numbering thesis

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Q. How do I number pages differently in the various sections of my thesis or dissertation?

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Answered By: Jeff Beuck Last Updated: Apr 03, 2020     Views: 1476790

See Also:  How do I add page numbers in Microsoft Word?

To use different page numbering schemes in different sections of your Word document, there are two tricks: 1) you must include a "Section Break - Next page" between each section of your document where the numbering will change, and 2) you must "unlink" each section's footer from the one before it.

To start, temporarily turn on the viewing of hidden formatting symbols by clicking the "Show/Hide" symbol on the "Home" tab in the "Paragraph" box -- this will enable you to see the Section Breaks between sections of your document.

One of the required page numbering changes for your thesis or dissertation is that you need to use Roman numerals (e.g., "i, ii, iii") for your introductory sections (Abstract, Table of Contents), and then switch to Arabic numerals (e.g., "1, 2, 3") and begin the page numbering at "1" at the start of Chapter I of your main text.

If you do not already have a "Section Break" between these two sections of your document, you will need to add one.  Place your cursor at the very end of the text in the first section (after your Table of Contents and any Lists of Tables and Figures), being careful NOT to place it in the footer where the page number is (if the text above becomes grayed out, you are in the footer – try clicking higher).

Add a "Section Break – Next Page" by selecting the "Page Layout" tab on the menu, clicking the arrow next to "Breaks", and selecting "Next Page" under Section Breaks.

After doing this, you should see a "Section Break (Next Page)" code inserted into your document.  This tells Word that the next page begins a new section which may have a different header or footer.

Go down to the next page below the section break (in this example, the first page of Chapter I), and click on the page number in the Footer.  If your cursor is in the Footer, you should see "Footer -Section [#]-" to the left, and "Same as Previous" on the right.

You should also see a new tab appear on the menu, labeled "Header & Footer Tools: Design".  Select this.  (Be careful not to confuse this with another tab labeled "Design" between the "Insert" and "Page Layout" tabs.)  In the "Navigation" section of this tab, you will see a highlighted button labeled "Link to Previous" which tells Word to link the footer in this section to the previous section and to continue its page numbering scheme.  Click the "Link to Previous" button to UNSELECT it.

After clicking this, the "Link to Previous" button should no longer be highlighted.  The "Same as Previous" box to the right of your footer should also disappear.

Confirm your cursor is still next to the page number in the Footer, then go back to the Header & Footer Tools – Design tab on the menu, and in the "Header & Footer" section, select Page Number > Format Page Numbers.

The "Page Number Format" window will appear.  Select the appropriate "Number format" for this section ("1, 2, 3," or "i, ii, iii", etc.), and tell Word whether to continue the page numbering from the previous section or to start at "1" or another number.  In this example, we want Section 2 (which begins at Chapter I and contains the main text of our thesis or dissertation) to use Arabic numerals and to start numbering this section from page 1.  Click "OK" to finish.

You will notice that the page numbering for the current section has now been corrected, and if you unlinked it properly from the previous sections, the numbering in those sections should remain as it was before.

Next, you will need to change the page number format to lower-case Roman numerals (i.e., "i, ii, iii, ...") for the section with your Abstract and Table of Contents.  Click your cursor on the footer of your Abstract or Table of Contents page.

Open the "Format Page Numbers" window by going to the Header & Footer Tools – Design tab on the menu, and in the "Header & Footer" section, select Page Number > Format Page Numbers.

Next to "Number format", select the "i, ii, iii, ..." option for lower-case Roman numerals, then click "OK".

The page numbering for the section with your Abstract and Table of Contents should change to lower-case Roman numerals.  As long as you correctly unlinked the following section from this one, the page numbering in the following section, the main body of your text, should remain Arabic numerals starting with 1.

You will also need to remove page numbers completely from the title page and other preliminary pages of your thesis or dissertation.  To do this, you will use the same method as above, but delete the page numbers from the first section of your document.

Place your cursor at the very end of the last page which will not be numbered (probably your approval page, dedication, or acknowledgment), being careful NOT to place it in the footer where the page number is (if the text above becomes grayed out, you are in the footer – try clicking higher).

After doing this, you should see a "Section Break (Next Page)" code inserted into your document on the page before your Abstract.

Go down to the next page below the section break (in this example, the Abstract), and click on the page number in the Footer.  If your cursor is in the Footer, you should see "Footer -Section [#]-" to the left, and "Same as Previous" on the right. Be sure you are not in Section 1 of your document.

