English Usage

Grammar Review


  1. Grammar Review
  2. Mechanics
  3. Punctuation
  4. Usage Points from Eisenberg and Higham
  5. Frequently Asked Questions

Grammar Review

From: Harbrace College Handbook

Sentence Structure

Recognizing Subjects, Predicates, Verbs, Verb Phrases, and Verb Markers

SENTENCE PATTERN: Subject + Predicate


    ---------------------     -----------------
    Enthusiastic freshmen  +  were registering.
    ------SUBJECT--------     ----PREDICATE----

Verb may function as predicate or as part of predicate:

    As predicate:           I teach.
    As part of predictate:  I teach every day.

Verb phrases:

A verb consisting of more than one word.


    Class had started.
    I am going to try.

Verb markers:

Commonly used words in verb phrases: has, have, had, be, am, is, are, will, ....

Example: You will never completely finish learning.

Recognizing Subjects and Objects of Verbs

PATTERN: Subject + verb + indirect object + direct object


The bookstore always sells to students many books.

To find subject, use verb and ask a question beginning with who or what:

Who sold the books?

To find direct object, find subject and verb; then use them in a question ending with whom or what:

The bookstore sold what?

Transitive verb: Verb that requires a direct object to complete its meaning. Example:

High winds leveled the building.

Learn to recognize meaningful English word orders. The most commonly used patterns are:

PATTERN 1: Subject + verb

PATTERN 2: Subject + verb + direct object

PATTERN 3: Subject + verb + indirect object + direct object

Sometimes these patterns are rearranged:

Example: His last question I did not answer.

PATTERN: Object + subject + verb

Recognizing the Eight Parts of Speech


A part of speech used to make a statement, to ask a question, or to give a command or direction.

Examples: notify, notifies, are notifying, notified

Note: Do not confuse verb forms with verbs! Examples of verb forms:

"a word having the characteristics of both verb and adjective; an English verbal form that has the function of an adjective and at the same time shows such verbal features as tense and voice and capacity to take an object" [Webster Ninth New Collegiate Dictionary]

"She gave him written instructions."

("Written" is a modifier.)

"the English verbal noun in -ing that has the function of a [noun] and at the same time shows the verbal features of tense, voice, and capacity to take adverbial qualifiers and to govern objects" [Webster Ninth New Collegiate Dictionary]

"His writing all night long tired him."

("Writing" is the subject!)

"a verb form normally identical in English with the first person singular that performs some functions of a noun and at the same time displays some characteristics of a verb and that is used with to (as in ``I asked him to go'') except with auxiliary and various other verbs (as in ``no one saw him leave'')" [Webster Ninth New Collegiate Dictionary]

"I want to write."

("To write" is the direct object.)

"The urge to write left him."

("To write" is a modifier.")


Examples: man, men; kindness, kindnesses; United States; an understanding; nation's, nations'

A part of speech that names a person, place, thing, idea, animal, quality, or action.


The breakthrough came just before midnight.


Examples: I, me, my, mine, myself; they, you, him, it, this, these; who, whose, whom; which, that one, ones, one's; both, everybody, anyone.

A part of speech that serves the function of a noun in a sentence.


He paid them for it.


Examples: good; young, younger; youngest; a, an, the three men, educated people, this day

A part of speech that modifies or qualifies nouns and pronouns; sometimes they modify gerunds. Generally adjectives are placed near the words they modify.


Tired and disheartened, she decided that the problem was unsolvable.


Examples: rarely saw, call daily, soon left, left sooner , nearly always cold, very short

A part of speech regularly used to modify a word or word group other than a noun or pronoun.


Do you write well?


Examples: at times, between us, because of rain, before class

A part of speech that is used to show the relationship of a noun or the object of the preposition to some other word in the sentence.


The answer is in the book.

(Shows the relationship of the "book" to the noun "answer.")


