charlesli.org Blog http://charlesli.org/blog Charles Li's Blog Tue, 27 Apr 2010 07:09:59 +0000 http://wordpress.org/?v=2.8.4 en hourly 1 Kilford’s Modular Forms, A classical and computational introduction http://charlesli.org/blog/2010/04/27/kilfords-modular-forms-a-classical-and-computational-introduction/ http://charlesli.org/blog/2010/04/27/kilfords-modular-forms-a-classical-and-computational-introduction/#comments Tue, 27 Apr 2010 07:06:15 +0000 charles http://charlesli.org/blog/?p=41 There are a lot of excellent books on the theory of modular forms.  Kilford,’s book Modular forms, A classical and computational introduction, by Imperial college press is definitely one of them.  Chapter 1-4  cover  the basic theory of the modular forms,  at the general setting.  Chapter 5 covers interesting applications, among them are approximating of pi, quadratic forms, Picard’s little theorem, Fermat’s Last theorem.  The book is very pleasant to read.  Suitable for any graduate students or mature undergrad who want to learn more about modular forms.  Interesting computations are mentioned throughout the book. Although the title mention about computation. The computer related material is only mentioned in chapter 7.

I strongly recommend this book to anyone who wants to learn modular forms.  I will also suggest this book as the first modular forms book to any students.

In below is also a list of books that cover classical theory of modular forms (the list is not intended to be complete, and are not in particular order)

The 1-2-3 of modular forms (chapter 1)

Serre,  A Course in Arithmetic

Ogg,  Modular forms and Dirichlet Series

Diamond, Shurman, A first course in modular forms

Iwaniec Topics in Classical automorphic forms

Bump, Automorphic forms and Representations (Chapter 1)

Miyake, Modular forms

]]> http://charlesli.org/blog/2010/04/27/kilfords-modular-forms-a-classical-and-computational-introduction/feed/ 0 Journal of Number Thoery and youtube http://charlesli.org/blog/2008/05/23/journal-of-number-thoery-and-youtube/ http://charlesli.org/blog/2008/05/23/journal-of-number-thoery-and-youtube/#comments Fri, 23 May 2008 03:36:31 +0000 charles http://charlesli.org/blog/?p=40 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)?

]]> http://charlesli.org/blog/2008/05/23/journal-of-number-thoery-and-youtube/feed/ 0 Computer books online http://charlesli.org/blog/2008/03/02/oreilly-books-online/ http://charlesli.org/blog/2008/03/02/oreilly-books-online/#comments Sun, 02 Mar 2008 03:51:03 +0000 charles http://charlesli.org/blog/?p=39 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.

]]> http://charlesli.org/blog/2008/03/02/oreilly-books-online/feed/ 0 Crash of my external Hard Disk http://charlesli.org/blog/2007/11/17/crash-of-my-external-hard-disk/ http://charlesli.org/blog/2007/11/17/crash-of-my-external-hard-disk/#comments Sat, 17 Nov 2007 09:31:21 +0000 charles http://charlesli.org/blog/?p=37 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!

]]> http://charlesli.org/blog/2007/11/17/crash-of-my-external-hard-disk/feed/ 0 Some introductory articles of the Langlands program http://charlesli.org/blog/2007/10/12/some-introductory-articles-of-the-langlands-program/ http://charlesli.org/blog/2007/10/12/some-introductory-articles-of-the-langlands-program/#comments Fri, 12 Oct 2007 07:33:09 +0000 charles http://charlesli.org/blog/?p=36 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

]]> http://charlesli.org/blog/2007/10/12/some-introductory-articles-of-the-langlands-program/feed/ 0 彪記 Pewkee Trans Worldwide Express http://charlesli.org/blog/2007/08/05/%e5%bd%aa%e8%a8%98-pewkee-trans-worldwide-express/ http://charlesli.org/blog/2007/08/05/%e5%bd%aa%e8%a8%98-pewkee-trans-worldwide-express/#comments Sun, 05 Aug 2007 05:12:43 +0000 charles http://charlesli.org/blog/?p=34 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.

]]> http://charlesli.org/blog/2007/08/05/%e5%bd%aa%e8%a8%98-pewkee-trans-worldwide-express/feed/ 0 Your printer may spy on you! http://charlesli.org/blog/2007/08/05/your-computer-may-spy-on-you/ http://charlesli.org/blog/2007/08/05/your-computer-may-spy-on-you/#comments Sun, 05 Aug 2007 04:50:40 +0000 charles http://charlesli.org/blog/?p=33 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 .

]]> http://charlesli.org/blog/2007/08/05/your-computer-may-spy-on-you/feed/ 0 Lagrange’s four-square theorem http://charlesli.org/blog/2007/07/26/lagranges-four-square-theorem/ http://charlesli.org/blog/2007/07/26/lagranges-four-square-theorem/#comments Thu, 26 Jul 2007 10:15:53 +0000 charles http://charlesli.org/blog/?p=32 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

  • Generalization of Euler’s infinite descent method.
  • Use quaternion number
  • Minkowski ’s geometry of number.

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

4\.\.\sum_{m|n, m\text{ odd }}(-1)^{\frac{m-1}{2}}

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.

]]> http://charlesli.org/blog/2007/07/26/lagranges-four-square-theorem/feed/ 0 Borel’s Essays in the History of Lie Groups and Algebraic Groups http://charlesli.org/blog/2007/07/26/borels-essays-in-the-history-of-lie-groups-and-algebraic-groups/ http://charlesli.org/blog/2007/07/26/borels-essays-in-the-history-of-lie-groups-and-algebraic-groups/#comments Thu, 26 Jul 2007 09:29:56 +0000 charles http://charlesli.org/blog/?p=31 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.

]]> http://charlesli.org/blog/2007/07/26/borels-essays-in-the-history-of-lie-groups-and-algebraic-groups/feed/ 0 Affordable textbook campaign http://charlesli.org/blog/2007/07/23/affordable-textbook-campaign/ http://charlesli.org/blog/2007/07/23/affordable-textbook-campaign/#comments Mon, 23 Jul 2007 05:45:36 +0000 charles http://charlesli.org/blog/?p=30 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

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