and
are different? LaTeX automatically knew
to print the former, which has a so-called ligature between the
consecutive f's.
In this course, we have been working in the UNIX and X-Windows environment. This is a powerful working environment that we all have access to on campus, and it is an environment that is widely available at universities around the globe.
However, the world at large (homes and non-academic businesses) is dominated by personal computers whose common operating system is Microsoft® Windows. It is worthwhile to be acquainted with the technology that exists in the PC world, so today we are going to take a tour of some PC software. (That is why we are meeting in the PC lab, Blocker 132.)
If you have not already done so, find the icon for either Netscape or Mosaic in the Communications group, and double click on the icon. Then go to the home page for today's class, which has the address http://www.math.tamu.edu/~harold.boas/courses/communication/assignments/class12.html.
In working on the PC, you are going to notice some similarities to X-Windows and some differences. If you cannot figure out how to do something simple, like how to use the mouse or how to lower a window, ask your neighbors (some of whom have PC experience) or ask me.
One difference you have probably noticed already is that the screen seems small. This is partly due to the size of the monitor, and partly due to the resolution of the monitor. The x-terminals we have been using have high resolution (many pixels per inch), so images displayed on the x-terminals take up less space on the screen than they do when displayed on the PC monitor.
Before we proceed to explore PC software, let's take stock of what we have accomplished this semester.
To travel hopefully is a better thing than to arrive, and the true success is to labour.
---Robert Louis Stevenson
We have come to the end of our semester's journey together, and I hope you have found the trip worthwhile. I have enjoyed it.
When I was beginning to design this course, some of my colleagues asked what skills I expected the students to have by the end of the semester. I told them that at a bare minimum, the students would be able to typeset a calculus quiz in LaTeX, verify the solutions with Maple, and give a coherent verbal presentation of the solutions. As the course has developed, we have gone far beyond these minimal competencies. You have all greatly exceeded my expectations.
I hope and believe that your accomplishments this semester include the following.
I would like to have your feedback on the course. You have been the guinea pigs for the first draft of this course, and your reactions will help me in making revisions for next year. The one required activity for tonight is to fill out the course evaluation form.
The course evaluation is your opportunity to tell me what you liked about the course and what you did not like; what I should keep the same and what I should change in the future.
Please say what you think. Course evaluations are anonymous, and in any case I will not see them until January, long after I turn in grades.
Traditionally, evaluations are written by hand, which somewhat compromises their anonymity. (In a small class, the instructor likely recognizes the handwriting of most students by the end of the term.) In this class, you are going to typeset your evaluation!
To start our PC experience, we are going to use Microsoft® Word to
prepare the evaluation. I have made a template named eval.doc that
you should complete. Then print the finished evaluation and give
it to the student who is assigned to turn in the evaluations to
room 623 Blocker.
To grab the template with your Web
browser, try holding down the Shift key while you click the
mouse. You should get prompted for a location to store the
file. An appropriate location is the scratch directory, probably
named D:\TEMP. After you grab the template, open Microsoft® Word by
double clicking on its icon, select Open from the drop-down File
menu, and click on eval.doc.
After you have finished the course evaluation, try playing around with some of the programs that are installed on the PC. Most of them have on-line hypertext help available. Here are brief descriptions of some of the PC software. See below for information about free or inexpensive software you can get for your home PC (if you have one).
The higher you climb, the wider the horizon. Here is a brief travel guide for your continuing journey.
We have seen how to make Maple and LaTeX communicate. Can we fit the World Wide Web into the picture too? In principle yes, but you may need to wait a few months.
There exists a program called latex2html that
translates LaTeX documents into HTML code for the World Wide
Web. It is installed on fourier, laplace, and tam2000, but in my
recent experience it is a bit erratic. My inference from
browsing the archives at the latex2html
home page is that the program only works properly with the
right version of perl (the underlying programming
language). Presumably the bugs will shake out in a few months,
and then you will have another useful tool. If you want to try
it, just run your LaTeX document through latex and
then execute the command latex2html filename (but
don't blame me if it doesn't work).
In principle, you should be able to execute a remote Maple worksheet
over the World Wide Web. To do this, you would need to configure the
preferences or applications section of your Web browser to start
Maple when you click on a .ms file. Unfortunately,
the x-windows version of Maple lacks the capability to open a
file from the command line. When this feature is added (one hopes
in the forthcoming Maple V release 4), then it will be possible
to open Maple sessions over the Web. (However, there are some
security concerns, since Maple can make calls to the operating
system.) To see something that works right now, take a look at
the bottom of Michael
Pilant's home page, where there are some interactive Maple demos
that run with a Web browser interface.
