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With Numerous Explicit Illustrations Stanford University Libraries Dept. o. Special Collections g _ Col) DOg^ Title — box _^_ fT^x n** O.A v tiro Gourmet Guide to Typesetting Technical Text by Computer WITH NUMEROUS EXPLICIT ILLUSTRATIONS MICHAEL SPIVAK, Ph.D. THE JOY OF Tj^C by Michael Spivak c c c c Copyright. (C) I'JSO by tlic American Society M;U!irm..tU\.l This is version —3 of the _A_4__r-T£X manual. _X_^ls_f-T[s( is meant to be used by some one who knows nothing about computers, except how to use a text editor, but this version is net meant for such technical typists. It is a very incomplete preliminary version, for l£X hackers, from whom suggestions for improvements arc being solicited. Please excuse the appearance of this version—it's not a very good advertise- ment for TVJ-, which is supposed to produce beautiful books! There arc lots of reasons and excuses for this (mainly lack or time), but things will look better later on; at the moment only the bare-bones output routine from Appendix B of the T]^< manual has been used, so there aren't even running heads to tell you what Chapter and section you are in. Some of the nifty macros mentioned here don't actually exist yet, but they should be operating soon (at certain points it will be clear that some are still oug;/y). Also, some of the fonts and symbols mentioned here aren't available yet, so some things were actually written in by hand. In particular, the symbols for "sidetrips" and "cautions" that are mentioned in the Introduction haven't been designed (on metafont) yet, so SIDETRIP and CAUTION appear instead; also the sidclrip:; haven't been set in smaller type, although they eventually will be. The ellipses . appear at several places. Sometimes this material hasn't been written because some design considerations still have to be made; sometimes I .was just too lazy. Anyone familiar with the T£X manual will know what to do about th.se points. Chapter 4 is quite incomplete—we just wanted to assure people thai if will be real easy to set matrices (none of this \vcenter{\halign{ stuff!. Eventually, we will be able to set partitioned matrices of all sorts and many kinds of commutative diagrams. There will also be a way of setting simple tables, the kinds that might actually appear in a math paper. A macro package to handle ___■ 1 1 the various sorts of tables, like ibl in troff, is clearly possible—it's just a question of getting some one to do it (it's not clear whether such a macro package should be part of this manual). Finally, only a few Exercises have been included. Basically, there just wasn't time to make the others. But we'd also be interested in suggestions for Exercises (interesting or tricky typesetting problems which you've come across). All suggestions and corrections, major and minor (misprints, complaints about the exposition, bugs, suggestions for nicer syntax in the macros, new macros that arc needed, etc.) will be gratefully received (but probably not acknowledged). They can he sent to the author by ordinary mail, the only kind he reads, c/o Publish or Perish, Inc., 2000 Center Street, Suite 1404, Berkeley, CA 94704. Or they can be sent via computer to palais mit-mc. Q Introduction. WHAT 1&X CAN DO (and _.mnot do) The title of this book is a little deceptive. It might give you wrong ideas about the pronunciation or T£.X, which actually stands for TAU EP3ILON CHI; according to its creator, Donald E. Knuth, insiders pronounce T^X so that it rhymes with blecchhh. Ts_ is thus an upper-case, or capital letter, form of rex, the beginning of the Creek word that means art, and that is also the root of English words like technology. This name emphasizes two basic features of '_£X:' il is a romputcr system for typesetting technical text, especially text containing n lot uf mathematics; and il is a system for producing beautiful text, comparable to the w-.. k of the finest printers. One other feature of the system needs to be emphasized: TfJ< allows you to do all of this easily . In fact, this is a manual for someone who knows nothing about computers (written by someone who knows nothing about computers). Actually, that last statement isn't quite true: the one thing we assume is that ycu ah .;..dy know how to use a computer terminal to create a file (in prac- tice, this knowing how to use an "editor", so lha* you can easily correct or change a" file). Nothing