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Writing amath paper:Structure

Structure

Title

Abstract

Introduction

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Appendix

References

Writing a paper in mathematics: StructureWith material from “Writing a Math Phase Two Paper” by

Steven L. Kleiman

Writing a math paper: Structure

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Most papers have an abstract, an introduction, a numberof sections, which are numbered and titled, and a list ofreferences.

Only long papers will occasionally have a formal table ofcontents or index. This tends to happen in Proceedingsvolumes, but is usually suppressed by journals.

In some fields, papers routinely have a conclusion. Theconclusion discusses the results from an overall perspective,brings together the loose ends, and makesrecommendations for further research.

In mathematics, these issues are almost always treated inthe introduction, where they reach more readers.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Only long papers will occasionally have a formal table ofcontents or index.

This tends to happen in Proceedingsvolumes, but is usually suppressed by journals.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

In some fields, papers routinely have a conclusion.

Theconclusion discusses the results from an overall perspective,brings together the loose ends, and makesrecommendations for further research.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Title

Abstract

Introduction

Body

Appendix

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Sectioning

Sectioning involves more than merely dividing up thematerial;

you have to decide what to put where, what toleave out, and what to emphasize.

If you make wrong decisions, you will lose your readers.

There is no simple formula for deciding, because thedecisions depend heavily on the subject and the audience.

However, you must structure your paper in a way that iseasy for your readers to follow, and you must emphasizethe key results.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Sectioning

Sectioning involves more than merely dividing up thematerial; you have to decide what to put where, what toleave out, and what to emphasize.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Sectioning

Structure

Title

Abstract

Introduction

Body

Appendix

References

Sectioning

Structure

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Abstract

Introduction

Body

Appendix

References

Sectioning

Structure

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Introduction

Body

Appendix

References

The title

The title is very important.

If it is inexact or unclear, it will not attract all the intendedreaders.

A strong title identifies the general area of the subject andits most distinctive features.

A strong title contains no distracting secondary details.

If possible, avoid formulas in titles.

A strong title is concise.

Structure

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Introduction

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Appendix

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The title

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The title

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Introduction

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Appendix

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The title

Structure

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Introduction

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Appendix

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The title

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Introduction

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Appendix

References

The title

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Title

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Introduction

Body

Appendix

References

The abstract

The abstract is like the trailer of a movie.

First it identifies the subject; it repeats words and phrasesfrom the title to corroborate a reader’s first impression, andit gives details that didn’t fit into the title.

Then it lays out the central issues, and summarizes themost important results, if possible.

The abstract includes no general background material.

It is essentially a table of contents in a paragraph of prose.

Structure

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Introduction

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Appendix

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The abstract

First it identifies the subject;

it repeats words and phrasesfrom the title to corroborate a reader’s first impression, andit gives details that didn’t fit into the title.

Structure

Title

Abstract

Introduction

Body

Appendix

References

The abstract

First it identifies the subject; it repeats words and phrasesfrom the title to corroborate a reader’s first impression,

andit gives details that didn’t fit into the title.

Structure

Title

Abstract

Introduction

Body

Appendix

References

The abstract

Structure

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Introduction

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Appendix

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The abstract

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Introduction

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The abstract

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The abstract

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The abstract

The abstract allows readers to decide quickly about readingon.

While many will decide to stop there, the potentiallyinterested will continue.

The goal is not to entice all, but to inform the interestedefficiently.

Remember, readers are busy. They have to decide quicklywhether your paper is worth their time.

They have to decide whether the subject matter is ofinterest to them, and whether the presentation will enablethem to follow the arguments.

A well-written abstract will increase the readership.

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The abstract

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Introduction

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The abstract

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Introduction

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The abstract

Remember, readers are busy.

They have to decide quicklywhether your paper is worth their time.

Structure

Title

Abstract

Introduction

Body

Appendix

References

The abstract

Structure

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The abstract

They have to decide whether the subject matter is ofinterest to them,

and whether the presentation will enablethem to follow the arguments.

Structure

Title

Abstract

Introduction

Body

Appendix

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The abstract

Structure

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The abstract

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The introduction

The introduction is where readers settle into the “story,”and often make the final decision about reading the wholepaper.

Start strong; don’t waste words or time.

Your readers have just read your title and abstract, andthey’ve gained a general idea of your subject and treatment.

However, they are probably still wondering what exactlyyour subject is and how you’ll present it.

A strong introduction answers these questions with clarityand precision.

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The introduction

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The introduction

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The introduction

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The introduction

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The introduction

It identifies the subject precisely and instills interest in it bygiving details that did not fit into the title or abstract, suchas how the subject arose and where it is headed, how itrelates to other subjects, and why it is important.

A strong introduction touches on all the significant points,and no more.

A strong introduction gives enough background materialfor understanding the paper as a whole, and no more.

Put background material pertinent to a particular sectionin that section, weaving it unobtrusively into the text.

A strong introduction discusses the relevant literature. It ishelpful to cite a good survey or two, if available.