Like the Web itself, Hypertext Markup Language (HTML) is evolving at a rapid pace. I have written the pages for this course in HTML 2.0, which is the latest version that has an essentially final specification. However, there is a draft specification for HTML 3.0 that includes options for tables, alignment, mathematical formatting, and style sheets.
There is a good description at Sandia National Laboratories of the current status of HTML . At the moment, different browsers support different subsets of the new features of HTML 3.0. Some browsers (notoriously Netscape) have introduced their own formatting features separate from the ``official'' standards; Sun Microsystems, with its Java language, has introduced the concept of ``applets,'' which are bits of interactive code for Web pages. A further complication is that currently no browser implements the ``official'' standards with 100% fidelity.
All this ferment leaves the writer with a difficult design decision. Should you make your Web pages flashy with the latest and greatest new HTML features (in which case not everybody can read your pages), or should you write more pedestrian HTML code that all browsers can display?
My personal decision has been to use HTML 2.0 on the grounds that virtually all browsers support it. However, capabilities such as tables (and eventually equations) are sufficiently important that I will likely convert to HTML 3.0 the next time I teach this course. If you are seriously interested in putting information out on the Web, you need to keep up with the developing technology and learn about new features as they come along.
Of course, it is also possible to make information available on
the Web in formats other than HTML. The difficulty is that the
end user needs to have the appropriate software to read your
files. In the scientific community, it is common to make LaTeX
.dvi files available, on the theory that the likely
users will have a dvi previewer available. Even more common is to
put PostScript files on the Web, on the theory that most people
have access to a PostScript printer.
Adobe Systems Incorporated is pushing its Acrobat software that writes in Adobe Portable Document Format (PDF), which is the next generation of PostScript. A viewer is available free, but you have to pay Adobe for software to write files in this format. The New York Times has chosen PDF as the language for its free eight-page Internet edition. There is an on-line journal Acropolis that is devoted to the advancement of electronic publishing with Adobe Acrobat.
We have learned the basics of LaTeX, but there are many features that we did not investigate. In particular, LaTeX is the only tool I would consider for writing a long document or a book. It will automatically build the table of contents and the index, and it has an associated package for managing a bibliographic database.
LaTeX does many sophisticated operations behind the scenes to
make the printed output look beautiful. It uses an elaborate
scheme to fine-tune interword spacing while justifying lines, and
it has an ingenious algorithm for hyphenating words when
necessary. LaTeX takes of typographical niceties that you may not
even be aware of. Can you see that and
are different? LaTeX automatically knew
to print the former, which has a so-called ligature between the
consecutive f's.
LaTeX can typeset in many languages via its babel
package. Some of the supported languages are Esperanto, French,
German, Portuguese, and Turkish.
Like HTML, LaTeX is currently under development. The LaTeX3 Project aims to make LaTeX more powerful and more user-friendly. There are also various efforts to integrate LaTeX with the World Wide Web: besides latex2html, there is HyperTeX, which builds Web links into the dvi file, and Hyperlatex, which builds one source file that can produce both LaTeX and HTML output.
Of course, no single tool is appropriate for every job. If you are designing a poster or a party invitation that needs visual formatting, then you may want to use a WYSIWYG program like Microsoft® Word. If you are printing extensive tables, then perhaps a spreadsheet or a database program is what you need.
As you have discovered from Maple's help browser, Maple
knows a lot of mathematics. Before you try to do something
complicated in Maple, it is worthwhile to browse a bit to see if
the operation is built in. For example, I recently wanted to make
pictures of the five Platonic solids. It would not be too
difficult to create pictures of these solids by hand, but I
discovered the Maple command
polyhedraplot([0,0,0], polytype=dodecahedron, style=PATCH,
scaling=CONSTRAINED, orientation=[71,66]);
that automatically draws a pretty dodecahedron. Try it!
We concentrated on basic functions of Maple, such as might be used in calculus. However, Maple is now an integral part not only of the engineering calculus sequence (Math 151, Math 152, and Math 251), but also of differential equations (Math 308) and soon linear algebra (Math 304). Maple was used extensively this semester in Denise Kirschner's Math 489 course on Chaos and Dynamical Systems.
Like the other tools we have been using, Maple is under continuing development. Maple V Release 4 is not yet shipping, but it has been announced and will surely be available for classes next fall. Samples of some new capabilities are available.
TCI Software markets the pair of products Scientific Word and Scientific WorkPlace that integrate Maple with LaTeX. (In effect, you can have a live Maple worksheet inside a LaTeX document.) Maple has announced a similar product MathOffice that integrates Maple with Microsoft® Word.
Now that you have some experience with Maple, you should be able to learn other comprehensive computer mathematics systems easily. Here is a list of some competing products that you may run into. Each of them has its own true believers.
