Tools for the imath10 REU students.  

18may10


\textit{$\C$  2010, Prof. George K. Francis, Mathematics Department,
University of Illinois} 

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\maketitle

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\section{Introduction}
We will be using various tools for various purposes. While there is some
time to learn some of them when they are immediately needed, it is not 
possible to follows the advice "never learn something until it is needed"
exclusively. No real work would get done in the short 8 weeks of the REU.
Therefore, here is a review of what we'll use sometime, together with two
additional pieces of information: where to obtain the tool and what it will
be used for. 

\section{Documentation}
We will document all work on an on-going basis. But the documentation
will be part of developing a webtree, rooted in the portal page, and 
branching into project pages and also into your personal webpages connected
to the REU. That way we'll all have a usable draft of the documentation 
by the end of the summer, and finishing it off for publication won't get
neglected.

\subsection{LaTeX}
While a document can begin as an ascii file, like this one, it will be 
transmuted into an .html which displays proper mathematical notation 
based on a rudimentary subset of the LaTeX typesetting language as 
invented by Knuth (TeX) and Lamport (LaTeX). Please note the conventional
spelling in ascii, with capitalized consonants and lower case vowels.

\subsubsection{Real LaTeX}
Historically, TeX consisted of three files with suffixes .tex, .dvi and 
.ps. Putting pictures into .ps (for "postscript") was a pain. The .tex
file was and still is an ascii file. The .dvi intermediary was a binary
file, and the .ps file is ascii again, but written in a language nearly
incomprehensible to humans using ascii editors. Some decades ago matters
were improved by replacing the second and third files by a .pdf file,
which is again ascii and even more unreadable. To turn a plain ascii
.tex file into the .pdf you need a LaTeX package which has to be installed
separately on your computer.

\subsection{texWins}
There are websites where you can ship your .tex file and receive back
the .pdf. In such so-called "webservices" the package exists on the 
remote server. One that was built right here is called "texWins", and
with a little effort, you can learn how to use texWins to help you learn
LaTeX itself.



\subsection{MathML and fake TeX}
Modern web browsers, like Firefox and IE7 or above, have a built-in 
language, called MathML, for "Mathematics Markup Language". This language
can produce excellent mathematical typesetting on the web which is 
(almost) indistinguishable from real TeX. While the family of markup 
languages, such as MathML, XML, and HTML, are in ascii, and hence their source 
files (with suffixes like .xml, .html)  could theoretically be 
composed on an ascii line editor. In fact, however, all those angle brackets
make such files unreadable too. 

To write such files one uses tools which translate much simpler text into 
MathML. REU students in illiMath2008 used such a factory, called "AsciiDoc".
This language also lets you compose mathematical symbols without having to 
learn proper TeX. While easier in the beginning, it is much harder to ever
learn proper LaTeX starting with this "PidginTex". Asciidoc, like all 
ascii-to-MathML translators, make heavy use of Java Scripts and Cascading
Style Sheets (suffixes .js and .css respectively). 

\subsubsection{The Pudding ... as where the proof is.}
As a result, we now use now use a huge simplification of this process in 
the form of the tiny Pudding factory (built by two now graduated math 
students) consisting of just two files, named
ltmml.js and ltmml.css. The ltmml is just an abbreviation for 
"LaTeXMathML". The design problem that ltmml solves is this:

\begin{itemize}
\item Begin with a .tex file with relatively modest demands on LaTeX and 
"put it on the web" (by embedding it inside an ltmml assisted .html file). \\
\item And conversely, after composing an ltmml assisted .html file, convert it,
into a .tex file to be compiled into a .pdf. \\
\item Do both with minimal editorial effort. For instance, using only an ascii
line editor, like vim, and a MathML capable browser.  \\
\end{itemize}

\subsubsection{texPad}
One of 2 additional aids to learning how to write .tex files is a small, somewhat
limited tool that uses your browser's MathML facility, just like the Pudding. Because
it also has the texWins appearance, it may be useful for writing simple .tex phrases
off line, when you not able to reach the webservice, texWins.

\subsubsection{LaTeX examples}
This is a repository of examples for real LaTeX. The way to use this is to download the
examples .tex files. (If there is a .pdf too, download it so you know what it's supposed
to look like.) Edit the preamble suitable for texWins, and feed it to texWins, making
changes until it "works", i.e. returns the expected .pdf.

\subsubsection{iPaint editor}
There are many editors for making simple (iPaint for macs, Paint for pcs) changes to 
\textit{bitmap graphics} picture files. There are two kinds of files types in current usage. Files with
suffixes like .png, .bpm, .jpg, contain information about what color to fill each pixel
with in a specific region. The industry standard for an editor for bitmap files is
Adobe Photoshop. When bitmaps are reduced in size they are sampled and perhads dithered
to improve the smaller image. They cannot be enlarged without "pixilation", i.e. the 
visual distortions associated with corser graphics.

By contrast, there is \textit{vector graphics} files are scaleable without distortion. They 
containt the instructions on how to draw the picture, rather than the picture itself. Good
type setters (TeX, for example) are based on vector graphics. When you change the font size,
the same TeX code generates a larger or smaller letter which looks as good as the original. 

The iPaint (for macs) and the Paint (for pcs) editors are the simplest of their kind for 
editing the former kind of files. Vector graphics files must always be edited by the 
proprietary editor that created them in the first place. 
 
\section{End of edition 1 of these notes.}

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