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The introduction

Structure

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The introduction

Structure

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Introduction

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The introduction

Structure

Title

Abstract

Introduction

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Appendix

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The introduction

A strong introduction discusses the relevant literature.

It ishelpful to cite a good survey or two, if available.

Structure

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Abstract

Introduction

Body

Appendix

References

The introduction

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The introduction

Finally, a strong introduction describes the organization ofthe paper, making explicit references to the sections.

It summarizes the contents in more detail than theabstract, and it says what can be found in each section.

It gives a road map, which indicates the route to befollowed and the prominent features along the way.

This road map is normally placed at the end of theintroduction to ease the transition into the next section.

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The introduction

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The introduction

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The introduction

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The body

The body discusses the various aspects of the subjectindividually.

In writing the body, your hardest job is developing astrategy for parcelling out the information.

Every paper requires its own strategy, which must beworked out by trial and error.

There are, however, a few guidelines.

First, present the material in small digestible portions.

Second, beware of jumping haphazardly from one detail toanother.

Third, if possible, follow a sequential path through thesubject.

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The body

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The body

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The body

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The body

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The body

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The body

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The body

If such a path doesn’t exist, simply break the subject downinto logical units, and present them in the order mostconducive to understanding.

If the units are independent, then order them according totheir importance to the primary audience.

There are three main reasons for dividing the body intosections:

(1) the division indicates the strategy of your presentation;

(2) it allows readers to quickly and easily find the informationthat interests them; and

(3) it gives readers restful white space, allowing them to stopand reflect on what was said.

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The body

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The body

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The body

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The body

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The body

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The body

When you title a section, strive for precision and clarity;then readers will have an easier time jumping to aparticular topic.

Don’t simply insert a title in the text, as is often done innewspaper articles, to recapture interest; rather, wind downthe discussion at the end of a section in preparation for abreak, and then restart the discussion in the next section,after the title.

When you refer to Section 3, remember to capitalize theword “Section”; it is considered a proper name.

Don’t subsection a short paper; the breaks will make theflow too choppy.

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Introduction

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The body

Don’t simply insert a title in the text,

as is often done innewspaper articles, to recapture interest; rather, wind downthe discussion at the end of a section in preparation for abreak, and then restart the discussion in the next section,after the title.

Structure

Title

Abstract

Introduction

Body

Appendix

References

The body

Don’t simply insert a title in the text, as is often done innewspaper articles, to recapture interest;

rather, wind downthe discussion at the end of a section in preparation for abreak, and then restart the discussion in the next section,after the title.

Structure

Title

Abstract

Introduction

Body

Appendix

References

The body

Structure

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The body

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The body

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Appendix

On occasion, papers have appendices, which may serve oneor more of the following purposes:

give special detailed information,

offer an alternative view of a topic in the paper,

provide a new proof (possibly more elegant than what isfound in the literature) of an important theorem that isused in the paper,

provide necessary general background to secondaryaudiences.

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Appendix

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Appendix

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Appendix

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Appendix

An appendix may be written by the author(s) of the paper.

In this case, it can be numbered like the sections, onlydistinguished from them by having the word “Appendix” inits title.

A paper may contain several appendices. In this case, theycan be distinguished from the other sections by beingnumbered with letters in place of numbers.

This sort of appendix usually appears before (and may alsocite from) the list of references.

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Appendix

An appendix may be written by the author(s) of the paper.In this case, it can be numbered like the sections,

onlydistinguished from them by having the word “Appendix” inits title.

Structure

Title

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Introduction

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Appendix

An appendix may be written by the author(s) of the paper.In this case, it can be numbered like the sections, onlydistinguished from them by having the word “Appendix” inits title.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Appendix

A paper may contain several appendices.

In this case, theycan be distinguished from the other sections by beingnumbered with letters in place of numbers.

Structure

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Abstract

Introduction

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Appendix

References

Appendix

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Appendix

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Appendix

An appendix can also be written by another author.

In thiscase the appendix can be thought of as a small separatepaper that is more closely linked to the paper it appearswith than if it would appear separately.

This sort of appendix may (but does not have to) appearafter the list of references, and may even have its own listof references.

Structure

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Appendix

An appendix can also be written by another author. In thiscase the appendix can be thought of as a small separatepaper that is more closely linked to the paper it appearswith than if it would appear separately.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Appendix

This sort of appendix may (but does not have to) appearafter the list of references,

and may even have its own listof references.

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Appendix

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The list of references

The list of references contains bibliographical informationabout each source cited.

The style of the list is different in technical andnontechnical writing; so is the style of citation.

In fact, several different styles are used in technical writing.

Different journals prescribe different styles for the articleand the list of references. Follow the prescriptions and usetheir style files and templates in order to avoid delays inpublication.

As to the precise appearance of the bibliographicalinformation, it is always a good choice to take it fromMath Reviews.

Structure

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Appendix

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Structure

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Structure

Title

Abstract

Introduction

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Appendix

References

Different journals prescribe different styles for the articleand the list of references.