On the main menu, select the "Header & Footer Tools: Design" tab, then in the "Navigation" section of this tab, click the "Link to Previous" button if it is highlighted to UNSELECT it and unlink this section from the section above.  This will allow you to modify the page number in the first section without affecting this or subsequent sections.

Return to your Title Page (or any page in Section 1 which will not be numbered) and click on the page number in the footer.  Click-and-drag your cursor over the page number to select it.

Click the "Delete" key on your keyboard to delete the page number from this section.  As long as you removed the "Link to Previous" connection from the next section, you should the page number disappear from the first section, but remain in the following sections.

If your paper includes additional sections (for example, if your Approval Page was added as a separate section from your Title page), you may have to experiment with linking and unlinking sections from each other -- unlink a section if its page numbering will be different from the one before it, but link together any sections where the page numbering will continue from the one before it.  It is generally a good idea to start with the last section of your document and work your way backwards.

When you are finished, don't forget that you can hide the formatting symbols to make it easier to view your text by turning off the "Show/Hide" symbol on the "Home" tab in the "Paragraph" box.

Footer Sections and page numbering can be very complex, especially if your document has multiple sections.  If you need additional assistance getting your page numbering correct, contact Jeff Beuck at 216-523-7486 to set up an appointment.

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Comments (378)

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Related Topics

Formatting Theses & Dissertations using Word 2010: Numbering

• Footnotes and Endnotes
• Images, Charts, Other Objects
• Cross-References
• Applying a Style
• Modifying a Style
• Setting up a Heading 1 Example
• Setting Margins
• Creating and Using Templates
• Combining Chapters
• Finalizing Without Styles
• Adding Page Numbers
• Landscape Pages
• Automatic Table of Contents and Lists
• Commenting and Reviewing
• Quick Links

Page Contents

Learn about making subsections and appendices easier to number

• Customizing Your Numbers (different numbers in different places on the page on different pages)

Automatic Chapter and Subsection Numbering

Outline numbering in appendices, customizing your numbering, add different page numbers or number formats to different sections.

Let's say you want to use different page numbers or number formats and styles in different parts of your document. You could use page numbers such as i, ii, iii… for the introduction and table of contents and 1, 2, 3… for everything after. The trick is to divide the document into sections and to make sure those sections aren’t linked. Then, set the page numbering for  each  of those sections by following these steps.

Notes:  

If you're using Word Online, you can add page breaks but not section breaks. If you have the Word desktop application, use the  Open in Word  command to open the document. When you’re done and you save the document, it will continue to be stored where you opened it in Word Online. If you don’t have Word, you can  try  or  buy  it in the latest version of Office now.

Click at the very beginning of the first page where you want to start, stop, or change page numbering.

Choose  Layout  (or  Page Layout ) >  Breaks  >  Next Page .

Tip:  You might find it helpful to see section breaks and other formatting marks as you type. On the  Home tab, in the  Paragraph  group, choose  Show/Hide  (¶) to turn on the display of formatting marks. Choose the button again to turn off the display.

On the page after the section break, double-click in the header (top of page) or footer (bottom of page) area where you want to display page numbers. This will open the  Design  tab under  Header & Footer Tools .

Click  Link to Previous  to deselect the button and disconnect your header or footer from the header or footer in the previous section.

Note:  If  Link to Previous  is dimmed, it means there is no section break between the page you're on and the previous page. Make sure you've successfully added a section break (see step 2) and that you've opened the header for the appropriate section.

In the  Header & Footer  group, click  Page Number , pick a location, and then choose a style in the gallery.

Note:  If your change only affects the first page of your section, make sure  Different First Page  is not selected. Double-click the header or footer area of the first page of the section, and look in the  Options group on the  Design  tab.

To choose a format or to control the starting number, in the  Header & Footer  group, choose  Page Number  >  Format Page Numbers  to open the  Page Number Format  dialog box.

Do either or both of the following:

Click  Number format  to select the format for the numbering, such as a, b, c or i, ii, iii.

Under  Page numbering , choose  Start at  and type a number that you want to start the section with.

Tips:  

If you just want to change or delete the first page number of a section, double-click to open the header or footer on that page, and in the  Options  group on the  Design  tab, click  Different First Page . Then delete or format the first page number as you like.

You also can change the appearance of the page numbers. On the  Home  tab, choose  Font , and change, for example, the font style and family, and font size and color.

When you’re done, choose the  Close Header and Footer , or double-click anywhere outside the header or footer area to close it.

Format Page Number in Word 2010 and 2007 .

To Format the page numbering for different sections, follow these steps.  

