Up: Class 3, Math 696
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Activities for Class 3

Learn from experience.
Learn about moving files between different computers.
Write a LaTeX paper to hand in today.
Learn how to embed images in Web pages.

Learn from experience

I would like to share with all of you some of the ideas, problems, and errors that I encountered in reading your homework papers. Most people learn by a process of successive approximations: this is a reason why homework exercises are useful. I sometimes say that the best students are those who make every possible mistake---once.

Maple

Everybody succeeded in getting results from Maple, but some presentations were prettier than others. You should always put some sentences of explanation in your Maple worksheets. This not only helps your reader, it also helps you when you look back at your work in the future.

For example, it would be possible (but not recommended) to solve the problem about the polynomial as follows.

     p:=n->a*n^3+b*n^2+c*n+d:
     q:=unapply(subs(solve({p(1)=2,p(2)=3,p(3)=5,p(4)=9},{a,b,c,d}),p(n)),n);
                    q := n -> 1/6 n  - 1/2 n  + 4/3 n + 1

This solution is hard to understand! It would be better to split the solution into several steps and to explain each step.

Here are some more comments about Maple.

Maple worksheets can be used in a primitive way as word processors. In Maple V Release 3, you can change command regions into text regions by holding the mouse down on the button and selecting ``Text.'' For example, to insert your name at the top of a worksheet, put the cursor at the extreme left of the top command region, from the ``Edit'' menu choose ``Split Region at Cursor,'' put the cursor on the new line above, change the input region to a text region as just indicated, and type in your name.
The new Release 4 of Maple V, which is coming soon for UNIX (it is already available on the PCs in the ACC), has an improved worksheet interface that simplifies changing regions between text and input; it also allows for section headings, collapsible and expandable cells, etc.
Notice that the Maple command evalf(exp(1),1); returns 3, not 2.7. Maple's floating point evaluation gives a specified number of digits, not decimal places.
Here is a little quirk of Maple that some of you encountered.
```
       > a:=5; b:=7; f:=x->a*x+b;

                                     a := 5

                                     b := 7

                               f := x -> a x + b
       
```
Why didn't Maple respond f := x -> 5x + 7 instead? This is a situation in which Maple behaves better with expressions than with functions. To get the expected result (as an arrow-defined function), you have to say f:=unapply(a*x+b,x);.

Why study math?

I enjoyed reading your papers on the subject "Why study mathematics?" There was a wide range of responses. One person chose to defend the heterodox thesis that there is no good reason to study mathematics! Another person wrote amusingly in rhymed verses.

Content

I read your papers first of all for content, to see what interesting ideas you had. Here are some of the common themes mentioned.

Practical considerations
1. Mathematics is needed in everyday life, from such mundane situations as making change in the grocery store and understanding mortgage payments to more sophisticated concerns such as modeling world population growth and evaluating the data on global warming.
2. Mathematics is fundamental to modern technological developments that make possible everything from cordless telephones to CAT scans.
3. Studying mathematics can lead to many careers, not just in scientific disciplines like particle physics and marine biology, but also in business and industry. (Of my three college roommates---all mathematics majors---one became chairman of the statistics department at a major state university, one works at Bell Laboratories, and one went to law school and got a job at a Manhattan law firm. I also know a PhD mathematician who went on to medical school.)
Spiritual considerations
1. Just as you might go to the student recreation center to exercise your body, studying mathematics exercises your mind. A good workout makes you feel good.
2. If we accept that abstract reasoning is a feature of our intelligence that distinguishes us from lower animals, then we can infer that studying mathematics is a means to developing our full potential as human beings. While nobody was willing to push this point too far, it would be conceivable to develop this argument into a case for studying mathematics as a religious activity.
3. Mathematics, like music, is a universal language, and learning it is a way to develop commonalities with people from other cultures. Would it be going too far to elaborate this point into an argument for the study of mathematics as a contribution to world peace?

Style

Secondarily, I looked for good style and organization in your papers. I would like to reinforce two points about communicating ideas in print. (Three of my four grandparents were English teachers, so good writing is appreciated in my family.)

