Identify a typical reader.
What background does the reader have?
Does the work build on past works that the reader is likely to have read, or is it a novel approach?
Does the work combine two or more distinct fields (inter-disciplinary)?
The audience will determine the slant of your paper:
A paper about Toeplitz matrices for engineers would phrase properties and results in terms of the applications in which these matrices arise.
A paper for mathematicians typically considers the matrices in isolation from their applications.
Use the notation and terms that fit your intended audience; otherwise you may confuse the reader and the work may be impenetrable.
"Least squares problem" for linear algebraists versus "Linear regression problem" for statisticians
When writing, ask yourself why a member of the intended audience should want to read your paper.
The question should be easy to answer in a well written paper.
Otherwise, consider altering the design of the paper, or doing more research before continuing the writing.
With a little effort it should be possible to make a paper partially understandable to non-experts:
"The titles, abstracts, and introductions of many mathematical papers say: "Outsiders keep out! This is of interest only to those few already in the know."
Examples of alternate themes for a particular paper: (ranked from weakest to strongest)
Rank your contributions, to identify the most important. Use the rankings to decide where to put the emphasis. The rankings also help you to write the title and abstract.
"A decomposition of compact continua and related results on fixed sets under continuous mappings"
"Simple links and fixed sets"
Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
[lively and informative]
How and how not to check Gaussian quadrature formulae
["How to" titles immediately arouse the reader's interest]
Gaussian elimination is not optimal
[A short, one sentence paper summary can make a great title]
How near is a stable matrix to an unstable matrix?
[A title that asks a question is direct and enticing]
ALGOL68 with fewer tears
[One can't help be curious enough to read the abstract!]
The art of programming
[Knuth's provocative title has inspired similar titles on other papers]
The ubiquitous B-tree
[An unusual but apt word catches the browser's attention]
Rules of thumb
Bad: Numerically Stable Parallel Algorithms for Interpolation Better: Numerically Stable Parallel Algorithms for Interpolation
Bad: An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators Better: An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators
Bad: A Method for Cutting and Pasting Text Segments Better: A Method for Cutting and Pasting Text Segments
Sometimes two authors that frequently publish together may swap orders on each paper (e.g., Hennessy and Patterson).
Always date your work.
Even if you do not publish the work, if you give a copy to someone else they will want to know when it was written.
Dating helps to avoid confusing drafts. I usually put the date into the header or footer to avoid confusing sheets of paper on my desk.
Put the date on a line by itself, usually after the author's name, on the first page of the document.
An algorithm given by Boyd [Linear Algebra Appl., 9 (1974), pp. 95-101] is extended in this paper.
Some conferences request submission of extended abstracts -- typically 50% the length of a full paper.
Conferences often publish poster abstracts -- typically one or two page summaries.
If you give a talk or serve on a conference panel, you may be asked abstract your presentation for publication in a proceedings.
Journals may ask for one or both of the following:
Five to ten author-chosen words that best characterize the paper. Words are used in computer searches, therefore anticipate words a reader might search.
The Computing Reviews Classification System is a four-level tree that has three numbered levels and an unnumbered level of descriptors. The top level consists of eleven nodes, denoted by letters A (General Literature) to K (Computing Milieux).
G.1.3 [Numerical Analysis]: Numerical Linear Algebra - sparse and very large systems.
The first sentence of a paper should
Formation of models of physical behavior underlies science. Yet our ability to construct behavioral models of parallel and distributed programs is very limited.
These opening sentences had enough impact on one reader that the reader quoted them in the opening paragraph of that they later wrote!
motivate why you are examining a problem area
define problem (which may first require some notation)
outline your solution to the problem:
summarize contributions in a thesis or dissertation
summarize the organization of the rest of the paper, at the end.
Keep the introduction short: About 10% of the paper.
Try deleting the first one or more sentences of your introduction, and see if it still makes sense:
To understand the central challenge in distributed and parallel processing, one only needs to read the popular press. Recent Sunday editions of The Washington Post contain articles querying business and academic leaders on whether parallel processing will fulfill its touted benefits. A common theme emerges in each: although we can manufacture parallel computers, can we program them?
