Last revised 24jan16

# Lesson on Writing Mathematics on Tests and Homework

\begin{document} \maketitle \begin{document} \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 in texPad . \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} \section{Documents Produced by texPad} 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 computers without downloading and installing one of the free LaTeX packages. (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. Indeed, you could use texPad to write short answers, such as filecard answers, 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. \end{document}