A well-organized essay should have an introduction that states the thesis, a middle section that develops the argument, and a concluding section that recapitulates the theme. The way I learned it in high school, ``first you say what you're going to say, then you say it, and then you say what you said.''

Technical research papers often do not follow this model, but they probably should. I always start off a research paper with an introductory section that summarizes the results. I like to close a research paper with a section on open problems and directions for future investigations.
It is often said, with justification, that you should write from experience. Give concrete examples to support your points. Instead of writing ``mathematics is a foundation for many careers,'' write ``studying mathematics can lead to careers in accounting, economics, chemistry, ....'' Better yet, write ``Arthur Pancoe, one of the nation's ten best stockbrokers, attributes his success to the analytical skills he learned as a mathematics student.''

Here are two books I recommend on style.

William Strunk and E. B. White, The Elements of Style, third revised edition, New York, Macmillan, 1979. This is also available on computer disk for both Mac and PC, and on videocassette. You can browse the first edition on line. It is a classic little book of advice on good writing.
Mary-Claire van Leunen, A Handbook for Scholars, revised edition, New York and Oxford, Oxford University Press, 1992. This is essential reading if you are writing a research paper, a dissertation, or a vita.

Language

When I read your papers, I marked some errors in grammar, spelling, punctuation, and so forth. Many of you are not native speakers of the English language, and I expect you to make some mistakes. Your grade will not suffer if your English is imperfect, but I assume that you are interested in improving your English, so I will continue to correct language errors on your papers.

I always feel embarrassed that I cannot communicate with my German in-laws in their mother tongue. I hope that those of you who are foreign-born will not feel embarrassed about your English. After all, in being able to speak more than one language you are more capable than many of your fellow students. In this connection, I am rather fond of a joke that Europeans tell.

Question: if a person who speaks three languages is called ``trilingual,'' and a person who speaks two languages is called ``bilingual,'' what do you call a person who speaks only one language?

Answer: an American.

Those of you who are native speakers of English---be careful! I have a talent for proofreading.

If you are interested in building your vocabulary, or if you just like words, check out A Word A Day.

LaTeX

Finally, I marked some errors stemming from improper LaTeX markup. Here is a list of a few LaTeX idiosyncrasies that you should know about.

Do not use the " key to make quotation marks in LaTeX. Instead, make ``smart quotes'' by doubling the ` key for opening quotes and doubling the ' key for closing quotes. (Of course, if you are typing in some language other than English, then quotation marks may have a different style---but then you probably should be using LaTeX's babel package that supports multiple languages.)
LaTeX normally ``stretches'' spaces after periods, because it expects periods to end sentences. Therefore, if a period follows an abbreviation (but is not the end of a sentence), you need to alert LaTeX not to stretch the following space. LaTeX interprets a backslash followed by a space as an unstretchable space. For example: Washington Univ.\ is in St.\ Louis. (Do not go overboard with this. It is not good style to use a lot of abbrevs.)
Usually you can prevent LaTeX from printing page numbers at the bottom of the page by putting \pagestyle{empty} in the preamble of your LaTeX source file. (You might want to do this for a one-page document, for example.) However, \maketitle overrides the global pagestyle declaration, so you may have to use \thispagestyle{empty} to disable the page number on the title page.
LaTeX has its own ideas about typesetting trigonometric functions, so you should type \sin, \cos, and so on (in math mode) to get the sine, cosine, etc.
Last time, following page 233 of the LaTeX manual, I warned against using $$ as a delimiter for display math mode. (Instead use \[ ... \] or \begin{displaymath} ... \end{displaymath} or \begin{equation} ... \end{equation}.) Someone asked why, and it happens that there has just been some discussion of this point in the comp.text.tex newsgroup. The upshot is that (a) the recommended \[ ... \] has improved error detection when your LaTeX code has syntax errors; and (b) the fleqn document-class option, and possibly other LaTeX packages, redefine the style of \[ ... \] (but not of $$).