• Click between two parts of your document that you want to number differently.
• on the  Page Layout Tab , Click  Breaks .
• Click  Next Page ,  Even Page , or  Odd Page , and then click  OK .
• Click in the first section of your document.
• On the  Insert  Tab Click  Header  and then Click Ed it Header
• Click in the header or footer where you want the page number
• On the  Header & Footer Tools tab  Click  Page Number
• Click The option that puts the page number where you would like
• On the  Header & Footer Tolls tab  Click  Page Number
• Click  Format Page numbers
• In the  Number Format  box, click the format that you want for the numbers in this section.
• Do one of the following:
• If you want the page numbering for the first page in this section to start at a particular number other than the first number in the format series, click  Start at  under  Page numbering , and then enter the first number that you want to appear on the first page of the section.
• If you want the page numbering to continue from the previous section, click Continue from previous section.
• Click  OK
• On the  Header and Footer  tools tab, click  Next  in the Navigation Group
• Repeat steps 1 through 3 and 9 through 11 to change the page numbering for another section
• On the  Header and Footer  tools tab, click  Close

Important Note: Not everyone needs this type of numbering; if your discipline doesn’t require it, skip this section!

Word can automatically number sections (Chapter 1, 1.1, 1.2, etc.) of your document and include the chapter number in the captions (Figure 1.2, 2.2, etc.).

• Make sure each of your chapter titles are in the Heading 1 style, and then click on one of your chapter titles.
• Click OK when you are finished.
• If you typed in the text “Chapter #”, and now it is duplicating your efforts, delete the text you typed and leave the automatically generated chapter number.
• To follow the automatically generated chapter number with the title of your chapter on a new line, click just before the text of your title, hold down the Shift key on the keyboard, and then press the Enter key.

Note: If you have any problems with word automatically adding outline numbering to parts of your front matter, simply delete it.  Your chapter numbers will reset to show the correct number of chapters.

Start Numbering on Page 2

How do i start page numbers on the second page of my word 2010 document.

Word 2010, by default, starts page numbers on the first page of a document. If the first page is a cover page, or a title page, then the second page of the document should be page 1.

• Insert page numbers by clicking on the Insert tab and choosing Page Number in the Header & Footer tab. Then select the position of the numbering.
• Because the new page numbers will be selected, the Design tab for Header & Footer Tools will appear. Under Options , select Different First Page . ( This will start page numbering page 2, but the second page will be labeled "2". This isn't what we wanted. There is an extra step to making this page say "1". )
• While the Design tab for Header & Footer is still up, select Page Number in the Header & Footer group. Then choose Format Page Number .
• The resulting window is shown to the right. Change the radial button at the bottom to Start at and type in 0 . Then click ok .

Follow the instructions at this link for roman numerals .

This was taken from the Just Tips webpage from the website for Mission Critical Training in Denver.

Customizing Your Numbers

If you want to change anything about the numbers – for example, you are using the 1.1, 1.2, etc. style but would like the word “Chapter” to display automatically in front of the Heading 1 number, you want to change Arabic numbers to Ordinal, or you want to change the spacing after the numbers, you can.

Click one of your headings, then go back to the Home Ribbon, and in the Paragraph Group click the Multilevel List icon (see screen shot above) and select Define New Multilevel List….   Click the More>> button, then select the relevant list level.

• You can use the Number style for this level: pulldown menu to choose from a various styles, as seen in the screenshot (below the Enter formatting for number: box).
• In the screenshot, with the Level on the left set at 1, we added the word “Chapter”. Moving to the second level, you can change the period in between the level and sublevel to a dash or anything you want in the Number format box.

You may also restart number for captions in your appendices or other separate areas of your dissertation.  You will need to change your outline numbering settings before inserting your captions.

We are going to do a variant of the steps above, but instead of defining new levels for your list, you will be editing the first level from this point forward. This should work, but sometimes Word acts up, and even though you’ve followed all the steps, it doesn’t take. If that happens, set up an appointment with the KNC and we’ll help you out.

