a math sequence who verb is equal

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a mathematics sequence whose verb is equal

The Grammar according to West

by Douglas B. West


I have actually been accumulating observations around writing math for plenty of years.

These conclusions developed both from writing textbooks and from noting writing errors commonly made by mine thesis students and in files submitted come journals.

My first objective was to train my students, in order to reducing the time necessary to edit their theses.

As the document grew, ns made that publicly easily accessible in the hope the others may discover it useful. I have received a broad selection of responses, mainly positive.

If friend don’t uncover it useful (or if you object to that on principle), then please overlook it. Ns hope to do some authors of mathematics

(especially students and also non-native speakers of English) aware of worries they might not have actually considered;

small transforms can produce mathematical writing that is easier to check out by more comprehensive audiences.

why treatment in writing math is needed

After an introduce explanation of why care in writing mathematics is needed, I talk about (1) math style, (2) notation and terminology, (3) punctuation and also English grammar as supplied in math writing, and (4) English usage for non-native speakers.

Some points room minor distinctions, but even these make mathematical composing clearer when used consistently.

My intent is not to make writing rigid, yet rather to make it transparent to avoid distracting the reader by ambiguities or awkwardness in the flow of the narrative.

I note that a variety of other articles and even publications have been released on writing mathematics;

see several of these here.

I perform these simply to make alternate viewpoints available, without judgment pro or con. One contrast to note is that my list listed below focuses on reasonably specific items.

I have actually not yet consisted of much discussion of the basic structure of one article; several of these references comment on that.

Introduction and Motivation

Live math conversations use numerous shortcuts that room inappropriate in an accurate mathematical writing. The paper definition is recognized by all participants, and also shortcuts evolve to conserve time. Furthermore, the speaker can automatically clarify ambiguity.

Without immediate access to the author, written mathematics must usage language an ext carefully.

Also, mathematical ideas are abstract, without context from everyday experience, therefore the writing need to be an ext consistent to make the an interpretation clear.

Outside mathematics, imprecise writing can still it is in understood because the objects and also concepts questioned are familiar.

Some mathematicians object to some of my recommendations. Plenty of time-honored techniques in the writing of mathematics are grammatically incorrect.

These mistake in writing cause no difficulty for readers with enough mathematical sophistication or familiarity v the subject,

but it is unnecessary come restrict the audience to such readers. A bit of treatment leads come clearer composing that makes mathematics much more easily easily accessible .

and readable come a broader and less specialized audience.

usage or grammar

Some languages have actually conventions of usage or grammar that lead to typical errors in English mathematical writing by their indigenous speakers.

Habits die hard

I apologize in breakthrough for my very own grammatical errors. Habits die hard, and also it is simple to err in applying principles that writing.

In particular, there are inconsistencies between what i propose here and also what I composed in my earlier books. Those publications were created in the vault millennium.

and I have learned numerous things about writing because then.

Also, i am a speaker of American English, and also some points are consistently different in british English (such together the treatment of “which” vs. “that” and the aversion to serial commas).

Some of my conclusions conflict with manuals the English style.

My conclusions room intended to produce clear mathematical writing that is an ext logically consistent than publishers’ conventions.

This uses especially to punctuation and also to native that serve as logical connectives.

I welcome corrections, suggestions/inquiries, and also “pet peeves” that may lead to additional items in later versions of this guide.

a math sequence whose verb is equal

Mathematical style

Abstract, Introduction, and also Conclusion.

We begin with the in its entirety structure of a research short article in mathematics.

The abstract states the outcomes as totally as feasible in a quick presentation.

Crucial devoted terms the reader demands to know to recognize the statements have to be defined.

The abstract stands on its own, especially in the age of electronic communication where it might be different from the rest of the paper.

and for this reason it consists of no numbered reference to the bibliography.

The an initial section the the document is one “Introduction” that need to motivate the problem.

discuss connected results, state the results an ext completely, and perhaps summarize the methods or the framework of the record or vital definitions.

concluding remarks

The development should also contain any concluding remarks or key conjectures.

There is generally small or no worth in a separate section of break up remarks. Together remarks either room redundant or contain details that reader usually look for in the introduction.

Readers who examine the complete details of the proofs have no require of a review in a finish section. Reader who do not check out the full details have no desire to go on come a finish section.

A math research short article is not read like a novel or even like an essay that looks for to “persuade” the reader; the does not require an epilogue.

Terminology and also notation (especially in discrete mathematics)

definition symbol “:=”. Part mathematicians usage this prize to show that the preceding symbol is being characterized to mean the succeeding object. If this wake up in a sentence prefer “Let :=

1,…,n“, climate the verb claims that the notation is being defined, and also the unique notation is unnecessary. If it wake up in a sentence about the object being defined.

“Consider a colour of :=1,…,n“, then it is an not correct Double-Duty meaning and need to be rewritten: “Consider a color of , where =1,…,n.”

Reading “:=” requires thinking “be identified to be” once preceded by “let”,

and it needs even an ext convoluted phrases when inserted in a Double-Duty Definition. This awkward notation is never ever needed and encourages grammatical errors.

English consumption in mathematics writing

introductory words. Indigenous or phrases favor “nevertheless”, “for example”, “to the contrary”, and “on the other hand” usually need to be be separate by commas indigenous the rest of the sentence.

Introductory preposition phrases are a little different. Ns am told the a phrase with one preposition (“In 1995”) go not require a comma.

but a phrase with 2 prepositions (“In respectable of 1995”) does. An additional reader speak me the an introductory expression with at least five words.

(perhaps we need to say five syllables) have to be followed by a comma. Ns would use the comma uneven the will is come lead into what follows as a solitary thought (see Hence/Thus/Therefore).

a math sequence whose verb is equal

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Mathematics (from Greek: μάθημα, máthēma, ‘knowledge, study, learning’) consists of the examine of together topics as amount (number theory),<1> structure (algebra),<2> an are (geometry),<1> and readjust (analysis).<3><4><5> It has no generally accepted definition.

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