Examples: Math and Computer Science, in or out, long but informative, long because it is complex

A part of speech used to connect words, phrases, or clauses.


Ouch! Oh, pardon me.

A part of speech used for simple explanations.

Recognizing Phrases and Subordinate Clauses

PHRASE: A group of related words without a subject and a predicate and functioning as a single part of speech.


   Verb phrase:  The computer has crashed.

   Noun phrase:  The fastest processor is the DEC alpha.

   Prepositional phrases:  The class is in McBryde Hall.

   Participial phrases:  A borken eyeglass is useless..

   Gerund phrase: Reading a manual is tiring.

   Infinitive phrases:  That is the problem to be solved now. 

CLAUSE: A group of related words that contains both a subject and a predicate and that functions as a part of a sentence.

SUBORDINATE (or dependent) CLAUSE: A subordinate clause is not a sentence, and functions as a single part of speech -- as a noun, an adjective, or an adverb.


I must admit that CS5014 is my first computer science class.
     (Noun clause functioning as a direct object)

The first Computer Science class that I ever had was CS5014.
     (Adjective clause modifying "class")

Recognizing Main Clauses and Various Types of Sentences


     When I arrive on campus, I first check my mailbox.


     When I first arrive on campus.


     I first check my mailbox.

Classifications of sentences:

  1. Simple sentences: those with only one subject and one predicate
  2.      Example: The proof is straightforward.
  3. Compound sentences: those made up of at least two main clauses
  4.      Example:  One window contains text, and the other window
         contains graphics.  
  5. Complex sentences: those made up of one main clause and at least one subordinate clause
  6.      Example: The proof is omitted because it is lengthy.
  7. Compound-complex sentences: those made up of at least two main clauses and at least one subordinate clause
  8.     Example:  The proof is omitted because it is lengthy, but
        a proof outline is given below.

Sentence Fragment


Never put a period at the end of a fragment.


A part of a sentence -- such as a phrase or a subordinate clause -- written with the capitalization and punctuation appropriate to a sentence


     A computer consists of
     1. A CPU.
     2. A main memory.
     3. I/O devices.

Correctly written:

     A computer consists of
     1. a CPU,
     2. a main memory, and
     3. I/O devices.

(Click here for rules on display lists, and here for rules on colon use.)

Test for Sentence Completeness:

When proofreading a manuscript, test each word group written as a sentence to see if it passes the following two tests:

  1. it has at least one subject and one predicate, and
  2. the subject and predicate are not introduced by a subordinating conjunction or by a relative pronoun.

Example of violation of test (2):

When the input is negative, especially if a user hits the wrong key.

(Subject is "input," verb is "is." However, they are introduced by subordinating conjunction "when.")

Comma Splice and Fused Sentence

Do not carelessly link two sentences with only a comma (comma splice) or run two sentences together without any punctuation (fused sentence).


Sentences: The processor is a Pentium. It runs three times faster than an 80486.

Comma splice: The processor is a Pentium, it runs three times faster than an 80486.

Fused sentence: The processor is a Pentium it runs three times faster than an 80486.

How to correct a comma splice or a fused sentence

Comma splice example:

The processor is a Pentium, it runs three times faster than an 80486.

Correct either a comma splice or a fused sentence by one of the following methods:

  1. Subordinate one of the main clauses -- usually the best method.
  2. Corrected: The processor is a Pentium, which runs three times faster than an 80486.

  3. Make each main clause into a sentence.
  4. Corrected: The processor is a Pentium. It runs three times faster than an 80486.

  5. Join the main clauses with a semicolon.
  6. Corrected: The processor is a Pentium; it runs three times faster than an 80486.


  7. Join the main clauses with a comma plus a coordinating conjunction (and, but, or, nor, for, and sometimes so and yet).
  8. Corrected: The processor is a Pentium, and it runs three times faster than an 80486.