• Apply the Heading 1 style to the title of your Appendix.
• On the Home Ribbon, go to the Paragraph Group , click the Multilevel List icon and select Define New Multilevel List….   Make sure the whole dialog box is showing by clicking on the More>> button (if it says <<Less instead, you are all set).
• Under Enter formatting for new number :, replace “Chapter” with “Appendix.”
• Choose the appropriate style, (such as A,B,C,… ) from the Number style for this level: pulldown menu.
• Set the correct letter or number in the Start at: pulldown.
• In the Apply changes to: pulldown, choose This point forward .
• Click OK to close the dialog box.
• << Previous: Setting Margins
• Next: Creating and Using Templates >>
• Last Updated: Jul 18, 2024 11:16 AM
• URL: https://research.auctr.edu/dissertation

• University of Michigan Library
• Research Guides

Microsoft Word for Dissertations

• Page Numbers
• Introduction, Template, & Resources
• Formatting for All Readers
• Applying a Style
• Modifying a Style
• Setting up a Heading 1 Example
• Images, Charts, Other Objects
• Footnotes, Endnotes, & Citations
• Cross-References
• Appendix Figures & Tables
• Table of Contents
• List of Figures/Tables
• Chapter and Section Numbering
• Landscape Pages
• Combining Chapter Files
• Commenting and Reviewing
• Tips & Tricks
• The Two-inch Top Margin
• Troubleshooting
• Finalizing Without Styles
• Preparing Your Final Document
• Take a break

Page Contents

If you're having problems with page numbers restarting at 1 for some chapters, see our Troubleshooting section .

This page will inform you about page numbers, including:

• Adding page numbers general information
• Using sections to control page numbering
• Breaking the connection between sections
• Adding the page numbers

Adding Page Numbers

Again, please remember that our template (available on the Main Page of this Guide ) has all of this already built in.

Page Numbers are placed in the footer of your document, which is a shared space among all your pages. Anything you put in the footer will appear on all pages of your document, though you can also use Breaks to divide your document into different sections. This is how we get small Roman numerals in the front matter section, and Arabic numerals in the rest of the document, for example.

You edit the headers and footers by double clicking in the space in which they appear on the document. When you are finished editing, you can get back to the rest of your document by clicking the  Close Header and Footer button in the  Header Design  Ribbon.

Microsoft Word provides you with the option of selecting a numbering style (e.g. “Roman Numeral”, “Arabic”) and gives you the option of selecting the “starting at” number.  You can set the page numbers for your entire document, or if you need more control, you can do it section-by-section as well.

If you want continuous pagination that is all in the same format, go to the Insert Ribbon, and in the Header & Footer Group , click on the Page Number icon. Choose the appropriate placement of the number and a style.

If you are writing a Rackham dissertation, you have somewhat more complicated pagination. For example, Rackham’s guidelines require that the page numbers begin on the third or fourth page of your document (depending on if you include a graphical frontispiece) and the page number on that page should be Roman numeral “ii”. Page numbering should continue on in Roman numerals until the first page of Chapter 1 is reached.  At that point, the numbering should restart in Arabic (“1, 2, 3…”). Rackham requires that all of your page numbers be placed at the bottom center of your pages.

View this video  (despite the Word 2010 references, it's still accurate), or read below on how to achieve this.

Step 1: Using Sections to Control Page Numbering

Using Sections to Control Page Numbering

The following instructions demonstrate numbering a dissertation document according to Rackham’s guidelines.  These steps assume you are including a title page, a copyright page, dedication and acknowledgements and other front matter, and then the body of your dissertation.

• Put your cursor before the first letter of “Dedication” or whatever is the first thing that comes after your copyright page.
• On the Page Layout Ribbon, in the Page Setup Group , click on the arrow next to the Breaks icon () and select Next Page under the Section Breaks section.
• If you turn on the paragraph markers, you should now see a section break on the previous page.
• Put your cursor before the first letter of your first chapter and repeat steps 2 and 3.

You have just separated your dissertation into sections. If you want to see what section you are working in, on the left end of Status Bar (at the bottom of your Word document), Word tells you what page you are on, how many words are in your document, which section you are in, and so on.

If you don’t see the section information, right-click on the Status Bar, and select Section in the menu that appears.

Step 2: Breaking the Connection Between Sections

Breaking the Connection Between Sections

By default, the headers and footers of each section are connected to those of the sections before and after it.  Therefore, if you want different page number styles to vary from one section to the next (such as Roman or Arabic), you’ll need to break the connection between the sections. Particularly with landscaped pages, it is often helpful to break the connection in the header as well as in the footer.

• Put your cursor on the first page that needs the Roman numeral.
• On the Insert Ribbon, in the Header & Footer Group , click on the arrow under the Footer icon and select Edit Footer .
• You should now be in the footer of that page; in the Header & Footer Tools Design Ribbon , in the Navigation Group , unlink this section’s footer from previous sections’ footer by clicking the highlighted Link to Previous icon.
• Put your cursor in the header area, and again click the highlighted Link to Previous icon.
• Scroll down to the first page of the body of your dissertation (the chapters), make sure your cursor is in the footer, and click the highlighted Link to Previous icon again.