Follow the prescriptions and usetheir style files and templates in order to avoid delays inpublication.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

Title

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Introduction

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Citing references in the text

The citation is treated somewhat like a parentheticalremark within a sentence.

Within the brackets and after the reference key, place as aservice specific page numbers, section numbers, theorem orequation numbers, preceded by a comma, as for instance in[5, Theorem 3.7, p.9]. However, it can be considered moreelegant to write “We use Theorem 3.7 of [5]” in place of“We use [5, Theorem 3.7]”.

If the citation comes at the end of a sentence, put theperiod after the citation, not before the brackets or insidethem.

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References

Within the brackets and after the reference key, place as aservice specific page numbers, section numbers, theorem orequation numbers, preceded by a comma,

as for instance in[5, Theorem 3.7, p.9]. However, it can be considered moreelegant to write “We use Theorem 3.7 of [5]” in place of“We use [5, Theorem 3.7]”.

Structure

Title

Abstract

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Appendix

References

Within the brackets and after the reference key, place as aservice specific page numbers, section numbers, theorem orequation numbers, preceded by a comma, as for instance in[5, Theorem 3.7, p.9].

However, it can be considered moreelegant to write “We use Theorem 3.7 of [5]” in place of“We use [5, Theorem 3.7]”.

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Footnotes and special abbreviations

In former times, bibliographic information was often givenin footnotes,

rather than in a separate list of references.

In these footnotes, the abbreviations “loc. cit.,” “op. cit.,”and “ibid.” were abundantly used.

Now footnotes are only used occasionally to add someinformation that would disrupt the flow of the text.

Bibliographic information should be given in a list ofreferences. In this way, it is more easily accessible. Lists ofreferences are even extracted by Math Reviews and put inthe review of the paper.

Footnotes are not used in references.

The abbreviations “loc. cit.,” “op. cit.,” and “ibid.” havebecome rare and rather appear in the text.

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In former times, bibliographic information was often givenin footnotes, rather than in a separate list of references.

Structure

Title

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Introduction

Body

Appendix

References

Structure

Title

Abstract

Introduction

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Structure

Title

Abstract

Introduction

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References

Bibliographic information should be given in a list ofreferences.

In this way, it is more easily accessible. Lists ofreferences are even extracted by Math Reviews and put inthe review of the paper.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Bibliographic information should be given in a list ofreferences. In this way, it is more easily accessible.

Lists ofreferences are even extracted by Math Reviews and put inthe review of the paper.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

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Introduction

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Structure of the list of references

For all that follows, keep in mind that the style andstructure of the list of references depends on theprescriptions of the journal or book in which your paper ispublished.

The following guidelines can be safely followedwhen such prescriptions are absent.

The reference key, usually a numeral, is enclosed in squarebrackets.

In the list of references, give the full page numbers of eacharticle appearing in a journal, a proceedings volume, orother collection; do not give the numbers of the particularpages cited in your text.

Structure

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Abstract

Introduction

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Appendix

References

For all that follows, keep in mind that the style andstructure of the list of references depends on theprescriptions of the journal or book in which your paper ispublished. The following guidelines can be safely followedwhen such prescriptions are absent.

Structure

Title

Abstract

Introduction

Body

Appendix

References

Structure

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Appendix

References

In the list of references, give the full page numbers of eacharticle appearing in a journal, a proceedings volume, orother collection;

do not give the numbers of the particularpages cited in your text.

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Referring to a journal article

The information about a paper in a journal is usually given inthe order and style shown below.

Author(s). Give at least one full name.

Title of article. In italics, first initial capitalized.

Name of journal. In abbreviation form.

Series number. In parenthesis, if applicable.

Volume number. In bold face type.

Year of publication. In parenthesis.

Page numbers. Give span of pages covered.

Recently, often the journal name is italicized, instead of thearticle name.

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Referring to an article or chapter in a book

The information about a paper (or chapter) in a book (such asa Proceedings volume) will first list author(s) and article orchapter title,

then insert “in” or “In:”, and then:

Title of book. Not in italics.

Editor(s). Insert “(ed.)” or “(eds.)” after the name(s) ofthe editor(s), or “edited by” before the name(s).

Series name, volume number and edition.

Publisher. Abbreviation form. Include name of city or statewhere published.

Year of publication. There can be several years, forinstance one referring to the year in which a conference washeld, and one referring to the publication of the book.Follow Math Reviews.

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The information about a paper (or chapter) in a book (such asa Proceedings volume) will first list author(s) and article orchapter title, then insert “in” or “In:”, and then:

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Editor(s). Insert “(ed.)” or “(eds.)” after the name(s) ofthe editor(s),

or “edited by” before the name(s).

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Year of publication. There can be several years,

forinstance one referring to the year in which a conference washeld, and one referring to the publication of the book.Follow Math Reviews.

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Abstract

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Year of publication. There can be several years, forinstance one referring to the year in which a conference washeld, and one referring to the publication of the book.

Follow Math Reviews.