Knuth, Larrabee, Roberts. Mathematical writing (free web version, 1987)(118s)_LEn

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Knuth, Larrabee, Roberts. Mathematical writing (free web version, 1987)(118s)_LEn_.pdf

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Date May 17, 2005

Don.) Typographers help by using slightly larger parentheses for the outer pair in a nested set. An entire paper or pro of in capital letters is distracting. It gives the impression of sustained shouting. Same go es for boldface, etc. Paul Halmos intro duced the handy convention of placing a box at the end of a pro of; this box serves the same function as the initials ‘Q.E.D.’. If you use such a box, it seems best to leave a space between it and the ﬁnal perio d. Try to make it clear where new paragraphs begin. When using displayed formulas, this can become confusing unless you are careful. Using notational or typographic conventions can be helpful to your readers (as long as your convention is appropriate to your audience). Boldface symbols or arrows over your vectors are each appropriate in the correct context. When using a raised ‘st’ in phrases such as ‘the i + 1st component’, it’s better to use roman type: ‘i + 1st ’. Then it’s clear that you aren’t speaking of “1 raised to the power st.” Avoid “psychologically bad” line breaks. This is sub jective, but you can catch many such awkward breaks by not letting the ﬁnal symbol lie on a line separate from the rest of its sentence. If you are using TEX, a tilde (~) in place of a space will cause the two symbols on either side of the tilde to be tied together. (Other text pro cessors also have metho ds to disallow line breaks at speciﬁc points.) Some of us are much better at spelling than others of us. Those of us who are not naturally wonderful spellers should learn to use spelling checkers. Allowing formulas to get so long that they do not format well or are unnecessarily confusing “violates the principle of ‘name and conquer’ that makes mathematics readable.” For example, ‘v = c + u(ci − cj + 1)’ should be ‘v = c + k u, where k = ci − cj + 1’, if you’re going to do a lot of formula manipulation in which (ci − cj + 1) remans as a unit. Be stingy with your quotation marks. “Three cute things in quotes is a little to o cute.” Remember to minimize subscripts. For example, ‘pi is an element of P ’ could more easily be ‘p is an element of P ’. Remember to capitalize words like theorem and lemma in titles like Lemma 1 and Theorem 23. Remember to place words between adjacent formulas. A particularly bad example was, “Add p k times to c.” Be careful to deﬁne symbols before you use them (or at least to deﬁne them very near where you use them). [ 12 § 5.
COMMENTS ON STUDENT ANSWERS (2) ]...

Don discussed the labours of the bo ok designer and showed us specimen “page plans” and example pages. The former are templates for the page and show the exact dimensions of margins, paragraphs, etc. His designer also suggested a novel scheme for equations: They are to be indented much like paragraphs rather than being centered in the traditional way. We also saw conventions for the display of algorithms and tables. Although Don is doing his own typesetting, he is using the services of the designer and copy editor. These professionals are well worth their keep, he said. Economists in the audience were not surprised to hear that the prices of bo oks bear almost no relation to their pro duction costs. Hardbacks are sometimes cheaper to pro duce than paperbacks. For those interested in such things, Don recommended a paperback entitled One Bo ok / Five Ways (available in the Bo okstore) that describes the entire pro duction pro cess by means of actual do cuments. Returning to the editing of his Concrete Maths text, Don went through more of the Before and After pages he began to show us on Monday, picking out speciﬁc examples that illustrate points of general interest. He exhorted writers to try to put themselves in their readers’ sho es: “Ask yourself what the reader knows and expects to see next at some point in the text.” Ideally, the ﬁnished version reads so simply and smo othly that one would never suspect that had been rewritten at all. For example, part of the Concrete Math draft said (Before) The general rule is ( . . . ) and it is particularly valuable because ( . . . ). The transformation in (5.12) is called ( . . . ). It is easily proved since ( . . . and . . . ). [§7.
PREPARING BOOKS FOR PUBLICATION (2)...

From esoteric mathematics we moved on to reference bo oks. Don showed us six such bo oks that he likes to have next to him when he writes. [And he added a seventh later.] 1. The Oxford English Dictionary (usually called the OED). He showed us the two volume “squint print” edition rather than the 16-volume set. This compact edition is often oﬀered as a bonus given to new members upon joining a bo ok club. (There is a pro ject in Toronto that will so on have the entire OED online.) 2. The OED Supplement. The supplement brings the OED up to date. The supplement comes in four volumes, each of which costs $100 or more, so you may have to go to the library for this one. 3. The American Heritage Dictionary. Don likes this dictionary because of the usage notes and the Appendix containing Indo-European ro ot words. (For example, the usage notes will help you cho ose between ‘compare to’ or ‘compare with’ in a speciﬁc sentence.) 4. The Longman Dictionary of Contemporary English. Instead of the historical words found in the previously mentioned dictionaries, this one has the words used on the street. Current slang and popular usage are explained in very simple English. [§9.
HANDY REFERENCE BOOKS...

Should this course have been named “Computer Scientiﬁcal Writing” or “Informatical Writing” rather than “Mathematical Writing”? The Computer Science Department is oﬀering this class, but until now we have been talking about topics that are generally of concern to all writers who use mathematics. To day we begin to discuss topics speciﬁc to the writing of Computer Science. We are not abandoning mathematical concerns; Don says that a technical typist in Computer Science must know all that a Math department typist must know plus quite a bit more. He showed us two examples where mathematical journals had trouble presenting programs, algorithms, or concrete mathematics in papers he wrote. In order to solve the ﬁrst problem, Don had to convince the typesetters at Acta Arithmetica to create “ﬂo or” and “ceiling” functions by carving oﬀ small pieces of the metal type for square brackets. The second problem had to do with typographic conventions for computer programs; The American Mathematical Monthly was using diﬀerent fonts for the same symbol at diﬀerent points in a pro cedure, was interchangeably using “:=”, “: =”, and “=:” to represent an assignment symbol. Stylistic conventions for programming languages originated with Algol 60. Prior to 1960, FORTRAN and assembly languages were displayed using all uppercase letters in variable width fonts that did not mix letters and numbers in a pleasant manner. Fortunately, Algol’s visual presentation was treated with more care: Myrtle Kellington of ACM worked from the beginning with Peter Naur (editor of the Algol report) to pro duce a set of conventions concerning, among other things, indentation and the treatment of reserved words. [ 20 § 10.
PRESENTING ALGORITHMS ]...