Grammar and style suggestions and references

I read too many reports with poor grammar, structure, ideas etc., so I'm going to start compiling the advice which I find myself writing. If you're going to be writing a report/project/thesis for me, then you may find it useful to glance through the rest of this page.

Here follow three grammar references, from elsewhere on the Internet, which may be of use, although they vary in purpose and thoroughness:

  1. Condensed grammar description.
  2. The eight parts of speech.
  3. Guide to grammar and style

The document is divided into four parts, which will be of varying relevance depending upon the relative strengths and weaknesses of your writing style.

Punctuation: Apostrophes, Colons, Commas, and Semi-Colons ...


Many non-native English speakers, especially those used to a different alphabet (such as Arabic or Chinese), seem to use inconsistent spacing in their writing. Colons, semi-colons, commas, periods are never preceded by a space and always followed by one:

Hello! What shall we do today? Three ideas: study, read, or exercise.

Pairwise punctuation (quotes, brackets etc.) have opposite spacing arrangements at the two ends, thus

In a sentence, parentheses (like these) or brackets [like these] are surrounded by spaces.
There is no space before following punctutation (like this period).
Quotes work the same way: "Hello", not " Hello "

I am not aware of uniform agreement regarding punctutations and quotes. My personal feeling is that punctutation for a quoted word goes outside of the quotes

Then he said "hello", and I shouted "hi".

whereas punctuation for quoted phrases or sentences may be placed inside or outside. I have a preference for inside:

"Let's go to the library," he suggested.
Then he said "I would like to read your thesis."

The position of a question mark should be inside the quotation if the quotation asks the question, outside if the remainder of the sentence asks the question:

Did he say "I don't know"?
Then he said, "What would you like to do?"


Use the apostrophe correctly. The most common error is to confuse "its" with "it's":

"it's" ALWAYS means "it is": It's raining today.
"its" is a possessive: His car, her house, its colour.

Do not use the apostrophe to create plurals, a problem which occurs most frequently with acronyms. Reserve the apostrophe to indicate the possessive tense:

The PTA's meeting on ABCs went well.
NATO's F18s are expensive.


Sentences with mis-used colons are very irritating to read. It is very simple to do it right!

The part of the sentence preceding the colon must be a complete sentence!!! So the sentence ...

Our ideas are: idea one, idea two, and idea three.

is wrong!! "Our ideas are." is not a complete sentence, nor is it a header (discussed below). The irony is that this would have been just fine without the colon:

Our ideas are idea one, idea two, and idea three.

If you wish to use a colon to introduce a list, make sure that it ends a complete sentence, then followed by one or more clarifiers:

We have three ideas: idea one, idea two, and idea three.
We have the following ideas: ...
Our report is very interesting: reason one, reason two ...

Note that what follows a colon does not need to be a list. The purpose of a colon is to separate a complete sentence phrase from some related, clarifying remark(s):

I have a great idea: let's read a book on grammar.
My thesis contains a profound result: the solution to cold fusion.

There is some judgement required in constructing such sentences:

  • If the two phrases are completely separate, it is best to separate them with a period.
  • If the two phrases are somewhat related, but not that the latter directly serves to clarify the former, then a semi-colon may be used.
  • If the two phrases are related, and the second serves to clarify or define the first, then a colon is appropriate.

Although grammatically not correct, the occasional use of colons following headers can be effective in giving emphasis. This is similar to writing in point form, and should be avoided in formal writing.

Three ideas: idea one, idea two, and idea three.

An overview of our algorithm: step one, step two, and step three.

In each case, the header preceding the colon is a noun phrase; no verb is present.

In general, avoid colons unless you know how to use them. If you use one, do not leave the part of the sentence preceding the colon "hanging".

Commas and semi-colons:

Most students don't use semicolons, so they consequently don't get mis-used very much either. The rule is very simple: only put a semicolon where you could put a period. That is, a semicolon separates two grammatically complete sentences:

We will develop an algorithm; we'll also do other stuff.

