English

References

• mybusinessenglish.com on YouTube
• John Owens, Common Errors in Technical Writing
• Markus Kuhn, How (not) to write an abstract
• Jerzy Trzeciak, Writing Mathematical Papers in English
• Georgios Varsamopoulos, How to Write a Technical Paper: A Structure and Style of the Epitome of your Research

Tools:

• Academic-Writing-Check

Papers I like (clear, good style):

• Dan Boneh, Twenty Years of Attacks on the RSA Cryptosystem, February 1999, Notices of the AMS, http://www.ams.org/notices/199902/boneh.pdf
• Daniel J. Bernstein, Enumerating and counting smooth integers, 1991, 950518 (draft T).

Expressions

In my defense it was dark	Pour ma défense il faisait noir.
Don't get your knickers in a twist/knot	~ Calm down, ne fait pas de noeuds dans tes sous-vêtements
spritzing the SKUNK with eau de cologne.
hanging garlands from the corpses' ears
People go to the site looking for things → Things people go to the site looking for
X is 99 times more than Y, but it is 100 times that of Y.
As opposed to smthg	Au contraire de qch, au lieu de qch
By my count, you have...	D'après mes calculs, vous avez...
Your h*ar of a mother (should find a more appropriate example...)	Votre c*tin de mère
He doesn't know much, but he makes up for it by asking lots of questions	Il ne sait pas grand chose mais compense en posant beaucoup de questions
(about questions) I take it that those have been settled?
your hair would stand on end	Tes cheveux se dresseraient sur ta tête
Cry me a river build a bridge and get over it.

Don't say but say...

Some examples on how to say things simply and clearly

Don't say ...	... but say ...
there is still a correlation check to make sure that the OBE indeed reported that it was at the same location as the enforcement equipment and at the same time as reported by the equipment	there is also a specific check of location given by OBE against location of enforcement equipment
My coin has fallen	My penny dropped
The weight equals to the number	the weight equals the number — or the weight is equal to the number
fully determines the two others ones	fully determines the other two
convert conditions on bits to conditions	convert conditions on bits into conditions
In the light of	In light of
Our first attempt to such a reference model	Our first attempt at such a reference model
appeared in [4] by the name of	appeared in [4] under the name of
To spend some time to refine ...	To spend some time refining ...
Later we wrote our findings ...	Later we wrote up — or put — our findings ...
It has success probability of at most 2^...	It has success probability at most 2^...
both in the temporal as in the 1080 three spatial dimensions	both in the temporal and in the 1080 three spatial dimensions
we replaced our original padding by the multi-rate padding	we replaced our original padding with the multi-rate padding
Factorizing large integers	Factoring large integers (Factorizing is correct though but factoring seems better [1])
Evaluate a function for some input	Evaluate a function on some input
With probability of at least 1/2	With probability at least 1/2
Logarithm of x in the base 2	Logarithm of x to the base 2
To my opinion	In my opinion

Spelling mistakes

Bad	Good
fixed input length	fixed input-length or fixed-length input

Grammar

• Not to or to not ?

The default construction is not to + INF (like in I decided not to go). However the split infinitive construction to not + INF seems to be allowed as well (like in I decided to not go). Note that I decided not to go is not the same as I did not decide to go!

• half or half of?

[2], [3]

Both are usually valid (She spends half (of) her time travelling., Half (of) my friends live abroad.)

When using plurals, better specify the scope correctly (Half (of) my friends live abroad better than Half (of) friends live abroad)

half of before pronouns (Half of them)

half a usually ((half an apple is not a lot)), but a half also valid in measurements (a half pound)

• punctuations

comma — In an enumeration, a comma , before and is optional. Choose your favorite option and stick to it [4]. Adding this comma may clarify the enumeration if items are complex. This comma is called the serial comma or Oxford comma [5].

Tongue Twisters

Source: [6]

Bill Badger brought the bear a bit of boiled bacon in a brown bag.

