UK MA 330 - A Sample Article for Mathematics Magazine

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A Sample Article for Mathematics MagazineJack Q. Firstauthor1XXXX UniversityCity, State [email protected] P. SecondauthorDepartment of Physics2ZZZZ CollegeCity, State 12345-6789This document is meant to help you prepare an Article for submissionto Mathematics Magazine. Of course, editorial decisions depend entirelyon what you say and how you say it. Nonetheless, we will all save time ifyou exercise s ome care in how you first present the paper.Now that I have caught your attention with an interesting introductoryparagraph, here is what you will find: specific information about the styleof Articles in the Magazine and a description of the LATEX code we preferthat you use to prepare your manuscript.Since this section is very clearly an introduction, I thought that labelingit “Introduction” would add nothing. Note that I am willing to use the firstperson in an Article and you might be as well. Another equally respectablechoice is “we,” even when there is only one author; this can create an author-reader partnership to work through the mathematics together. Whatevervoice you choose, consistency is important.You may be looking at this document in a variety of ways: the .p df or.ps files are meant to be viewed on a screen or printed, while the .tex file1Supp orted by the National Science Foundation.2Authors are in alphabetical order unless there is an extraordinary reason to do oth-erwise. Also, the author address includes a department only if the department is notmathematics. We use as few footnotes as p os sible in the Magazine. This one, for instance,contains information that really belongs in the body of the paper. The previous footnoteprobably belongs among the Acknowledgments at the end.1contains the codes used to create those viewable versions via the programLATEX. Even if you are a novice with TEX, there may be enough here toteach you what you need to know. And if you are an ace with TEX, we havea warning: please do not overload your document with special kludges andtricks that will only be removed later by our compositor.This document is prepared with extremely simple LATEX formatting, usingthe unadorned article template. It is designed for simplicity and easeof handling—not to imitate the Magazine’s final, typeset style in everydetail. For authors less familiar with LATEX, we offer a brief lesson, showinghow certain common elements of mathematical style are typeset using thisprogram. For hardcore technical specifications, please s ee the ElectronicPublication Guidelines [7].Notes on writing an ArticleArticles in the Magazine tend to be longer and more substantial than Notes,offering a broad overview of some field or making new connections. Beinglonger, they often benefit from more sectioning. We use the \subsection*command to create titles for these sections, which are not usually numbered(the * in \subsection* accomplishes this).To judge the length of your piece, consider that this document printsto six pages with the current code, but would run about four pages in theMagazine. The current settings produce a document that is generouslyspaced in consideration of referees’ eyesight.Few pieces of mathematical writing are entirely self-contained, althoughwe try to make Articles reasonably so. Consider providing a section ofbackground material that our more knowledgeable readers can skip. De-fine enough terms to enable an eager undergraduate student to read yourpiece without having to consult too many references.For readers intrigued by your exposition, you should provide friendlyreferences. Bibliographies may contain suggested reading along with sourcesactually referenced. In all cases, cite sources that are currently and readily2available.LATEX has a way to keep track of references automatically, which is il-lustrated in the code that ends this file. To refer to Halmos [3], you usea codename that you have created as a mnemonic, often the author’s lastname. LATEX keeps track, numbering the references in the order they appearin your list. If you add a reference (positioning it correctly in the list) thenumbers will be adjusted accordingly.Please follow our bibliographic format carefully, based on the examplesbelow. Entries may appear either in alphabetical order or in order of citation(but choose one order and stick to it). Journal titles are abbreviated as inMathematical Reviews, for instance, Amer. Math. Monthly; volume numbersof journals are set in bold. Authors names are not inverted: Frank A. Farris,not Farris, Frank A. [2]. The abbreviation pp. is used for books, but notjournal articles. Note the slightly different style for citing articles in theMagazine.How to do things in LATEX Roman letters used as variables will becorrectly italicized if enclosed with $s in your code, as in “functions f , g, andh.” This makes for typing lots of $s when writing in TEX. Other popularfonts are A, for sets and the like, and Z for the integers, etc.This last symbol, the “blackboard” Z, actually is not part of basic LATEX.If you look in the preamble of this document, the part before the \begin{document}command, you will se e the instruction \usepackage{amssymb} . This enablesyou to use the blackboard font, as well as certain special symbols:d , e , b , c , and so on.If you do not have this package, you are welcome to mark these symbols in byhand. While we are talking about packages, please do not use any packagethat redefines major environments, such as the theorem environment.LATEX is able to number theorems automatically, using what is called atheorem environment. This is usually overkill for pieces in the Magazine.3The following example shows a simple method for displaying theorems; thetheorem need not even be numbered unless you refer to it by number later.Theorem 1.Let a be any real number. Then a2> −1.Proof. The result follows from well-known properties of flabby sheaf co-homology over algebraically closed fields. This parody of a proof, the likes ofwhich you would not see in the Magazine, ends here, but you don’t need toinsert an end-of-proof marker. You could put a comment in the file to markthe e nd of the proof.A remarkable result that has been the target of many proofs in the Mag-azine is the Pythagorean theorem. If a, b, and c are the sides of a righttriangle, thena2+ b2= c2. (1)The equation above is called a displayed equation. The reference numberwas added using the equation environment (enclosing the code f or the equa-tion between


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