You have now successfully unlinked footers of these sections. Any page numbers you put in the body of your document will not affect the page numbering of your front matter, and vice versa.

Step 3: Adding the Page Numbers

Adding the Page Numbers

• Scroll up to the section that contains your front matter and click in the footer of any page (don’t do anything for your title page and other pages that don’t require a page number).
• On the Insert Ribbon, in the Header & Footer Group , click on the arrow next to the Page Number icon and select the positioning you’d like.  Generally, Bottom of the Page is the choice, and either Plain Number 2 (centered) or Plain Number 3 (right aligned).
• To change to Roman Numerals, on the Insert Ribbon, in the Header & Footer Group , click on the arrow next to the Page Number icon and select Format Page Numbers… to set the “start at” number and the style of numbering.
• Scroll down to the first page of the next section (where your chapters start) and click in the footer.

• Mardigian Library
• Subject Guides

Formatting Your Thesis or Dissertation with Microsoft Word

• Page Numbers
• Introduction
• Copyright Page
• Dedication, Acknowledgements, & Preface
• Headings and Subheadings
• Citations and Bibliography
• Tables and Figures
• Rotated (Landscape) Pages
• Table of Contents
• Lists of Tables and Figures
• List of Abbreviations
• Some Things to Watch For
• PDF with Embedded Fonts

Page numbers

Microsoft Word will keep track of page numbers for you, so you can add and delete pages, move tables and figures from one page to another, etc. Then, you can create a Table of Contents, a List of Tables, a List of Figures, etc. and Word will automatically create those lists (or, you can update the lists by clicking an update button). This will save you much time compared to manually adding page numbers to your pages and manually creating your Table of Contents, List of Tables, etc. However, in order for Word to do all this automatically, page numbering needs to be set up appropriately. The video tutorial below demonstrates how to set up the page numbering.

• << Previous: Citations and Bibliography
• Next: Tables and Figures >>
• Last Updated: Jul 23, 2024 5:50 PM
• URL: https://guides.umd.umich.edu/Word_for_Theses

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Formatting your Thesis and Dissertation:Tools,Tips and Troubleshooting

• I am a new Graduate Student at Florida Tech!
• Thesis and Dissertation Templates
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• Do I need to embargo my thesis or dissertation?
• I'm ready to submit my electronic copy - now what do I do?
• What is the process for obtaining print copies of my thesis or dissertation?

Formatting Page Numbers

Page Numbers (also Header & Footer)

1. On the Insert tab, in the Header & Footer group, click Header, Footer or Page Number.

2. Click the design that you want from the options.

3. The header or footer is inserted on every page of the document. You will also see the body text is now lighter.

4. You can now add/modify the text, format the text or change the position.

5. You will also notice the Ribbon bar has popped up header and footer, tools Design tab

Click on the header and footer tools Design tab to activate working in headers and footers. You also have options that can be applied to the Header & Footer bars.

Inserting page number in footers

In the header and footer design tab, select page number.

A. click on Bottom of page and select Plain number 2 (centered page number). As mentioned before, depending on the instructions.

B. This will take you back into the Design menu

C. You will notice in this menu whether Link to Previous is highlighted. Click on this to turn it off. This controls text and page numbers following through from section to section.

D. Click on Page number again and this time select Format page number.

E. Select the type of numbers you need. Select small Roman numerals (I, ii, iii etc.) for all pages from Contents to Chapter 1. Start the Arabic numerals (1, 2, 3 etc) from the first page of chapter 1. The title page has no page number. (In double-sided printing, you will need to turn off same as previous on the first odd and the first even page of each new section).

F. If you want page numbers to continue from the previous section/chapter, check ‘ continue from previous section’

G. If you want to start fresh numbering in the section or chapter, select ‘ start at’ and enter the starting number (usually 1).

Sections in the ‘Preliminaries’ file will have small Roman numerals for page numbering, while the rest of the document will have Arabic numerals. This is one of the reasons why it is important to keep the ‘same as previous’ option turned off. If it is on, all numbers or text in the header or footer will be the same throughout the entire document.

When working in headers and footers, you must have the cursor blinking in the header or footer space on the page, otherwise nothing will happen. When you click into the header or footer space, the Design menu will appear, which includes the header and footer sub-menu.

The page numbers also have to fit within the 1 - 1.2-inch margins of the page. In the Header and Footer design tab you will see options to adjust the margins of the header and footer. Adjust Footer from Bottom to your required spacing.