Heather was hoping to hop to Taihiti To hack a hibiscus to hang on her hat. Now Heather has hundreds of hats on her hat rack. So how can a hop to Taihiti help that?

Peter Piper picked a peck of pickled peppers. A peck of pickled peppers Peter Piper picked. If Peter Piper picked a peck of pickled peppers, How many pickled peppers did Peter Piper pick?

Red lorry, yellow lorry

Red leather robots, yellow leather robots

Seventeen slimy slugs in shiny sombreros sat singing short sad songs.

She sells seashells by the seashore. The shells she sells are surely seashells. So if she sells shells on the seashore, I'm sure she sells seashore shells.

The sixth sick sheik's sixth sheep's sick.

Six thick thistle sticks. Six thick thistles stick.

I slit a sheet, a sheet I slit. Upon this slitted sheet I sit.

Do scientists see thieves seize skies? If scientists see thieves seize skies, then where are the skies, the scientists see the thieves seize?

Thirty three thin Finns throw forty three frogs into four Thracian theatres.

The Awfullest Thistle: The successful thistle sifter, in sifting a sieve full of unsifted thistles, stuck three thousand thistles through the thick of his thumb.

Theophilus Thistle, the successful thistle sifter In sifting a sieve full of unsifted thistles, Thrust three thousand thistles through the thick of his thumb. If Theophilus Thistle, the successful thistle sifter, Can thrust three thousand thistles through the thick of his thumb, See thou, in sifting a sieve full of unsifted thistles, Thrust not three thousand thistles through the thick of thy thumb.

Which witch winds white weasel wool well?

How Much Wood Would A Woodchuck Chuck If A Woodchuck Could Chuck Wood? A Woodchuck Would Chuck As Much Wood As A Woodchuck Could, If A Woodchuck Could Chuck Wood.

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo

Writing tips

• Avoid passive voice
• Avoid unnecessary details
• Set the scene progressively (step by step)
• Use the colon correctly

We obtain the following theorem:           // -- BAD --
We obtain the following theorem.           // -- CORRECT --
Theorem 8. foo ...

From John Owens [7],[8]:

• Use et al. correctly. "et al." means et alia. Use it when there are 3 authors or more

AuthorOne
AuthorOne and AuthorTwo
AuthorOne et al.

• Don't use citation as words :

A similar strategy is described in [15].                        // --BAD-- citation as word, 
A similar strategy is discussed by 15.                    // ... imagine if citation uses superscript -> looks really silly
A similar strategy is discussed by AuthorOne et al. [15]        // --CORRECT--

• Use short citation to avoid repeat:

AuthorOne discusses this point further in her dissertation [AuthorOne 2002].  // --BAD-- name repeated
AuthorOne discusses this point further in her dissertation [2002].            // --BETTER--

• First person, passive voice: Please write in first person and avoid the passive voice.
• Hyphenation: “We built a high-performance implementation.” “high-performance” is hyphenated because “high” modifies “performance” not “implementation”. It's not a “high implementation”. Here, “high-performance” is an adjective. But: “Our implementation has high performance.” Here, “performance” is a noun. No hyphen. Similarly: “throughput-oriented workloads” or “GPU-based implementation”.
  For some words, it's not clear if it should be hyphenated or not (e.g. “e-mail” vs. “email”). The general trend in English is to move toward non-hyphenation (e.g. “to-morrow” became “tomorrow”) so if I'm unsure, I usually trend toward non-hyphenation.
• Serial comma: “The serial comma is the comma used immediately before a coordinating conjunction (usually and or or, sometimes nor) preceding the final item in a list of three or more items.” (Wikipedia). Short rule: always use it in because it avoids confusion.
• Use of the word “only”: Be precise with this word! For example, “I only eat apples” (doing nothing but eating apple) and “I eat only apples” (because I'm a horse or something).
• Writing units: If you're writing, say, “ten meters”, these are WRONG: “10m” or “10m”. It's “10 m” (non-breaking space, not italicized, 10~m in LaTeX). See package [siunitx]. Also, since "bit" is already an abbreviation of "binary digit", don't write "10 kb" but "10 kbit". "10 kB" is ok.