about typesetting itself is assumed, although a few printers' terms will be introduced along the way. You can remain blissfully ig- norant of the complicated rules that typesetters have developed for the proper setting of mathematics formulas —TfcX knows them all. Nor is any knowledge cf mathematics required. But you will still need to have a general idea of what printed mathematics ought to look like. Mathematicians and experienced tech- nical typists -who already know this—will find that 7&X allows them to specify mathematics formulas with less effort than before, yet with greater control over the finished product. Novice technical typists have a dual task: learning what mathematicians want, and learning how to get Tp/C to produce it. This manual will tell you all about the second, and give you as much help as possible with the first. In order to get some idea just how TjJ< works, we will examine a recent paper from a w.ll-known journal that was typeset by IfcX. 0-1 .nc.'n:, (. « BULLETIN (New Series) OF THE ASININE MATHEMATICAL SOCIETY Volume 23, Number 6, November 2001 co 2001 Asinine Mathematical Society 0002-990 1/01/0000-0503/502.00 WHAT EVERY YOUNG MATHEMATICIAN SHOULD KNOW K. ELVIN ( ABSTRACT. We evaluate an interesting definite integral. The purpose of this paper is to call attention to a result of which many math ematicians seem to be ignorant. THEOREM. The value off^^e -^dx is < c~x dx = >/*. /oo-oo PROOF: We have {I>'^-{IX'-'^lXy-^) /"°° f°° _ 2 _ 2 = / cx c v dxdy by Fubini J—oo J—oo *-&+*) dydx /oo-oo J/ oo 2 — * _ 2 r' r r = / / c rdrdO using polar coordinates r rlit\ _r - =°o" -f[_]" = 7T . Remark.t. A mathematician is one to whom that is as obvious as that twicetwi two makes four is to you. INSTITUTE FOll HAUGHTY ATTITUDES ( flcrrivrd by the editors April 2001 Hc-.r_irch supported in pari by ihr* National Foundation Mathematical Mubjrct cttts#ifirut ion(IU.)0). Primary '20A 00 Keywords: ( /-oo I, Snobbishnrss Obvious. The author first wrote this paper by hand, and then, being a lazy fellow himself, gave it to a to c technical typist produce a computer file. Parts of this file are shown below, in a style of type which will always be used to indicate input typed on a terminal, as opposed to the output I^X will produce, or the contents of this manual itself; don't worry if your keyboard lacks some of these symbols— T£X has a way of getting around this. C Xbeginpaper Xtitle What Every Young Mathematician Should Know\endtitle Xauthor K. Elvin Xendauthor Xbegintext The purpose of this paper is to call attention to a result of wiiich many mathematicians seem to be ignorant. Xtheorem Theorem\\The value of $\int4.<-\infty>T\infty -.T-C-xT2>\, dxs is ?s\inti-C-\infLy>T\infty eT<-xT2>\, dx= c XsqrtXpi . ss\endtheorem Xproof ProofXX We have $$\al ign XleftC \intJ.{-\infty>T\infty eT<-xT2}\ , dx \right)T2 __=\left( \ir.t4-<-\infty>T\infty eT{-xT2>\, dx \right) c MeftC \int-K-\infty>?\infty eT-C-yT2>\, dy \right) \\ _.=\intJ.-C-\infty>T\infty \intJ-C-\infty>T\infty eT-OxT2>eT-C-yT2>\ , dx\, dy Even a cursory examination of this file gives some idea how T^X is used. C For example, all of the English words that appear in the article are embedded somewhere in the file, while specifications for formulas are set off either by $ signs (when the formula is set within text), or by $$ signs (when it is displayed). In addition to the English words and the letters in formulas, there are lots of cryptic combinations,' called control sequences , which begin with \. Some con- trol sequences, like Xtitle, Xtheorem and \al ign, tell TgX how to process the input which follows. Other control sequences are the names of special symbols; for example, Xpi stands for tt, and \int stands for the "integral sign" /in /^° . Once this file was produced, a few simple instructions told T^X to set the paper in a style suitable for preprints, on a printer that quickly and cheaply produces output suitable for proofreading, though a little blurry: C 5 C c What Every Young Mathematician Should Know K. ELVIN Institute for Haughty Attitudes April 1, 2001 The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant. e~'i THEOREM. The value of f^a) dx is c~ lS dx = \fz. /oo-oo PROOF: We have (/->SX/_>S(E -^) ,oo = / / c xc y dxdy by Fubini J— cc J—00 /«oo / e-^A-v^dydx /oo-oo J—oo 2 c r rdrdO using polar coordinates '0 /"oo c~r\dr dO Jo/ —y- dO Remark.
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