The semicolon case be useful in reducing the number of very short sentences in a paragraph. The phrases connected by a semicolon are meant to be somewhat more related than those separated by a period, so a semicolon can be a useful tool, if used consistently, in helping a reader to understand degrees of relationship.

The use of the comma is more subtle and errors are frequent! If in doubt, leave the comma out; I see more bad commas than I do missing ones. You won't go wrong if you stick to the following:

  • Do not put a comma between phrases connected by "and":

(phrase one) and (phrase two).

I like this and I like that.

  • Do use a comma with phrases connected by "but":

I would like to go, but I can't.

  • Use a comma to separate items in a list:

I would like this, that, whatever, and that.

  • Use a comma to denote optional words in a sentence. The sentence has to make perfect sense with the words between commas removed:

I would like to read excellent grammar, if possible, from my students.

Removing "if possible" from the sentence still leaves us with a meaningful statement.

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Words: Latin Acronyms, Articles, Prepositions, If/Whether, and Plurals.

Latin acronyms:

The short forms i.e., e.g., n.b. are very widely used, but often incorrectly.

They are latin acronyms, so the periods are required; furthermore they must be followed by a comma, since their English equivalents are phrases which would have to be followed with a comma in the same way. Finally, do NOT interchange i.e., e.g., and n.b. They do NOT mean the same thing!


Latin Meaning

English Translation

Actual Meaning


Id est

That is

That is, specifically, thus


Exempli gratia

For the sake of example

For example


Note bene

Note well

Note well


Quod erat demonstrandum

Which was to be demonstrated

End of proof

Note the differences in the following three sentences:

I need a new workstation; i.e., a fast, expensive toy.
I would like a new toy; e.g., a new computer.
I want a new computer; n.b., it had better be fast.


Although rarely a problem for native English speakers, foreign students very frequently have problems with these, and the problems are VERY GLARING to native speakers, so it is worth getting these right. There are two types of articles: definite (the, these, this etc.) and indefinite (a, an, some). The choice of article is well defined:

  • To refer to some particular thing or things you MUST use a definite article. You use this only to refer to some specific noun, which must be very clear in the reader's mind.

Do you see THE dog?
What are THOSE people doing?
THIS book is interesting.

  • To reference an object whose specific identity is not clear, use an indirect article.

Was that A dog?
Are people doing bizarre things?
Do you want AN interesting book?

  • To state a general property, idea, or fact, you may use an indefinite article (usually "some") or no article at all, but the noun is always pluralized and a definite article is never used.

Dogs like to run.
SOME people do bizarre things.
Books are interesting.


Sentences having a preposition at the end are wrong! Each of the following is abominable:

Who are you going with?
Where are you coming from?
That is the idea I came up with.
That's something I won't put up with.

EVERY preposition needs to be followed by an object phrase (either a direct one or an indirect one). Some people argue in favour of having prepositions at the end of sentences, because the alternatives sound awkward:

Whence are you coming?
That is the idea with which I came up.
That is something up with which I will not put. (credit to W. Churchill)

However such contortions are unnecessary. One can almost always construct a perfectly reasonable, grammatically correct sentence:

With whom are you going?
From where are you coming?
I came up with that idea.

If you find yourself putting prepositions at the end of sentences, at the very least get used to looking for alternatives.


Far too many writers are ignorant of the use of "whether," substituting the word "if." "If" and "whether" represent very different forms of speech!

"If" always introduces a condition, making some part of the sentence subject to the condition introduced by "if":

If it is raining, we won't go outside.

"Whether" tests a condition, it doesn't introduce it:

Can you tell me whether it is raining outside?

Technically, the sentence

Can you tell me if it is raining outside?

is stupid. It says, if it is actually raining, then tell me something; if it isn't raining, then don't say anything. As a general rule it is hard to ask a question with "if"; you almost always want "whether".

Commonly confused words:


A main thing, something significant, head of a school

The principal rule is this: be nice to other people.


A philosophy, an idea

Try to live based on good principles, such as being nice to other people.


To make sure of, giving a promise

I assure you that I have turned the lights off.


