ࡱ> LNKW@ (8jbjbqq X2 l$$$$$$$88888148*pLd, `? _$z$$pzzz $$ z88$$$$ z&z $$ e &88  ;z; zFormatting a Mathematical Paper Using MS Word Charles F. Peltier June 9, 2005 This document, is an example of the use of the template for formatting papers written for your mathematics courses. A number of styles have been defined to make the formatting easier they will be available at the left side of the formatting toolbar when you use this template. The styles will set proper indents and spacing before and after paragraphs. In some cases, they will also take care of font adjustments, but in many cases (because of the limitations of the program) you will have to take care of such adjustments as bold or underline or italic font styles. General Formatting The margins are set at 1 all around. The Normal style, used for ordinatry text uses Tumes New Roman font in 12 point size, with a .25 indent for the first line of each paragraph. Note that pages are numbered, the title [in Heading 1 style], author and date (in Normal style, but centered) are at the top of the first page, the bibliography is at the end of the paper. You can use the examples of special formats by copying and pasting them into your paper and then replacing the text with your own text. For a longer paper with multiple sections and chapters, see the document ''Formatting a longer Paper in MSWord'' which will include chapter headings, numbering schemes, etc. The section headings in this paper are formatted using the Heading 3 style (from the formatting toolbar far left side) Theorems, definitions and other formal statements Mathematical writing involves a number of special structures, which are reflected in the formatting of the pages. There are several types of statements that are specially laid out - titled in bold, not indented, numbered in a sequence, and set in appropriate type. Here are templates that can be used for all types of theorems, a template for definition. All theorems(corollaries, lemmas, etc.), definitions, examples, and remarks are numbered in order within a section or chapter. The title [Theorem, Definition, etc.] is set in bold type, not indented. There is a blank line before and after each of these structures, and after a proof. Definition 1. This is an example of the style for a definition. A definition gives the meaning of a new term, using only previously defined terms. Notice the term being defined is emphasized by being italicized and the rest of the text is not italicized. Theorem 2. This is an example of the style for a theorem. A theorem is a statement which states properties of a known object, makes the claim that an object with certain properties exists [or cannot exist] or gives a relationship between two (or more) known objects. [Notice that the statement is set in italic type] Proof. Every theorem has a proof (even if the proof is not written in every paper). The proof is likely to be broken into paragraphs and otherwise appear very much like any other text. Additional paragraphs would be indented as usual for text. The end of the proof is marked by a symbol at the right-hand margin, as shown here, and there is a blank line after the end. ( Notice the label Proof is not indented, but is italicized and followed by a period. Lemma 3. This is an example of the style for a lemma. A lemma is a specialized theorem used to organize a long proof by breaking it into sections (a ''helper theorem''). Corollary 4. The style for a corollary is the same as the style for a theorem. A corollary is a theorem which is a quick and easy consequence of some other theorem (a ''cheap theorem''). Proposition 5. The style for a Propositiion is the same as the style for a theorem. A proposition is a theorem giving an interesting, but not major, result. Propositions often function as lemmas, giving steps on the way to a big result (a "minor theorem"). Big Famous Theorem. This is an example of a named theorem- quoted from some other source and not included in the numbering system. Example 6. This is an example of the style for an example. Every example should have a heading which indicates what it shows [as in Example 8, below]. Remark 7. This is an example of a Remark - a comment that is important enough to be highlighted, but that does not move the main discussion forward. It would rarely be longer than two sentences. Definitions, theorems (all types -- lemmas, corollaries,propositions), examples, remarks are all numbered in the same sequence - as shown here. Figures (diagrams, illustrations), equations, and tables each have their own numbering sequences. Formulas, symbols, equations [Note: this is the point at which the advantages of learning TeX, instead of working with MS Word, become very clear]. Single-character symbols such as ( and ( may be inserted in text by using the Insert>Symbol menu command (that is, on the Insert menu, Select Symbol...). Some will be available in the (normal text) font (the font in which you are typing preferably Times New Roman) and many mathematical symbols are available in the Symbol font. The other options are not useful. Symbols and letters representing variables (x, y , etc.) should be put in italic type and set off with two (rather than one) spaces before and after. [Let x be the height of a tree rather than Let x be the height of a tree] The Equation Editor For more complicated symbols and expressions (integrals, summations), you will need to make extensive use of the Equation Editor add-in. You Insert an equation box by going to the Insert Menu and selecting Object... , then selecting Microsoft Equation in the window that opens. [If you are running Word on your own computer, it is worthwhile to go to the Tools menu, select Customize and use the Commands tab to put the Equation Editor alias on the toolbar, so that you can click on it to create and equation box. Its worthwhile adding the Insert symbol alias, as well] You cannot directly edit (except to copy/paste/delete) expressions entered using the Equation Editor but must double-click the expression to open an Equation Editor window. You can copy and paste equation boxes and then open and edit the new expression in the new space this is useful if you want to show changes in an expression as you carry out calculations, and would prefer not to re-type the unchanged parts. You enter equations/formulas/expressions in the Equation Editor by typing (for letters and other keyboard symbols) or by selecting structures and objects from a toolbar (see Figure 1.). Each box on the tool bar contains a number of related structures or objects [for example, the top left box contains less than or equal does not equal is approximately equal to etc. ], you select the piece you want by clicking on it. The spacebar does not work in the Equation Editor (the program controls spacing) use the tab key to move around in the expression. The options for summations, fractions, superscripts, etc. all contain spaces (represented by dotted boxes on screen) in which you type what you need they can be nested the box for an integral can have a fraction template inserted, for example.  