Conjunctive Adverbs and Transitional Phrases Require Semicolons

CONJUNCTIVE ADVERBS: An adverb used to connect or relate main clauses:

     accordingly, also, anyhow, besides, consequently, 
     furthermore, hence, henceforth, however, indeed, 
     instead, likewise, meanwhile, moreover, nevertheless, 
     otherwise, still, then, therefore, thus, and so on. 

Example: I don't like the answer; however it appears to work.

TRANSITIONAL PHRASE: A phrase used to provide transition between clauses or sentences:

     as a result, at the same time, for example, in addition, 
     in fact, in other words, on the contrary, on the other hand, 
     that is  


Past papers conjectured that the answer is zero; on the contrary, it is one.

General rule:

Conjunctive adverbs and transitional phrases connecting main clauses are preceded by a semicolon.

Adjectives and Adverbs

Recall that:

Suffixes that turn nouns into adjectives: Noun -> Adjective

     -al, -ic, -ish, -like, -ly, -ous


The danger is clear. [Noun]

The answer is dangerous. [Adjective]

Suffix that turns an adjective into an adverb: Adjective -> Adverb



formal proof

formally prove

Sentence Patterns Containing Adverbs and Adjectives

First some definitions used in subsequent patterns:

Word or words that completes the sense of
Linking verb:
A verb which relates the subject to the subject complement.

Examples of linking verbs:

forms of to be, feel, look, smell, sound, taste, appear

PATTERN 1: Subject + Linking verb + Subject complement


He felt good.

He is good.

[In above examples, "good" is an adjective modifying "he."]

PATTERN 2: Subject + verb + adverb

In pattern 2, the adverb refers to the action of the verb.


He searched quickly for the answer.

[The adverb "quickly" qualifies "searched."]

PATTERN 3: Subject + verb + object + object complement

In pattern 3, the object complement is an adjective that modifies the object.


The boy dug the hole deep. ["deep" hole]

Do Not Misuse Noun Forms As Adjectives


I sometimes forget mathematics principles.


I sometimes forget mathematical principles.


Use the proper case form to show the function of pronouns or nouns in sentences.


  1. Subjective (or nominative)
  2. Possessive
  3. Objective

English is easier than some other languages because nouns and some indefinite pronouns (anyone, someone, everyone, and so on) have a distinctive case form only for the possessive (the student's notebook).

But a remnant of the origin of English is that the six pronouns have distinctive forms in all three cases and must be used with care:

Subjective:  I       we      he, she       they      you      who
Possessive:  my      our     his,her       their     your     whose
             (mine)  (ours)  (his),(hers)  (theirs)  (yours) 
Objective:   me      us      him, her      them      you      whom

Examples of Cases

Subjective case:

He and I solved the problem together.

Possessive case:

That is his solution.

His solving the problem was a breakthrough. [Varied order]

Which Case to Use for Pronoun in Apposition

Which of the following is correct?

Judging which is correct requires the definition of appositive:

A noun or noun substitute set beside another noun or noun substitute and identifying or explaining it.


I met Maria, a physicist.

[Physicist is in apposition with Maria.]

Rule: An appositive takes the same case as the noun or pronoun with which it is in apposition.

Thus only the second and third of the above sentences are correct.

Which Case to Use for Objects

Which of the following is correct?

In formal writing, use whom for all objects.

Thus only the first and last of the above sentences are correct.

Which Case to Use for Complement of "to be"

Which of the following is correct?

Use the subjective case for the complement of the verb "be."

PATTERN: Subject + linking verb "be" + subject complement

Thus "It was I who solved the problem." is correct!

Expressing Third Person Without Gender

The user should turn on his computer
was correct; now usually regarded as inapproriate

One should turn on one's computer.
regarded as stilted in Americal English

The user should turn on his/her computer.

Users should turn on their computer.
incorrect but frequently used

Users should turn on their computers.
pluralizing; one good solution

The user should turn on the computer.
Turn on your computer.
rephrasing; another good solution


Rule: Make a verb agree in number with its subject.