To make sure of

Ensure that the lights are turned off.


To secure against loss of money

I insure my house and my car in case of damage.


A good fit, a natural combination

Chocolate and milk are complementary: they taste great together.


Something free (ie, no cost), a nice statement

Thank you for the compliment; that was a very nice thing to say!


Normally a noun: anything produced by some cause

The effect of your actions has been significant.


Normally a verb: to act, to change, to cause an effect

Your actions will affect me significantly.


Get plurals right! To some people, Latin plurals (crocus - croci, arena - arenae) sound pretentious, whereas to others arbitrarily-anglicized plurals sound ignorant (datum - datums, quorum - quorums). In general, use your judgment; by and large I prefer Latin plurals. The rules for Latin pluralization are

the suffix *um pluralizes to *a, *a pluralizes to *ae, *us pluralizes to *i

The most common mistake occurs with "criteria", followed closely by "data" and "media":

One criterion, Two criteria.
One datum, Several data.
One medium, The television media.

Hence, the data are interesting, the media are biased. Do not treat "data" or "media" as singular! If the plural form bothers you, use one of many possible alternatives:

The dataset is ...
The results are ...
The collection of data is ...

Also frequently confused are sets and types. If you're referring to a set or a type of objects, even though there are many things in the set, there is only one set, so the singular case is required:

This group of people IS smart.
This bushel of apples IS heavy.
The apples in this bushel ARE red.
The set of points IS irrelevant.

Finally, comparatives are sometimes confused:

Comparator ...

Applies to ...

Example ...

Less, Lesser

Continuous values

I have less money than you.

Few, Fewer

Integer values

I have fewer dollars.

Great, Greater

Continuous values

I have great strength.

Many, More

Integer values

I can lift more pounds.



This light is less bright.



This book is more interesting.

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Sentences and Paragraphs


This topic logically follows a discussion of colons, since most lists follow a colon. The main issue with lists is that all elements in the list need to be grammatically consistent (e.g., same verb tense or sentence structure).

Individual preferences will vary widely, and to the extent that a list is meant to look like point-form writing no grammar rules really apply. However in a formal document I would recommend the following rules for all lists:

  • If the last phrase before the list ends in a colon, then the usual colon rules apply. For example, Good: We will consider four points: - point 1 - etc.
  • If the last phrase before the list does not end in a colon, then each of the phrases in the list must continue ... (in progress ...)


It will be very difficult to summarize paragraph writing in a few points, since it is a fairly subtle and creative topic. However I'll list a few points for now:

  • When using references such as "this", "these", "it" etc., especially at the start of a sentence (!!!), make sure that the reference is clear.

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Whole Document Structure

It is amazing how many formal projects I get which have no introduction or where the writing is in point form. Basic ground rules:

  • EVERY report and project has to have an Introduction and a Conclusion. Projects and theses MUST suggest future work or recommendations for future study, however it is permitted to include this material as part of a Conclusions section.
  • EVERY document needs to have numbered pages. Why you wouldn't number pages is something I can't understand.
  • EVERY document longer than about four pages needs a table of contents. A list of figures or list of tables is required only for theses.
  • For technical reports, it is strongly recommended that sections be numbered. Relying on font size and capitalization to imply sections is ambiguous.
  • I consider it poor form to have a chapter or section that moves directly to a subsection without introductory material:
  • Chapter 2: Background material
  • 2.1 Linear Operators
  • 2.1.1 Wavelets
  • The text for all of Chapter 2 starts here, in some detailed discussion of wavelets ...

Since chapter 2 consists of much more than section 2.1.1, presumably there is something which you might like to tell the reader about chapter 2 as a whole. Thus the following is preferred:

Chapter 2: Background material

A paragraph describing Chapter 2 as a whole, perhaps giving a brief overview for the reader.

2.1 Linear Operators

A brief overview of this section, now limited to the topic linear operators.

2.1.1 Wavelets

This is no longer the first text of chapter 2. This text focuses only on wavelets ...