Moving files between different computers

Some of you have inquired about how to move files between the calclab computers and the main mathematics server. Here are explanations of three different ways to accomplish this task: using xdir, using emacs, and using ftp.

`xdir`

If you are visually oriented, you may like to try out the graphical file browser xdir, which is available on both calclab and on the main mathematics server. (However, this method will not work for moving files to a system where xdir is not installed.)

picture of xdir window On calclab, click the mouse on the background of your screen to bring up the root menu, click on ``Programs,'' and click on ``Xdir.'' (On the main mathematics server, click on ``Tools,'' ``Other,'' ``Directory,'' ``Xdir.'') You can also start xdir by executing the command xdir & in a terminal window. You should get a window that looks something like the illustration.

In the graphical display, the icon indicates a file, while the icon indicates a directory. Double-clicking on a directory opens a display of the contents of the directory.

The row of buttons is used to select different formats for the directory display. The button determines whether or not double-clicking on a directory icon opens a new xdir window. The button toggles whether or not ``dot'' files like .cshrc are displayed. The button refreshes the display. The up-arrow moves to the parent directory. The button moves to your home directory. The button creates a new directory. Clicking on the trash can icon deletes any marked files (after a prompt for confirmation). The button deletes the xdir window.

You copy or move files in xdir via ``drag and drop.'' Position the pointer over a file or directory icon, and hold the left mouse button down as you drag the mouse. When you release the mouse button over a directory icon or the background of an xdir window, the original file or directory is copied to a new location. To move a file instead of copying it, hold the control key down when you release the mouse button.

To move or copy files between two different computers, click the word ``Connect'' on the menu bar at the top of the xdir window, and then choose ``Connect to Remote.'' You will be prompted for the name of a remote computer (which might be, for example, fourier.math.tamu.edu or calclab3.math.tamu.edu), your user name on the remote computer, and your password on the remote computer. If all goes well, you should get a second xdir window showing your home directory on the remote computer. You can drag and drop files between the two xdir windows in order to move or copy files between two different computers.

There is some brief on-line help for xdir via ``Help'' on the menu bar and then ``Getting Started.'' You can quit xdir by selecting ``Quit'' on the ``File'' drop-down menu.

`emacs` is a directory browser too

Do you remember that I said emacs is an all-purpose tool, not just an editor? You can use emacs to move and copy files, even to or from a remote computer.

If you press Control+x d in emacs, you will get a prompt at the bottom of the screen for a directory name. Type in the name of a directory and press Return to see a list of the files in the directory. You can Mark one or more files and then use items on the ``Operate'' menu to copy or rename (that is, move) the files.

To see a directory listing for your files on a remote computer, press Control+x d and then type in a remote directory name preceded by your remote user name and the name of the remote machine. You will be prompted for your password on the remote machine. For example,

/your-math-user-id@laplace.math.tamu.edu:~/

would list the files in your home directory (abbreviated by ~) on laplace, and

/your-calclab-user-id@calclab2.math.tamu.edu:~/public_html/

would list the files in your public_html directory on the calclab system.

If you are currently viewing a remote directory listing, you can move files to the local machine by using the ``Copy to'' item on the ``Operate'' menu. Moving files from the local machine to the remote machine is similar, except that when emacs prompts for the destination file name, you prefix the file name with your remote user name and remote machine name, as illustrated above.

`ftp`

Another way to transfer files between different computers is the program named ftp (which stands for File Transfer Protocol). This program can even be used to transfer files between machines running different operating systems.

In a terminal window, execute the command ftp. The prompt changes to something like ftp>. Then type in open name-of-remote-machine, for example open fourier.math.tamu.edu or open calclab3.math.tamu.edu. You will be prompted for your user name and password on the remote machine. After you connect to the remote machine, you can use the command put filename to move a file to the remote machine, and get filename to retrieve a file from the remote machine.

Be aware that if you are transferring binary files (for example, graphics or Maple worksheets), you need to alert the ftp program by executing the command binary. On the other hand, text files transferred between UNIX and DOS systems sometimes get messed up because UNIX and DOS have different conventions about how to mark the end of a line; such problems can be fixed on a UNIX system by using the commands dos2unix and unix2dos.