Figure 1. The Equation Editor Toolbar Example 8. An example of an expression built up in the Equation Editor Construction of  EMBED Equation.3  After opening the Equation Editor (with the cursor in the location where the expression is wanted]: 1. Select the box with stuff below[Third set in second row of the toolbar, take the middle choice in 3d row], 2. Type lim in upper box. 3. Type x in the lower box (click or use tab to get into it), then select arrow (from 5th set, upper row) then type 3. 4. Use the tab key to move to next space, type 5, 5. Select parentheses from grouping symbols set (lower left on toolbar)[typing parentheses with keyboard will not allow them to change size for the exponent]; 6. Inside the parentheses type x, then 7. Select superscript (third set of symbols in lower row of toolbar first choice) & type 2. 8. Use tab to come out of superscript, type , type 1. 9. Tab out of the parentheses, type =, type 40 Then close the Equation Editor window to insert the equation in your document Displayed formulas Formulas that are longer than about a third of a line, and any important formulas, should be displayed set on a separate line and centered. If you will refer to the formula later, it should be numbered (formulas/expressions are numbered in order, separately from theorems, definitions, and examples)). Here is an example of a displayed formula:  EMBED Equation.3  [The stacked conditional part is obtained using 1. the left brace ({) from the grouping symbols box at the bottom left of the menu bar 2. the 2x2 array from the array box at the bottom right of the commands bar and 3. selecting text from the Style menu to type the if (with some spaces) and the otherwise so that they appear as text rather than variables or functions.] Here is a displayed and numbered formula. (1)  EMBED Equation.3   EMBED Equation.3  [Note that a centering tab is used in the middle of the line and the equation box is tabbed over after the number is typed. To get the if and the on to appear properly, it is necessary to change to Text style (in the Equation Editor) for these words and the preceding and following spaces] Figures (diagrams and pictures): Bibliography and Citations: References used in preparing a paper are listed in a strandard format. Here is a set of templates for bibliography entries for a book, a journal article, an article in a book, an article or chapter from an on-line book or journal, and a website with no specifically identified author or editor. Note the authors name is in Small Caps (obtained with Format>Font - and then check Small Caps OR more easily by copying the template and replacing the Authors Name with your authors name), some elements are in quotes and some are in Italic font. URLs (web addresses) are enclosed in angle brackets (<>) and typed in a monospaced font usually Courier. For a book (see [3]): Authors Name, Book Title, Publishers Name, Year of publication. For an article in a journal (published on a regular basis) (see [1]: Authors Name, Article Title, Journal Name volume (date), pages. There are common abbreviations for many journal names (as in the example) For an article in a book (see [4]) Authors Name, Article Title, in Book Title, Publishers Name, Year of Publication, pages. This format can be used with Chapter #: Chapter Title in place of Article Title if only one chapter is relevant. For and article obtained from a website (adapted from [5]) (see [5] and [2]) : Authors Name, Title of Article (or Chapter Title), Site name, OR Electronic journal name OR Title of on-line text, volume (date) (if a journal) OR Publisher (if a book) OR organization maintaining the website, daate posted, date accessed, Section/part/page used (if this is different from the title), . For an on-line book(see [5]): Authors Name, Book Title, Publisher, year of publication, date accessed, . this is the same format as for a printed book, except that date accessed and URL are added. For information on a website with no clearly identified author: (adapted from [5]) (see [6]): Site Name, date published (posted), organization or individual responsible, date accessed, Section/part/page used (if site has multiple pages), . References are listed in alphabetical order by authors (last) name [unauthored websites use first letter of the site name], numbered, with a hanging indent, as shown here. Be sure to move the indented margin so that all the text is to the right of all the numbers (more space needed if you have ten or more references). To cite a reference in text, enter the number (from the list) in square brackets at the end of the text from the reference. References [1] R. P. Boas, Can We Make Mathematics Intelligible?, Amer. Math Monthly 88(1981), pp.727-731. [2] Keith Devlin, Staying the Course, MAA Online, The Mathematical Associataion of America, June 2005, 29 June 2005, Devlins Angle, . [3] Leonard Gillman, Writing Mathematics Well, The Mathematical Association of America, 1987. [4] Paul R. Halmos, How to Write Mathematics, in Selecta, Expository Writing, Springer, 1983, pp.157-186. [5] Andrew Harnack and Eugene Kleppinger, Using MLA Style to Cite and Document Sources, in online! a reference guide to using online sources, Bedford/St.Martins, 2003, 28 June 2005, . [6] MAA Online, 2005, The Mathematical Association of America, 29 June 2005, Information for Undergraduate Students, .  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