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KU Thesis and Dissertation Formatting: Page Numbering

• Formatting Specifics
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• Rotating Charts or Tables
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Office of Graduate Studies Thesis and Dissertation Formatting Guidelines

These rules are taken from the KU Office of Graduate Studies Thesis or Dissertation Formatting Guidelines. To see the full thesis or dissertation formatting requirements, visit https://graduate.ku.edu/submitting

Adding Page Numbers

Thesis and dissertation formatting requires different page numbering styles within the same document—for example, lower-case Roman numerals (i, ii, iii) for the front matter, and Arabic numerals (1, 2, 3) for the body of the document. To create the different page numbering styles as required, you will first set up the lowercase Roman numerals, then insert a section break, then set up the Arabic numerals. Step-by-step how-to instructions are included below for adding page numbers in Word 2010, Word 2013 or Word 2011 for Mac.

• Printed Instructions (Page Numbers Word 2010)
• Printed Instructions (Page Numbering Word 2013)
• Printed Instructions (Page Numbers Word 2011 for Mac)
• Printed Instructions (Page Numbers Word 2016 PC)
• Printed Instructions (Page Numbers Word 2016 Mac)

Subject Guide

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Thesis and Dissertation Guide

• « Thesis & Dissertation Resources
• The Graduate School Home

• Introduction
• Copyright Page
• Dedication, Acknowledgements, Preface (optional)
• Table of Contents
• List of Tables, Figures, and Illustrations
• List of Abbreviations
• List of Symbols

Non-Traditional Formats

Font type and size, spacing and indentation, tables, figures, and illustrations, formatting previously published work.

• Internet Distribution
• Open Access
• Registering Copyright
• Using Copyrighted Materials
• Use of Your Own Previously Published Materials
• Submission Steps
• Submission Checklist
• Sample Pages

II. Formatting Guidelines

All copies of a thesis or dissertation must have the following uniform margins throughout the entire document:

• Left: 1″ (or 1 1/4" to ensure sufficient room for binding the work if desired)
• Right: 1″
• Bottom: 1″ (with allowances for page numbers; see section on Pagination )
• Top: 1″

Exceptions : The first page of each chapter (including the introduction, if any) begins 2″ from the top of the page. Also, the headings on the title page, abstract, first page of the dedication/ acknowledgements/preface (if any), and first page of the table of contents begin 2″ from the top of the page.

Non-traditional theses or dissertations such as whole works comprised of digital, artistic, video, or performance materials (i.e., no written text, chapters, or articles) are acceptable if approved by your committee and graduate program. A PDF document with a title page, copyright page, and abstract at minimum are required to be submitted along with any relevant supplemental files.

Fonts must be 10, 11, or 12 points in size. Superscripts and subscripts (e.g., formulas, or footnote or endnote numbers) should be no more than 2 points smaller than the font size used for the body of the text.

Space and indent your thesis or dissertation following these guidelines:

• The text must appear in a single column on each page and be double-spaced throughout the document. Do not arrange chapter text in multiple columns.
• New paragraphs must be indicated by a consistent tab indentation throughout the entire document.
• The document text must be left-justified, not centered or right-justified.
• For blocked quotations, indent the entire text of the quotation consistently from the left margin.
• Ensure headings are not left hanging alone on the bottom of a prior page. The text following should be moved up or the heading should be moved down. This is something to check near the end of formatting, as other adjustments to text and spacing may change where headings appear on the page.

Exceptions : Blocked quotations, notes, captions, legends, and long headings must be single-spaced throughout the document and double-spaced between items.

Paginate your thesis or dissertation following these guidelines:

• Use lower case Roman numerals (ii, iii, iv, etc.) on all pages preceding the first page of chapter one. The title page counts as page i, but the number does not appear. Therefore, the first page showing a number will be the copyright page with ii at the bottom.
• Arabic numerals (beginning with 1, 2, 3, 4, etc.) start at chapter one or the introduction, if applicable. Arabic numbers must be included on all pages of the text, illustrations, notes, and any other materials that follow. Thus, the first page of chapter one will show an Arabic numeral 1, and numbering of all subsequent pages will follow in order.
• Do not use page numbers accompanied by letters, hyphens, periods, or parentheses (e.g., 1., 1-2, -1-, (1), or 1a).
• Center all page numbers at the bottom of the page, 1/2″ from the bottom edge.
• Pages must not contain running headers or footers, aside from page numbers.
• If your document contains landscape pages (pages in which the top of the page is the long side of a sheet of paper), make sure that your page numbers still appear in the same position and direction as they do on pages with standard portrait orientation for consistency. This likely means the page number will be centered on the short side of the paper and the number will be sideways relative to the landscape page text. See these additional instructions for assistance with pagination on landscape pages in Microsoft Word .