Electronics technology has reached the point today where we can manufacture parallel computers -- but can we program them?
Rarely do Computer Science "experiments" follow the classic science model: hypothesis, experiment design, results, conclusions.
More often, computer scientists report results of program measurements, referring to these as experiments.
Often papers report data collected from execution of programs to
Be sure to state clearly:
When showing convergence or accuracy of a method, tabulate errors rather than the values themselves.
Report normalized errors.
Repeat the experiment at least three times, and report at least the sample variance of three observations, or even better the confidence interval. Why repeat the experiment?
See Abrams .
See Abrams [ABR94a].
See Abrams 1. (Symbol "1" should be a superscript.)
See Abrams (1994a).
Awkward:  proves the theorem.
Better: Jones  proves the theorem.
Example: ...several variations exist [2, Chap. 7].
Several variations exist [1,3,9].
Variations have been developed by Smith (1974) ,
Barnes (1982)  , and Jackson (1989) .
Incorrect: Several variations exist [3,9,1].
Add a citation when:
But be careful not to overuse citations. Do not cite the same paper twice in one paragraph!
Be sure to clearly identify what part of a paper is your own creative idea and what is existing literature. I suggest using words such as
Locate the citation in a place that does not intrude on a sentence.
Awkward: The method was found  to be unstable. Better: The method was found to be unstable .
Be sure that the sentence reads properly when the citation is deleted.
Incorrect: This question has been addressed by . Correct: This question has been addressed by Ott .
Carefully choose what to include and exclude from your reference list!
The conclusions can:
It is dangerous to refer to works in progress -- they may never materialize! It is safer to put intermediate results into a technical report, and then cite the technical report.
The conclusions section should not:
You should acknowledge
"This research was supported by the National Science Foundation under grant DCR-1234567."
[Some funding agencies tell you the exact words to use!]
"This work was supported by an SERC Fellowship."
"I thank X for helpful comments on the manuscript."
[Note: X may be the anonymous referees.]
"I thank X for discussions during the development of this work."
"X provided the database traces used in this paper."
"The experiments were performed using the computer facilities of the Argonne National Laboratory."
"The illustrations were drawn using Jane Ott's pic software.
An appendix can be used to provide essential information that would distract the reader if it were placed in the paper body.
If I were paid based on the number of errors that I found in a manuscript, I would always start with the reference list!
J. H. Wilkinson, Error analysis of floating-point computation, Numer. Math., Vol. 39, No. 5, Nov. 1983, pp. 639-648.
I highly recommend use of an automated tool to maintain a bibliography for everything you write, and to automatically generate a reference list using a consistent style.
Every journal has its own style of references. Usually the copy editor will change your style to fit that of the journal.
Higham describes a paper by Vieira and Messing, cited as Viera only by one author. Afterwards subsequent authors ignored rule (1). As a result, the paper was placed too low in a list of most-cited papers.
H. A. Guvenir (that's me)
A. Guvenir (another person who works in something else)
You can inadvertently insult someone by failing to use their first name when you use the first name for other authors in a reference list.
K. M. Chandy and J. Misra, Parallel Program Design: a Foundation, Addison-Wesley, 1988.
0 = Publisher from English speaking country
89871 = Publisher (SIAM)
314 = book's individual number (Book 314 from SIAM)
5 = checksum
There is also an International Standard Serial Number (ISSN) for serial publications.
The result is proved in the following Theorem 3.13. If f is ...
5.1. Accuracy of the Computed Solution.
It depends on the machine precision....
LaTeX will automatically number equations, theorems, lemmas, definitions, ...
Example: The synonym problem in memory addressing is solved by ...
References to proper nouns should be capitalized:
See Theorem 1.5, the proof of Lemma 3.5, and the discussion in Section 6.
See the last theorem, the last lemma, and the next section.
This paper proves....
Section 3 shows....
We prove ....
We show ....
Theorem 2 states....