Last revised 24jan16

Lesson on Writing Mathematics on Tests and Homework

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\section{Introduction}
This lesson is on writing mathematics in this class, both sections. A separate
lesson, for MA348 students, will be presented separately.
It extends on the present lesson specifically to preparing a termpaper
or programming project using LaTeX, HTML and MathML. But it will be available
to all students who wish to learn how to use this opportunity to learn LaTeX.

The language of mathematics has evolved over three thousand years. Until printing on
paper became practical and cheap, writing by hand was the only option. Mathematical
notation began as a shorthand, but evolved into a synthesis of the cursive
notation for speech and an ideographic design for difficult concepts. Even though
it is not always a good idea, it is often used in a narrative to stand for the
phrase used to speak the symbols. However the reverse, to write out in the vernacular
narrative what is properly expressed by the symbols, is generally difficult to
understand, ambiguous and prone to misinterpretation. I strongly discourage
you to attempting that style of writing math.

The computer has made the writing of the symbolic vocabulary of mathematics easy,
effective, and necessary. Historically, mathematical books were typeset with great
difficulty and effort. Printers had to select individual typefaces and type blocks,
as is still the case with the symbol and equation editors of wordprocessors, such
as the ubiquitous Microsoft Word and its imitators.  The great computer scientist
,  Donald Knuth ,
invented the language TeX, which uses the symbols on the keyboard to typeset
mathematics, science and technology. Knuth gave TeX for free to mathematics, the sciences
and technology. You should never pay for any version of its implementation. There
is bound to be a free, and superior product elsewhere. Paying for manuals on how to
use it, and of course for books and journals written with it rewards the author of the
sense, not the typesetting of the idea.

Leslie Lamport, among many others, extended and
improved TeX. His LaTeX has pretty much won out over the other  extensions.
We will use LaTeX in this course, and this lesson is mostly about that. But first
a general note on other ways of writing math.

\section{Context Appropriate Writing}

To write math with LaTeX you need a computer with an interpreter of the LaTeX code
to the mathematical symbol. Sometimes you don't have one on your computer. Sometimes,
you're writing by hand on paper and don't need LaTeX to write math.

\subsection{Email TeX}

There are
instances when you are typing math without the use of LaTeX to write the symbols.
Of course your keyboad is based on the ASCII character set, which includes lower
case and upper case letters, numbers and a small set of symbols, such as + and -.
But rarely enough to write mathematics with unassisted.  On a computer you have as many choices
as there are apps available which interpret some
non-standard code using some standard character set, like UTF8. The most common of
these is Microsoft Richtext (RTF). In this course, I do not consider RTF acceptable.
Please do not use it for embedding math into typewritten text.

What most mathematicians now use in email, text documents, and other cases when
LaTeX is not available, is the LaTeX name for the symbol,
because it can be written in pure ASCII.
For example, to write the solutiontion to the quadratic formula,
you would write
ax^2+bx+c=0 => x=-b\pm\sqrt(b^2-4ac)/2
when they mean
$ax^2+bx+c=0 \Rightarrow x=-\frac{b\pm\sqrt{b^2-4ac}}{2}$.
When not writing math
with LaTeX, I do not approve your using computer codes, such as x**2 for x^2, and
b*x for bx. That would be email-CS, appropriate in its own context.

\subsection{Handwritten Homework}

When you are permitted to submit handwritten homework, and of course on tests
which are necessarily handwritten, and temporarily, when the fildcards need to be
submitted on paper because of AD-authentication problems you should consider
the following.

\begin{itemize}
\item It is never acceptible for you to rip a piece of paper out of spiral
notebook and hand your work in on that without first removing the ragged
edges.
\item Nor may you submit a nonstandard sized sheet of paper.
\item Do not write illegibly.
\item Never omit your name at the upper right hand corner of each page.
\item Do not write on the backside of any sheet of paper.
\item Use wide ruled paper. Always use college ruled paper, or unlined paper.
\item Do not use a red pen.
\item Put a title on the page to identify the work.
\item Write the day the assignment is marked as due on the syllabus, even if
the assignment was postponed, or you're handing it in late (with permission only!)
\item I urely forgot to mention here some obvious suggestion.
\item Remember,  make it as easy as
possible for the grader so that she does not waste time trying to figure
out what you have written.
\end{itemize}

\subsection{Typewritten Homework}
Short of LaTeX, there are hybrid ways of writing perfectly legible, but
typewritten work. This is always more professional than handwritten work.
But however it was produced, what you hand in has to be
in the PDF format. I will not accept any .doc or .docx or .rtf files.
In filecards, I do accept .txt (ascii) text. The principle to remember is that
a submitted document must be immutable, i.e. no-one, even you, can change it.
Even if you try to block other people from editing your Word document, there is
no guarantee that at a later date the submitted file is identical with the
the retained file.

Acceptable hybrids are:
\begin{itemize}
\item A PDF file produced with a word processor, provided the formulas are
mathematically correct. The best method is to produce mathematical formulas
\item Any figures you wish to add to the document, and which you did not
produce yourself (e.g. copied from the web) should have at least a url
of where you got it. Preferably, this url is embedded in the figure.
\item Finally, you can combine windows displayed on your
desktop into one document. Since the principal feature of this involves
the use of texPad, we next devote a separate section to it.
\end{itemize}

Nearly ten years ago, Michael Sommers developed a client/server web application
for writing LaTeX documents, named texWins, which works on every browser that
handls MathML. This made it possible
for students in math courses to typeset LaTeX documents on their personal
(This issue is not the subject of this lesson and will be treated in detail
in another lesson.)

A client/server LaTeX package is necessarily webbased. It requires
AD authentication and a good network. But Students also need a way of
learning and practicing LaTeX on their
personal computers. Abdul Dakkak adapted the ability of (some) browsers to
convert LaTeX coding into MathML typesetting without the need of a
LaTeX package, to a tiny, free standing, and most convenient app for this
purpose. Originally he called it "texWings" because it was easier to
use than texWins, but then to just texPad to sound like Wordpad. There are several more lessons on texPad
in our Advice pages. This lesson is a digest of the lessons on Advice.

Soon, students and instructors of online math discovered a second, even more valuable
use of texPad. It was possible to write LaTeX in real-time on texPad, although
is was only a rudimentary fraction of an entire LaTeX package. In particualar
you could use it to compose mathematical formulas and include them in other
electronic documents composed by word processors.
and copy-pase them into another web-based application, either as a LaTeX
source (left window), which you can later copy and paste into a real LaTeX
processor, or use its LaTeX output (right window) as a picture file (.png,
.bmp, .jpg whatever) to include in some other document. I use it in live
lectures and project it in a class.
For example, display a text window, one or more
texPad=composed equations, and the figure(s). Then take a
screen print of all the them.
Here is an example of this  made for a geometry course .

At this point you should take the time to watch
texWins_Intro.mp4 even though the intitial portion is a bit dated.

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