Format footnotes for your thesis or dissertation following these guidelines:

• Footnotes must be placed at the bottom of the page separated from the text by a solid line one to two inches long.
• Begin at the left page margin, directly below the solid line.
• Single-space footnotes that are more than one line long.
• Include one double-spaced line between each note.
• Most software packages automatically space footnotes at the bottom of the page depending on their length. It is acceptable if the note breaks within a sentence and carries the remainder into the footnote area of the next page. Do not indicate the continuation of a footnote.
• Number all footnotes with Arabic numerals. You may number notes consecutively within each chapter starting over with number 1 for the first note in each chapter, or you may number notes consecutively throughout the entire document.
• Footnote numbers must precede the note and be placed slightly above the line (superscripted). Leave no space between the number and the note.
• While footnotes should be located at the bottom of the page, do not place footnotes in a running page footer, as they must remain within the page margins.

Endnotes are an acceptable alternative to footnotes. Format endnotes for your thesis or dissertation following these guidelines:

• Always begin endnotes on a separate page either immediately following the end of each chapter, or at the end of your entire document. If you place all endnotes at the end of the entire document, they must appear after the appendices and before the references.
• Include the heading “ENDNOTES” in all capital letters, and center it 1″ below the top of the first page of your endnotes section(s).
• Single-space endnotes that are more than one line long.
• Number all endnotes with Arabic numerals. You may number notes consecutively within each chapter starting over with number 1 for the first note in each chapter, or you may number notes consecutively throughout the entire document.
• Endnote numbers must precede the note and be placed slightly above the line (superscripted). Leave no space between the number and the note.

Tables, figures, and illustrations vary widely by discipline. Therefore, formatting of these components is largely at the discretion of the author.

For example, headings and captions may appear above or below each of these components.

These components may each be placed within the main text of the document or grouped together in a separate section.

Space permitting, headings and captions for the associated table, figure, or illustration must be on the same page.

The use of color is permitted as long as it is consistently applied as part of the finished component (e.g., a color-coded pie chart) and not extraneous or unprofessional (e.g., highlighting intended solely to draw a reader's attention to a key phrase). The use of color should be reserved primarily for tables, figures, illustrations, and active website or document links throughout your thesis or dissertation.

The format you choose for these components must be consistent throughout the thesis or dissertation.

Ensure each component complies with margin and pagination requirements.

Refer to the List of Tables, Figures, and Illustrations section for additional information.

If your thesis or dissertation has appendices, they must be prepared following these guidelines:

• Appendices must appear at the end of the document (before references) and not the chapter to which they pertain.
• When there is more than one appendix, assign each appendix a number or a letter heading (e.g., “APPENDIX 1” or “APPENDIX A”) and a descriptive title. You may number consecutively throughout the entire work (e.g., 1, 2 or A, B), or you may assign a two-part Arabic numeral with the first number designating the chapter in which it appears, separated by a period, followed by a second number or letter to indicate its consecutive placement (e.g., “APPENDIX 3.2” is the second appendix referred to in Chapter Three).
• Include the chosen headings in all capital letters, and center them 1″ below the top of the page.
• All appendix headings and titles must be included in the table of contents.
• Page numbering must continue throughout your appendix or appendices. Ensure each appendix complies with margin and pagination requirements.

You are required to list all the references you consulted. For specific details on formatting your references, consult and follow a style manual or professional journal that is used for formatting publications and citations in your discipline.

Your reference pages must be prepared following these guidelines:

• If you place references after each chapter, the references for the last chapter must be placed immediately following the chapter and before the appendices.
• If you place all references at the end of the thesis or dissertation, they must appear after the appendices as the final component in the document.
• Select an appropriate heading for this section based on the style manual you are using (e.g., “REFERENCES”, “BIBLIOGRAPHY”, or “WORKS CITED”).
• Include the chosen heading in all capital letters, and center it 1″ below the top of the page.
• References must be single-spaced within each entry.
• Include one double-spaced line between each reference.
• Page numbering must continue throughout your references section. Ensure references comply with margin and pagination requirements.

In some cases, students gain approval from their academic program to include in their thesis or dissertation previously published (or submitted, in press, or under review) journal articles or similar materials that they have authored. For more information about including previously published works in your thesis or dissertation, see the section on Use of Your Own Previously Published Materials and the section on Copyrighting.