The risk of the experiments seems great.
[Singular subject/verb: risk seems]

The risks of the experiments seem great.
[Plural subject/verb: risks seem]

Rule: Make a pronoun agree in number with its antecedent.


The author types her own manuscripts.
["Author" and "her" are singular.]

The authors type their own manuscripts.
["Authors" and "their" are plural.]

Hint:To avoid mistakes, underline each subject/verb and antecedent/pronoun and compare their number.

Rules for Subject/Verb Agreement

  1. Subjects joined by and are usually plural.
  2. Ex.: Consequently, 0 and 1 are solutions. [plural verb]

  3. Singular subjects joined by or, nor, either...or, or neither...nor usually take a singular verb.
  4. Ex.: Either 0 or 1 is a solution. [singular verb]

  5. When used as subjects, such words as each, either, neither, another, no one, nothing regularly take singular verbs.
  6. Ex.: Each student knows the answer. [singular verb]

  7. When regarded as a unit, collective nouns, as well as noun phrases denoting quantity, take singular verbs.
  8. Ex.: The whole class is active. [singular verb because class is a unit]

  9. Nouns plural in form but singular in meaning usually take singular verbs. Consult a good dictionary when in doubt.
  10. Ex.: Physics fascinates me. [singular verb]

  11. The title of a single work, even when plural in form, takes a singular verb.
  12. Ex.: Kleinrock's Queueing Systems also contains the proof. [singular verb]


Abbreviations and Acronyms

  1. On first reference to a mnemonic (e.g., NCR) or acronym (e.g., LASER), use full spelling of term, followed by shortened form in parentheses.
  2. For subsequent references use the mnemonic (spell the letters) or acronym (readable).


    These theories and tools are the subject of the emerging field of knowledge discovery in databases (KDD). At an abstract level, the KDD field is concerned with the development of methods and techniques for making sense of data.

  3. Be sure to distinguish proper names from acronyms:
  4. Examples:

    I use Pascal.

    I use FORTRAN. (FORmula TRANslation)

  5. Form plural of all-capitalized mnemonics and acronyms by adding lowercase s; no apostrophe is necessary.
  6. Example:


Compound Words

  1. Compound words are words formed from the combination of two or more words.
  2. Compound words may be:

  3. Check the most recent dictionary to identify which of the three to use.
  4. For coinages too recent to appear in a dictionary, check with journals (especially IEEE Transactions or ACM Transactions) or professional societies.

  5. Sometimes recent coinages first appear as hyphenated, and eventually are written without the hyphen.
  6. Example: e-mail and later email

  7. Often a compound word is hyphenated when used as an adjective, but but not when used as a verb:
  8. Examples:

    Adjectives: sign-up sheet, pop-up menu

    Verbs: sign up, pop up


Parallel Construction

  1. In parallel construction, all the items in a series have the same grammatical form.
  2. Items joined by and, or, not, but, not only . . . but also, both/and, either/or, neither/nor should be parallel.
  3. Poor: A time not for action but words.

    Better: A time not for action but for words.

  4. Use parallel construction in definitions:
  5. Poor: To corrode is wearing away.

    Better: To corrode is to wear away.

  6. Use parallel construction for items in a series:
  7. Poor: To observe, to classify, deduce -- these are great pleasures for the scientist.

    Better: To observe, to classify, to deduce -- these are great pleasures for the scientist.


  1. Make all items in the list parallel. If, for instance, one item begins with a phrase, so must the others.
  2. Use hanging indents when formatting a list as a display.
  3. Use initial capitals when each item in a displayed list is a complete sentence. Close each sentence with a period.
  4. Each trial t (t = 1,2, ...) proceeds as follows:

    1. The learner receives instance vector xt in RN.
    2. The learner is required to compute a prediction yt in R.
    3. The learner receives a reinforcement signal rt in R.

