I haven’t updated my blog for millions years. I feel like I need to write something.
My friend send me the following link: youtube channel for Journal of number theory. The authors can send videos about the abstracts of their papers.
For the first few videos I saw, the words on the board are very unclear. I wonder will it be better to insert slides in the video by some video editing softwares (like Window Movie Maker)?
O’Reilly is a computer book publisher. Most of their books have distinguished animal covers. You can access their books online through Safari books online if you have a CUHK ID. Actually you can also find Prentice Hall and Addison Wesley’s books. Other publishers include Sams, Que, New Riders, Microsoft press.
Few months ago, I started to use an external hard drive as my main hard disk. The main reason is that I work between three computers. I am too lazy to bring my main notebook to my office on a daily basis.
Last night, my notebook can no longer access the hard disk. I can’t access my data. That means all my data there is gone! Luckily I back up my data from time to time. But still, some of my files, like my lecture notes for my classes are gone forever.
I always wonder what it the best way to store information. Web 2.0 helps every folk to create information. However, the problem of disappearance of electronic information shouldn’t be overlook. A lesson learned today!
Recently Langlands is awarded the Shaw prize. Here are some introductory articles to Langlands’ program. Beware that the articles are by no means easy. Knowledges of algebraic number theory and modular forms are assumed.
Gelbart: An elementary introduction to the Langlands program[pdf], Bull. Amer. Math. Soc. 10 (1984), 177-219.
Knapp: Introduction to the Langlands program[pdf], Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics61 (1997), American Mathematical Society, Providence, Rhode Island, pp. 245-302.
See also Vergne, All what I wanted to know about Langlands program and was afraid to ask
I was very impressed by Pewkee’s service. I shipped about 200kg’s stuff from Taipei to Hong Kong. They came to my house around 3pm and my stuff arrived my apartment in Hong Kong the next day at 10 am! Very efficient! It is not expensive. They charged me about 20HKD (around 2.7 USD) per kg (probably due to the high volume). The normal price may be around 30 HKD (around 4 USD) per kg.
Did you know that many (in fact, most) color laser printers are spying on you whenever you print a document? Though you may not have heard the news, the discovery was announced in late 2005. Manufacturers embed a pattern of tiny yellow dots on printed pages. The dots are too small to be seen with the naked eye (especially since they’re yellow, see the above photo to see what they actually look like), but under a microscope and blue light they’re revealed. The dots are placed in a pattern unique to each printer, and since most color laser printers are purchased through well-documented service providers or direct from the manufacturer, it’s simple to track any printed page back to the owner of the printer.
To read more, see Yahoo Tech .
Lagrange’s Four-square theorem asserts that every positive integers can be written as sum of four squares. It was proved by Lagrange in 1770. There are several proofs, most of them are generalizations of the proofs of Fermat’s theorem on sum of two squares. Same as the case for sum of two squares, there is an identity that shows the the product of two sum of four squares is still a sum of four squares. Here is a list of proofs
Today I found an interesting proof based on the formula of number of representations as sum of two squares . The number of representation of an integer n as sum of two squares is given by
The proof can be found in Davidoff, Giuliana; Sarnak, Peter; Valette, Alain Elementary number theory, group theory, and Ramanujan graphs. London Mathematical Society Student Texts, 55. Cambridge University Press, Cambridge. p.52 - p.57.
Essays in the History of Lie Groups and Algebraic Groups by Armand Borel is an excellent book. Anyone studying theories of Lie Groups and Algebraic groups should find this book inspiring.
Affordable textbook campaign by Bernard Russo in AMS notices.
The article contains a link to an online linear algebra textbook:
A First Course in Linear Algebra, by Robert Beezer
This is a nice passage written by Fields medalist John Milnor in Growing up in the old Fine Hall, Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University . p8-p.9.
……. This talk is about the past, but perhaps I should close by saying something with a bearing on the future, something about my philosophy of mathematics. What I love most about the study of mathematics is its anarchy! There is no mathematical czar who tells us what direction we must work in, what we must be doing. There are thousands of mathematicians all over the world each going in his or her own direction. Many are exploring the most popular or fashionable directions, but others work in strange or unfashionable directions. Perhaps many are going the wrong way, but cumulatively the many different directions, the many different approaches, mean that new and often unexpected things will be discovered. I like to picture the frontier of mathematics as a great ragged wall, with the unknown, the unsolved problems, to one side, and with thousands of mathematicians on the other side, each trying to nibble away at different parts of the problem using different approaches. Perhaps most of them don’t get very far, but every now and then one of them breaks through and opens a new area of understanding. Then perhaps another one makes another breakthrough and opens another new area. Sometimes these breakthroughs come together, so that we have different parts of mathematics merging, giving us wide new perspectives. Often the people who make these breakthroughs are those who are well known, those we expect to obtain good results; but not always. Many times major results are obtained by those who are not at all well known, or by people we may know but underestimate, so that we are completely surprised to find that they have accomplished so much. It is wonderful that no one has the power to turn such people off! Of course they can be discouraged, and often have to fight for recognition, but there are many universities, many places where one can do mathematical research, and no astronomical budget is required. Thus there is always hope that even people who have unpopular ideas will have a real chance to succeed.