You exit from the ftp program by typing close to kill the connection to the remote system, and then quit.

Today's LaTeX exercise

For the previous class, I wrote some instructions about basic equation formatting in LaTeX. Today you are going to practice implementing these techniques.

Your assignment is to write in LaTeX an explanation, suitable for high school students, about the method of completing the square. Include at least one displayed, numbered equation, and at least one reference to a numbered equation (the reference number generated automatically by LaTeX's \ref command). Turn in hard copy by the end of class today.

The point of this exercise is not only to practice with LaTeX, but also to practice principles of good exposition. Keep in mind that you are trying to communicate with a hypothetical teenager, not with your instructor.

Maple example By the way, what reasons can you think of for teaching the topic of completing the square, when Maple can do it automatically? (See the illustration.)

To avoid embarrassing mistakes, you may want to use Maple to check the examples that you put in your paper.

Incidentally, the LaTeX code for the formula in the illustration is (inside math mode)

10 \left( x + \frac{7}{20} \right)^2 + \frac{71}{40}.

You are going to observe a new feature of LaTeX in this exercise. The first time you executed the command latex filename in a terminal window, you got a message ``No file filename.aux,'' although you may not have noticed at the time. In this exercise, you are going to get a warning message about undefined references. This is because LaTeX acts as a multi-pass compiler: the first time through a file, LaTeX takes note of symbolic cross references and writes them into an auxiliary file named filename.aux; the second time through LaTeX inserts the cross references.

Therefore, we need to revise the procedure for using LaTeX by adding an extra step. We now know that the procedure is the following:

Use a text editor to edit your LaTeX input file. Save the file as filename.tex.
In a terminal window, execute the command latex filename.
If LaTeX halts with an error message and a question mark prompt, type h for some (probably cryptic) help, or x to exit from the processing. Return to step 1 and correct your input file.
If LaTeX successfully processes your file, but complains about undefined references or otherwise warns you to run LaTeX again, then repeat step 2.
To preview on the screen, execute the command xdvi filename & in a terminal window. There are buttons on the previewer that let you change the screen magnification (with no effect on the printed output). If you see that some revisions are needed, go back to step 1 to edit your input file.
To get hard copy on paper, first execute the command dvips filename in a terminal window to create a PostScript file. Then send this file to the printer with the command lpr filename.ps (and remember that in this final step, the extension .ps is required). Pick up your output in the ACC, room 133 Blocker.

Images in Web pages

How did I get that snapshot of a Maple window into the Web page? For practice, try the following procedure to put the same image on your own Web page.

First you need a copy of the image. Hold down the right mouse button on top of the image and select the ``Save'' option on the pop-up menu. The Web browser will probably suggest a filename for you something like /u/m696_600/xqz3952/complete.gif. Change this by inserting public_html; the above example would change to /u/m696_600/xqz3952/public_html/complete.gif. Now when you save the image, it will be stored in your public_html directory where Web browsers can find it.

Next open your index.html file in your favorite text editor and insert something like this:

     <p>This is a test image.
     <img src="complete.gif">
     </p>

Notice that the HTML tag img is an exceptional one that has no matching end tag. However, the img tag takes an argument src that identifies the source file of the image.

Finally, set the access permissions on the file complete.gif to world-readable: in a terminal window, execute the command chmod a+r public_html/complete.gif.

Now bring up your home page in a Web browser. You should see the embedded image.

You can follow a similar procedure to embed on your Web page any other image, for instance, a famous painting from the WebMuseum. (The WebMuseum copyright notice appears to permit personal, noncommercial use of the artwork.)

Finished?

If you have done all the above activities, and there is still time left, here are some other activities you can do.

Help someone else.
Start on the homework.
Start thinking about the projects.
Surf. Next time we will look at some ways of finding information on the Internet. If you already know something about how to do this, see if you can find some on-line information about the new largest known prime number that was discovered two weeks ago.