    When the list contains phrases:


    Graphs are either

    When displaying words or phrases that you want to set off each item visually, begin each with a capital.

    Know the location and use of all safety equipment:

  5. Use an enumerated list when the lead-in sentence states how many items are on the list, or when you refer to list items by number in another part of the document.
  6. See the discussion of the colon later for rules on when to use a colon to introduce a list.
  7. Numbers: Figures Versus Words

    Use figures:

    1. with units of measure:
    2. 5s


    3. when the context is mathematical:
    4. a factor of 3

    5. to designate items:
    6. Section 3

      Unit 4

    7. for figure or table references:
    8. See Figure 3.

    9. for all numbers in a series if one item in the series is 10 or greater:
    10. Experiments 1, 2, and 3 included 7, 29, and 8 subjects, respectively.

    Use words:

    1. for numbers below 10, both cardinal and ordinal, unaccompanied by a unit of measure:
    2. fifth instance

      five nodes

    3. for numbers below 10, even when accompanied by a unit of measure, if the use is not technical:
    4. I worked on the project five years ago.

    5. for numbers that begin a sentence:
    6. Fifty-four subjects participated.

    7. for common fractions:
    8. one-fourth of the sample



  1. Use 's to form possissives:
    1. Use 's to form the possessive of singular nouns.
    2. Example: Fermat's last theorem

    3. Usage varies if the noun ends in sibilant sounds (the sound of s or z). In most cases, simply add 's.
    4. Examples:

      The waitress's table

      Loise's book

    5. But there are exceptions.
      1. To form the possessive of (ancient) names ending in a sibilant sound, add only an apostrophe.
      2. Example: Moses' laws

      3. Use only the apostrophe with plural nouns ending in s or es. Add 's for all other plural nouns.
      4. Examples:

        Two months' delay

        For conscience' sake

        Children's department

    6. See rule 1 in Strunk for further information on possessives.
  2. Note that it's is the contraction of it is. Pronomial possessives (its, yours, his, hers, theirs, ours ) do not use an apostrophe.
  3. Use the apostrophe for the plurals of letters and symbols.
  4. Examples: Dot the i's and cross the t's.

  5. No apostrophe is needed for numbers.
  6. Example: during the 1990s

  7. No apostrophe is needed for the plural of all capitalized mnemonics and acronyms: PESs


Note: A space should never occur before a colon.

  1. Use a colon to introduce a list.
  2. Example: Select one category: poor, average, good.

  3. Use a complete statement before a colon. Don't insert a colon between verb and object, preposition and object, or verb and complement.
  4. Poor: The meetings are in: Iowa, Texas, and Utah.

    Better: The meetings are in the following states: Iowa, Texas, and Utah.

  5. Use a colon to introduce a restatement or explanation. The colon must link two sentences. The initial letter of the second sentence may be capitalized.
  6. Example: We are left with one question: Who will pay?


The six basic uses of the comma are

  1. to set off introductory expressions
  2. to set off parenthetical information
  3. to separate long independent clauses joined by and, but, for, or, nor, so, yet
  4. to separate items in a series
  5. to set off indirect and direct quotes
  6. to set off degrees and titles that appears after a name

Explanations of the six uses...

  1. To set off introductory expressions
    1. To set off introductory subordinate clauses:
    2. Example:

      Because we were running several tests that day, we were late to the meeting.

    3. To set off introductory adverbial phrases:
    4. Example:

      Due to a diminishing tax base, state financed universities increase tuition annually.

    5. If the adverbial phrase is short (e.g., fewer than five words), the comma may be omitted.
  2. To set off parenthetical information
    1. Use commas to set off parenthetical words and terms (however, therefore, consequently, e.g. [Latin "exempli gratia," English "for example"] ), i.e. [Latin "id est," English "that is"]).
    2. Example:

      We read the proof; few of us, however, were convinced that the theorem was true.

      The numbers are relatively prime (i.e., neither number divides the other).