There is also specialized software dedicated to specific tasks. The American Mathematical Society has a list of Software for Mathematics, and there is a collection of educational mathematical software at the Washington University archive.
I would like to close with some miscellaneous tidbits and some philosophical remarks.
There are a couple of useful graphics tools generally available
in the X-Windows environment. (They are installed on fourier and
laplace, for example.) There is a drawing tool
xfig that can draw lines, circles, spline curves,
and so forth, and annotate them with either LaTeX or PostScript
fonts. There is also a color drawing tool called
xpaint. Steven K. Baum of the
Department of
Oceanography has
compiled an extensive
list of graphics and data analysis software.
You can have fun with the background region of your x-display
with a command like xsetroot -fg maroon -bg cornflowerblue
-bitmap
/usr/openwin/share/include/X11/bitmaps/escherknot. Or try
xv -root your_favorite_graphic.gif -quit. (To undo
these, try xsetroot -default).
People may not take you seriously if
your writing contains egregious spelling errors. Many text
editors and word processors come with spelling checkers. I use
the editor emacs, which has an interactive spell
checker ispell that is smart enough to skip over
most LaTeX control sequences.
There is a spelling checker on the Web that will check your HTML documents. Try it!
However, using a spelling checker does not absolve you of the responsibility of proofreading what you write, as the following poem illustrates. (The poem circulated around the Internet a while back---author unknown.)
I have a spelling checker,
It came with my PC;
It plainly marks four my revue
Mistakes I cannot sea.
I've run this poem threw it,
I'm sure your please too no,
Its letter perfect in it's weigh,
My checker tolled me sew.
(The joke is that the poem has 13 errors, none detectable by the computer program.)
Part of scholarly writing is to verify the references, give proper credit, and spell the names correctly. There is a supposedly authoritative book on Fourier series produced a few years ago by a distinguished publishing house, and I refuse to buy the book because the author consistently refers to ``Gibb's phenomenon.'' I have no confidence in the mathematics of an author who is not careful enough to realize that the man's name is Gibbs, so the overshoot in the Fourier series of a jump function is properly ``Gibbs's phenomenon.''
With such examples in mind, my father once wrote the following verses, titled ``Spelling Lesson.''
Weep for the mathematicians
Posterity acclaims:
Although we know their theorems
We cannot spell their names.
Forget the rules you thought you knew---
Henri Lebesgue has got no Q.
Although it almost rhymes with Birkhoff,
Two H's grace the name of Kirchhoff.
The Schwarz of inequality
And lemma too, he has no T.
The ``distribution'' Schwartz, you see
Is French, and so he has a T.
In Turing's name---no German, he---
An umlaut we should never see.
Hermann Grassmann---please try to
Spell both his names with 2 N's too.
If you should ever have to quote
A Harvard Peirce, be sure to note
He has the E before the I;
And so does Klein. Rules still apply
To Wiener: I precedes the E;
The same for Riemann, as you see.
But Weierstrass, you must agree,
Has it both ways, with EIE.
Fejér, Turán, Cesàro, Fréchet---
Let's make the accents go that way;
Don't lose the squiggly little bits;
They don't mark stress---they're diacrits.
And as for (Radon)-Nikodým,
Restore the accent, that's my dream.
But there is one I leave to you,
Whatever you may choose to do:
Put letters in or leave them out,
Garnish with accents round about,
Finish the name with -eff or -off:
There is no way to spell.
(For a curious tale about the name given in Cyrillic characters at the end of the poem, see Philip J. Davis, The Thread: A Mathematical Yarn, Birkhäuser, 1983; call number PN6162.D376 1983.)
Have you got a PC at home? or you plan to get one? There is a lot of good, inexpensive software that you can install.
To teach is to learn twice.
---Joseph Joubert, Pensées
When I was an undergraduate, I would sometimes wander about in the stacks of Widener library. Occasionally I would pull a book off the shelf, blow the dust off it, open the cover, and discover that the book had not been checked out for over a hundred years. It was almost a religious experience to meditate in the gloam of the stacks on the immensity of knowledge contained within the walls of the library.
Knowledge is sterile, however, until someone opens the book, extracts the ideas, and reinvests them with new life. Those old authors surely had in mind, when they took pen in hand, that they were only the initial link in a chain of communication whose terminus was beyond sight.
One of my goals in this course was to remind you of something that you all knew as four-year-olds: learning and teaching are fun. It is my hope that as your career progresses, you will spread the message by example to your own students and colleagues.
I once took a course in quantum mechanics from Sidney Coleman, whom I remember as a flamboyant lecturer. He made a point, at the end of each class, of dropping his notes into the wastebasket. He did not preserve his lecture notes for use in future years because, he said, ``I don't want to get stale.''
And gladly wolde he lerne and gladly teche.
---Chaucer, The Canterbury Tales