Mathematics

Mathematics

$Mathematics$

Somewhere I saw the quotation "Mathematics has something that attracts people." I'm afraid of wrong remembrance, so I will sometime retrieve the source.

As the attracted one, I will introduce some topics. Possible policies are 1) little prior knowledge, 2) not too wide gap between the lines, 3) inserting concrete samples, 4) handing over something attractive. But in truth these are difficult.

177

176

99		78
		21		57
77	43
				16	41
	34		9
			25

by A. H. Stone in 1904

The first perfect squared square using 55 squares

by Roland Sprague in 1939

112

50			35						27
									8		19
			15			17		11
								6		24
29	25			9	2
					7		18
				16
							42
	4	37
33

by A. J. W. Duijvestin in 1978

Among a lot of mathematical web sites, I managed to arrive in the following ones.

The MacTutor History of Mathematics archive	More than 70 history topics, more than 60 famous curves, more than 1000 biographies, including 21 Japanese, Yasuaki Aida, Naonobu(Chokuyen) Ajima, Heisuke Hironaka, Taira Honda, Masatoshi Gündüz Ikeda, Kiyosi Ito, Kenkichi Iwasawa, Shokichi Iyanaga, Shizuo Kakutani, Tosio Kato, Kunihiko Kodaira, Hitoshi Kumano-Go, Yozo Matsushima, Shigefumi Mori, Kiyoshi Oka, Shigeo Sasaki, Takakazu(Kowa) Seki, Kenjiro Shoda, Zyoiti Suetuna, Teiji Takagi, Yutaka Taniyama.
Eric Weisstein's World of Mathematics (MathWorld ^TM)	is the web's most complete mathematical resource, assembled over more than a decade by internet encyclopedist Eric W. Weisstein with assistance from the mathematics and internet communities.
The On-Line Encyclopedia of Integer Sequences	Most people use this web site to get information about a particular number sequence.

Following software (and paper and pencils) assists my mathematical thinking.

TeX: is a computer language designed for use in typesetting; in particular, for typesetting math and other technical material. And LaTeX, biggest and most widely used TeX macro package, is the de facto standard for the communication and publication of scientific documents. Only learning some basic macros, you can typeset almost all of what you want to do.
LaTeX2HTML: is a converter written in Perl that converts LaTeX documents to HTML. Mathematical expression will be converted to png or gif image, and embedded in HTML documents. As LaTeX has many environments and extended highly, sometimes the result of convertion is contrary to my expectations, at that time I observe it and modify the LaTeX sources. On the other hands, translating dvi to pdf and registering it to your web is another method to launch information in the Internet. Now that (After the year around 2001), pdf is scanned by search engines and broad band network is spreading, it has become a effective way.
Risa/Asir: is an open source general computer algebra system developed in Japan. A part of functions in PARI which is a C library for computer-aided number theory developed in France are available. It's a good idea to run Risa/Asir from within Emacs.
Gnuplot: is a command-driven interactive function plotting program. It can be used to plot functions and data points in both two- and three-dimensional plots in many different formats, and will accommodate many of the needs of today's scientists for graphic data representation. It's a good idea to run Gnuplot from within Emacs.
Tgif: (pronounced t-g-i-f) is an Xlib based interactive 2-D drawing tool under X11 on Linux and most UNIX platforms.

$Gnuplot demo$

Updated on 2007.4.26

First edition : 2001.12.25