      Note: A space should never occur before a comma (e.g. , this is wrong).

    3. Use commas to set off parenthetical phrases.
    4. Example:

      The manuscript, along with a cover letter, was sent to the editor.

    5. Use commas to set off parenthetical clauses. A parenthetical clause gives nonessential or nonrestrictive information.
    6. Essential:

      He spent hours reading the paper that arrived in today's mail.

      Nonessential: He spent hours reading "Broadcast Algorithms for Hypercubes," which arrived in today's mail.

  3. To separate long independent clauses joined by and, but, for, or, not, so, yet
  4. Example: The experiments turned out to be a disaster, and I wound up canceling my vacation to repeat them.

  5. To separate items in a series
    1. Use commas to separate three or more items, phrases, or clauses in a series. I prefer the comma before the last item because its ommission may lead to ambiguity.
    2. Example: Experimental studies, theoretical models, and anecdotal evidence all suggest that the phenomena is real.

    3. Use commas to separate coordinate adjectives (adjectives that could be linked logically by and ).
    4. Example:

      Long, complex trajectories are hard to model.

      Long and complex trajectories are hard to model.

      Sometimes in technical writing strings of adjectives preceding nouns contain no commas:


      a 5-hp 230-V dc shunt motor

      a mass storage control protocol

  6. To set off indirect and direct quotes
  7. Examples:

    The manager asked, "Who will take responsibility?"

    The question we ask ourselves is, Who will take responsibility?

  8. To set off degrees and titles that appear after a name
  9. Example:

    Judith Sinclair, Vice-President, chaired the meeting.


[See also "Compund Words" for another use of the dash.]

A dash is typewritten as two hyphen keystrokes: - -

Some word processors and text formatters convert two successive dashes to a wide horizontal line (an em dash).

Note: Use three dashes in LaTeX or Tex.

Uses of dashes:

  1. to provide technical definitions
  2. Example:

    Using integrated circuits -- tiny slices of pure silicon embedded with traces of impurities -- engineers reduced a roomful of vacuum-tubes to a tiny black box.

  3. to set off parenthetical phrases
  4. Example:

    If he insists on visiting -- and I hope he won't -- then please let me know.

  5. to set off parenthetical remarks with commas within them
  6. Example:

    The triathlon events -- running, swimming, and biking -- test one's endurance.

  7. to set off summary statements
  8. Example:

    Okra, squash, and peas -- these are the vegetables that I most dislike.

    Strunk and White state, "A dash is a mark of separation stronger than a comma, less formal than a colon, and more relaxed than parentheses." [p. 9]


An ellipsis is three points: ...

Use an ellipsis to represent deleted material in a sentence. Use a space before and after an ellipsis if it occurs within a sentence.


Conrad defines visualization as "a representation ... of an abstract object through spatial relationships."

Use four points for ommissions at the end of a sentence.


Conrad defines visualization as "a representation of an abstract object through spatial relationships...."

In LaTeX, use \ldots to produce an ellipsis.


Use parentheses

  1. for figure and table citations
  2. Example:

    The curve resembles a sine function (Figure 3).

  3. to introduce abbreviations and acronyms
  4. Example:

    Neptune's atmosphere is dominated by the Great Dark Spot (GDS).

  5. for asides, particularly for information that clarifies procedures or results
  6. Examples:

    Omit commas after short introductory adverbial phrases (less than five words).

    Herbert J. Muller (1905-1967) states that instability is one of the conditions of life.

  7. in figure captions to identify, explain, or direct reader attention:
  8. Example:

    Figure 1. Two views of the keyboard: Installing the template (left); raising the legs (right)

  9. to enclose numbers of items in lists that are run into text, rather than displayed:
  10. Example:

    Two solutions are compared: (1) computational geometry and (2) analysis.

    There is no consensus on whether to put a period or other terminal mark after a whole sentence beginning with a capital within parentheses:


    (This is a whole sentence.)

