I've noticed three common writing scenarios in which non-native English speakers at SWS consistently omit a required article.
Few vs. a few: when a little article makes a big difference
Finally, a special note about the difference between few and a few, which look similar, but convey almost opposite messages. Few (without an article) means "not very many", or sometimes even "none", and is used to make a negative statement. For example, this sentence is stressing the absence or lack of prior work:
In contrast, a few (with the indefinite article) means "some" or "a small number". It still indicates that the number is small, but emphasizes that the number is greater than zero, and is used to make a positive statement. This sentence, for example, is stressing the presence of prior work:Few researchers have attempted to study the effect of ....
Another similar example: "We cite few such instances" should probably read "We cite a few such instances," because the author is trying to make a positive statement, that they do give citations. If you're not sure which form is correct, try substituting the phrases "a number of" and "not very many" for "few". If "a number of" fits better, you usually need an article.A few researchers have attempted to study the effect of ....
Here's a tricky case:
At first glance you might think that in this sentence few means "not very many," and so no article is needed. Indeed, if the adverb only was removed, in few hops would be acceptable (although the wording in a few hops is probably more common). However, the adverb only must always be followed by a positive statement (i.e., the presence of a short path), not a negative statement (i.e. the absence of a long path). For example, you can say "only seven students" but not "only no students". Thus, the sentence should read "only a few hops." If you do a google search for "only few" you will get many hits, but if you look carefully you will notice that most of the hits are in pages written by non-native English speakers, or in news article headlines, where space is tight so small function words are often omitted. In the Collins English corpus there are only four sentences which use the phrase "only few", whereas there are hundreds of instances of "only a few".The source node can be reached in only few hops.
The usage of little and a little is similar to few and a few, except that few is used for countable nouns and little is used to describe the quantity of some uncountable substance. The phrase "with little success" means that the person was for the most part unsuccessful, whereas the phrase "with a little success" means that the person experienced at least a small amount of success. Some other nouns that can be modified by little include attention, resemblance, involvement, experience, and distinction.
For more information on articles come by my office for information from a handbook.
A basic overview article on article usage is also available from Perdue's OWL website.