TO DO Have also a look at Writing Mathematical Papers in English (see References).

Writing advices

No needless words

Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline, but that every word tell.

— Strunk & White in The Elements of Style

How to write mathematics

The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do so, and to do it clearly, you must have something to say, and you must have someone to say it to, you must organize what you want to say, and you must arrange it in the order you want it said in, you must write it, rewrite it, and re-rewrite it several times, and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation. That’s all there is to it.

— P. R. Halmos in How to Write Mathematics

Examples

• AES operates on date blocks of 16 bytes.
• For ease of presentation, we omit this operation here
• Let .... Given ..., one can .... Conversely, given ..., one can .... Since ..., this proves the converse statement.
• Then with probability at least 1/2 (over the choice of g)
• Since x takes time linear in log_2 d, a small d can improve performance by at least a factor of 10.
• Apply function x prior to signing.
• A fraction of the bits, parts of one of the factors p,q
• protect the full key → protect the entire key
• Expose half the most significant bits of the key — or

Expose half of the most significant bits of the key

• relies on the intractability of factoring polynomials — or

the intractability of the discrete logarithm problem

• A keystroke saved is a keystroke earned (and not won)
• If you expect this behavior to carry over to Vim's visual mode, you're in for a surprise.
• We'll discuss it at greater length.
• We are working with integers expressed in binary notation.
• ... as quite a wide variety of ... can be so described.
• ... (discussed in the next section) ... (discussed in the section after that)
• But in this case, the conclusions overreach. [9]
• The addition of the mixed term

Mathematic papers

• Say: Fix an integer a ≥ 0.
• Number x is big (not great). But x is greater than y. x is bigger than y, also valid.

TODO

little / few

high
low

more
less

great
less?

big
small

large
small

huge=very large

little
lot of

few
?

many/much - more - most

From http://ell.stackexchange.com/questions/820/is-it-less-than-or-lesser-than:

Less, lesser, and littler are all comparative forms of little. They are used like this:

• little - littler - littlest when you mean "small in size" (note: littler - littlest are in fact childish speech)
• little - less - least when you mean "small in amount"
• little - lesser - least when you mean "inferior or smaller in importance"

So if you mean one quantity or number is smaller than another, you say "less than".

You would say *less than* or *the lesser of*(?). Not lesser than.

However, it largely depends on the sentence in which you're using your particular example, as it may be that using 'fewer than' instead of 'less than' is correct. 'Less' means not as much 'Fewer' means 'not as many'

For example, if I'm holding three apples I have 'fewer than 4 apples'.

If I'm holding half a kilogram of sugar, I have 'less than a kilogram of sugar'.

From http://news.bbc.co.uk/2/hi/uk_news/magazine/7591905.stm:

more than / less than

greater than / less than

less / lesser / least - more familiar

few / fewer / fewest - less familiar

"- fewer is for numbers of separate items or people,

- less is for quantities not thought of in numbers: there were fewer people in the shops because there was less money

6 weeks or less

10 items or less - not correct, it should be 10 items or fewer.

However, "less than six weeks" is correct because we refer to a single period of time lasting six weeks, not to six individual weeks".

Indeed, 5 weeks and 2 days is less than six weeks.

But one can say "there are fewer weeks in two months than there are in one month".

Little vs small - see http://english.stackexchange.com/questions/31216/difference-between-little-and-small:

• When denoting size, there is little difference between "little" and "small".
• When denoting quantity, only little can be used.
  Also there is a difference between a little (as in I have a little experience teaching english, which means I have some experience but not much) and little (there is little difference means there is no difference, I have little experience teaching english)