    The mistake (see Figure 7) is ubiquitous.

Note: Never put a space after ( or before ).


Use brackets

  1. to set off editorial corrections
  2. Example:

    He wrote, "Dear fiends [sic]."

  3. to set off interpolations in quoted matter
  4. Example:

    "Not once did he [Richard Wagner] compromise."

  5. to replace parentheses within parentheses
  6. Example:

    Read the old CS5014 text (Elements of Style [New York: MacMillan, 1979]).


Use a semicolon

  1. to link independent clauses
  2. Example:

    The answer is clear; let's act.

    Do not let an elliptical construction -- one in which words are omitted but clearly understood -- fool you.


      The logic and the mathematics are wholly impeccable; the premises wholly invalid.

      The second clause omits the word "are."

  3. to separate citations
  4. Example:

    A large number of decision tree and rule-induction algorithms are described in the machine learning literature (Quinlan 1992; Apta and Hong 1996; Breimann et al. 1984).

Quotation Marks

Enclose material copied from other sources in double quotes:

Rogers defines categorical data as "a set of values for which no total ordering exists."

If the material you copy contains double quotes, change them to single quotes:

The 1994 report argues that "extensive simulation of caches (e.g., 'proxy' servers) is required."

Use double quotations for the titles of works published within other works (e.g., conference and journal articles, book chapters):

The best paper title I've ever read is "Instance-Based Learning."

Should Punctuation Go Inside or Outside a Closing Quotation Mark?

The normal style rules in English follow those of printers:

  1. Put commas and periods inside the quotation mark:
  2. He said, "Call home."

  3. Put colons and semicolons outside the quotation mark.
  4. Put dashes, question marks, and explanation marks inside the quote only if they apply to the quoted material:
  5. The paper is called "Will C Survive?"

    What really is the definition of "chaos"?

However, in Computer Science Rule 1 can lead to confusion:

My address is "abrams@vt.edu."

Most editors suggest choosing clarity first. Thus they recommend putting the period outside the closing quotes anytime it might cause confusion. Therefore write:

My address is "abrams@vt.edu".

Micellaneous Usage Points

Verb Tense

Generally, try to use the present tense.

Use the present tense for the introduction:

This paper explores coupling the object model with concurrent execution. The first section reviews the literature...

Use the present tense in the introduction for statements of fact:

Shapiro's work shows that the problem is NP-complete.

Use the past tense for a procedural section:

The data was first subjected to a KW statistical test. Then the data was partitioned and was tested again.

Use the present tense for discussion:

This method provides a means for studying a new class of symmetries.... We are also investigating analogous transitions.

Use the present tense for results:

The data in Table 1 indicate that ...

Active versus passive voice

  1. Try to avoid the passive voice.
  2. Passive: The problem is stated in section 2.

    Active: Section 2 states the problem.

  3. Sometimes you must choose between using first person/active voice and using third person/passive voice:
  4. First person: We chose the first for simplicity.

    Passive voice: The first was chosen for simplicity.

Strengthening your writing with adjectives/adverbs

  1. Do not use an adverb with an adjective that cannot be qualified
  2. Wrong: most unique, absolutely essential, quite impossible

    Correct: unique, essential, impossible

  3. Do not use redundant adverbs
  4. Examples:

    The proof is very easy.

    I found the paper extremely interesting.

  5. Select a precise adjective that requires no adverbs, possibly with the aid of a thesaurus
  6. Weak: The proof is very easy.

    Stronger: The proof is elementary.

    Weak: I found the paper extremely interesting.

    Stronger: I found the paper captivating.

  7. Do not use nouns as adjectives
  8. Poor: A method for iteration parameter estimation...

    Better: A method for estimating iteration parameters...


  1. Use notation that is consistent with its meaning
  2. Poor: ker(A) denotes null-space, and null(A) denotes the kernel

    Poor: Let n and i denote, respectively, the capacity and number of jobs in a queue.