  • Don't number sections past three levels of depth (e.g., Section 3.2.4). Four levels of numbering gets tedious and suggests that the document is poorly organized. Also, you shouldn't have a section number and/or table of contents entry for anything less than about half a page in length. I routinely see Tables of Contents with about ten entries for three pages --- this is bad.
  • Avoid chapters having only one section, or sections having only one subsection - the document structure looks awkward and poorly thought out. In other words, if you have a section 2.1, there should be a 2.2 also. Otherwise, consider absorbing the lone section into its parent.
  • Use consistent spelling. Half American / half British spelling reads very poorly. For submissions to American journals, American spelling is encouraged. For projects and theses submitted in Canada, British spelling is preferred.
  • Bullets and lists are perfectly fine, however these must appear within paragraphs consisting of complete sentences. No part of the actual writing (prose) of your document can be in point form.
  • For theses and projects, it is not adequate to just give a list of references at the start of a section. Every time you introduce a non-obvious idea you need to give the reference(s) right at that point. Most importantly, if you say anything about "the field" or "the literature" or "other researchers" then you MUST have a reference to back this up (I see this problem ALL the time).

Any time to state a major fact or idea that you don't develop yourself then you require a reference. Without a reference you could just be making things up. Also, use only last names in referencing other people's work, never first name or initials.


Good figures are crucial to a good document. In general, my advice when writing is to determine all of your figures and tables first; these set the overall content and structure of the document. Once the figures are in place, the text follows easily.


    • Figures should be at the top of a page, at the bottom, or on a page on their own. Do not wrap text around figures, since you can end up with extremely poor figure placement and awkward text flow.
    • If a figure (or set of figures) uses more than about 75% of the page, then there shouldn't be any document text on the bottom of the page.
    • Create meaningful captions!! A figure or table should make sense from the caption alone, without having to read the document! (within reason) On the first pass, the reader is likely to look at figures and captions only; if these fail to grab attention, then the document is doomed.
    • Colour figures printed on a black-white printer often look pretty bad (in particular, the grey-scale equivalent of most colour-colourmaps is NOT monotonic). If you're going to be printing in black and white, prepare grey-scale figures.
    • There is a difference between monitors and printers!!! Monitors are sensitive near black, and insensitive near white. Printers are totally insensitive near black, and extremely sensitive near white (ie, 100% and 50% black look the same; 0% and 2% black look totally different!). Good rule: if it looks good on a monitor, then the negative will look best on a printer.
    • 3D/surface plots look slick, but are relatively poor quantitatively. If the actual values being plotted matter to the reader, use a contour plot or an image with a colourbar.
    • If most of the lines/symbols in a plot occupy a relatively small fraction of the plot area then the plot is probably not communicating effectively with the reader. Consider axis rescaling, a semi-log plot, a log-log plot, or changing what you are plotting (for example, plotting the difference or ratio of two values, rather than the values themselves).
  • It is naive to suppose that I can teach you anything substantial about writing style in a paragraph or two. Serious students should read a guide (e.g., Strunk and White). However, a few tips:
    • Flow is one of the most crucial, and difficult, elements to incorporate into writing. Paragraphs should meaningfully follow each other, as should subsections, sections etc. It is crucial that ideas follow one another in logical order!
    • Do not change more than one aspect of an idea at a time. That is, in going from A to B, go one step at a time!
    • Avoid excessive quoting of other authors - it reads awkwardly. Instead, paraphrase/rewrite whenever possible.
    • Do not try to explain mathematical ideas using prose (this happens all the time, it is a serious problem!). It makes sense to you, but not to the reader. Use mathematical notation, symbols, and equations for mathematical ideas.
    • Do not use arbitrary mathematical notation! Good notation takes work!
    • Do not try to explain algorithmic ideas using prose! Use a figure, table, pseudocode etc.
    • Whenever you use an acronym, define it in its first usage. In longer documents, such as theses, you may need to define acronyms more than once (that is, don't assume that the reader has read every obscure section in your thesis in using an acronym). Certainly avoid the excessive use of acronyms; if you absolutely have to use a lot, then define them all in a table.

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