posted in Miscellaneous | 4 Comments