    Better: Let c and n denote, respectively, the capacity and number of jobs in a queue.

  3. Do not suddenly use a synonym of a term
  4. Example:

    1. Factorization Program

    This section describes the algorithm to factor...

  5. Use consistent spelling
  6. Example: Consider an open queueing network. Recall that a product-form queuing network ...

Improving the flow of thoughts with linking words

Avoid abrupt changes in mood or direction from sentence to sentence within a paragraph.


Once we move from a convex program to a general nonlinear program, matters become far more complicated. Certain topological assumptions are required to avoid pathological cases. The results apply only in a neighbourhood of a constrained minimizer, and involve convergence of subsequences of global minimizers of the barrier function.


Once we move from a convex program to a general nonlinear program, matters become far more complicated. In particular, certain topological assumptions are required to avoid pathological cases. Furthermore, the results apply only in a neighborhood of a constrained minimizer, and involve convergence of subsequences of global minimizers of the barrier function.

However, do not overuse linking words!

A list of linking words is given on page 41 of [H].

Be Precise in What Your Sentences Express


"According to Theorem 1.1, a single trajectory X(t,x) passes through almost every point..."

The author meant to say that for every point there is a unique trajectory that goes through it.

A good test is to ask, "Can the reader take this sentence literally?" If the answer is no, then rewrite the sentence!

What to Call Yourself

Possible choices:

  1. I showed in [3] that...
  2. We showed in [3] that...
  3. The author showed in [3] that...
  4. It was shown in [3] that ...

Sentence (4) uses passive voice, which should be avoided.

Sentence (3) has a formal, stitled air, which is distracting.

Sentence (2) is permissible, even with a single author, in the sense of "the reader and I."

Sentence (1) is fairly uncommon today.

The choice of (1) or (2) is a matter of style. I suggest avoiding the first person whenever possible, but not at the expense of using the passive voice.

The Ten Commandments of Good Writing

Find all usage errors in the following 10 sentences

Source: N.J. Higham, Handbook of Writing for the Mathematical Sciences, Philadelphia: SIAM, 1993, p. 33

  1. Each pronoun should agree with their antecedent.
  2. Just between you and I, case is important.
  3. A preposition is a poor word to end a sentence with.
  4. Verbs has to agree with their subject.
  5. Don't use no double negatives.
  6. Remember to never split an infinitive.
  7. When dangling, don't use participles.
  8. (A participle is a verb form used as an adjective.)

  9. Join clauses good, like a conjunction should.
  10. Don't write a run-on sentence it is difficult when you got to punctuate it so it makes sense when the reader reads what you wrote.
  11. About sentence fragments.

Frequently Asked Questions

Q. When is "which" versus "that" used?

A. Rules:

  1. Use "that" (or "who") to refer to people.
  2. Example: He is the person that discovered X-rays.

  3. "That" defines and restricts; "which" informs and does not restrict.
  4. Examples:

    Consider the Pei matrix, which is positive definite. ("Positive definite" gives information about the matrix.)

    Consider the Pei matrix that is positive definite. (Distinguishes one from many Pei matrices.)

    Usually a which-clause appearing inside a sentence is surrounded by commas. A which-clause appearing at the end of a sentence is preceded by a comma.

Q. When is the article "a" versus "an" used?

A. I suggest two rules:

Rule 1:

"One of a class of speech sounds characterized by constriction or closure at one or more points in the breath channel."
"One of a class of speech sounds in the articulation of which the oral part of the breath channel is not blocked and is not constricted enough to cause audible friction."


a one-man show

a unit (The long "u" causes friction.)

a heavy load

an historic moment (The "hi" sound causes no friction.)

an honest man

Rule 2: For acronyms, pronounce the acronym to identify whether to use "a" or "an." For mnemonics, pronounce the first letter.


an IBM product ("I" is a vowel.)

a FORTRAN program ("FORTRAN" starts with a consonant.)