If your academic program has approved inclusion of such materials, please note that these materials must match the formatting guidelines set forth in this Guide regardless of how the material was formatted for publication.

Some specific formatting guidelines to consider include:

• Fonts, margins, chapter headings, citations, and references must all match the formatting and placement used within the rest of the thesis or dissertation.
• If appropriate, published articles can be included as separate individual chapters within the thesis or dissertation.
• A separate abstract to each chapter should not be included.
• The citation for previously published work must be included as the first footnote (or endnote) on the first page of the chapter.
• Do not include typesetting notations often used when submitting manuscripts to a publisher (i.e., insert table x here).
• The date on the title page should be the year in which your committee approves the thesis or dissertation, regardless of the date of completion or publication of individual chapters.
• If you would like to include additional details about the previously published work, this information can be included in the preface for the thesis or dissertation.

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University of South Florida

Office of Graduate Studies

Main navigation, page numbering.

The thesis/dissertation is comprised of several different sections which require a distinct numbering format.

All page numbers should be:

• Located on the bottom of each page that requires them
• Located between .5” and .75” inches from the bottom of the page
• The same font and size as the main body of text

Pagination for Front Matter , Table of Contents & Lists, and the Main Body should be formatted as follows:

No Page Number

• Acknowledgments

Lowercase Roman Numerals (i, ii, iii, iv, etc.)

• Table of Contents
• List of Tables
• List of Figures
• List of Abbreviations

Arabic Numerals (1, 2, 3, etc.)

• About the Author (if used, list as "End Page" in the Table of Contents)

How do you format different pagination for different sections?

There are two options:

Section Breaks You can insert section breaks in the document where the change in style happens, and then format the page numbers of each section. Check to ensure the sections are not linked so that the changes in page numbers are limited to a given section.

Separate Documents Create 3-4 separate Word documents - one for each style of page numbering. You will then save each as a PDF and combine the PDFs using Adobe Acrobat. 

Honors Guidelines: Page Numbering/Thesis Organization

• General Submission Guidelines/Approvals
• Submitting Your Project
• Page Numbering/Thesis Organization
• Support and Questions

Page Numbering Tips

There is no prescribed page numbering style for all honors project. We only ask that you do not print the page number on the title page.    The easiest way to format page numbers for different sections, for example using roman and arabic numbers, is to create section breaks in your document. Instructions for Word users.   . If you have difficulty with the page numbering appearing as would like, please do not hesitate to con tact us for help .

You may use the formatting style recommended by your discipline's style manual, or whatever style is acceptable to your advisor and department .  (For a list of print & online style manuals, see Style and Citation Guides, by Title or Subject .)  

You may also wish to view theses submitted by others in your department in previous years to get some ideas for formatting.

Below is an example of the order of pages, and the Roman or Arabic page numbering, as recommended in one of the style guides, Turabian’s  A Manual for Writers of Research papers, Theses, and Dissertations: Chicago Style for Students and Researchers, 8 th  ed. 

Not every thesis will contain all the parts listed below:

1.    Front Matter (preliminary pages):  use lower-case Roman numerals (i, ii, iii, iv, etc.) in this order:

Title Page (required):  counts as page i, but  the number is not printed on the page .  Title Page is  not  listed in the Table of Contents.

Dedication; Epigraph  (both optional): these count in sequence of Roman numerals, but the number is not printed on the page.  These are  not  listed in the Table of Contents.

Table of Contents (required for all papers divided into chapters; recommended for all)  Your Table of Contents would list all items shown below, IF your thesis includes them. (See  Chicago Manual of Style  for more about Tables of Content )

List of Figures, Tables, or Illustrations  (optional, but recommended if appropriate): should be listed in Table of Contents

Preface; Acknowledgments; List of Abbreviations or Glossary; Abstract  (all optional):  should be listed in Table of Contents

2.     Text:  includes everything between the front matter and the back matter; begins a new numbering sequence, using         Arabic numerals.   (Introduction, chapters and/or major sections typically are listed in the Table of Contents.)

Introduction  (optional): if included, this is page 1.

Chapters or Sections :  if no Introduction, Chapter 1 would be page 1.  Begin each new chapter on a new page.  Continue sequence of Arabic numbering.

 3.     Back Matter: continues numbering with Arabic numerals.   (List these parts in the Table of Contents.)

Illustrations  (optional)

Appendixes  (optional): this is where you could put black & white copies of color images from the body of the text.

Endnotes, Bibliography, or Reference List  (required in most papers): One of these lists will be the final section of the paper.

If you have difficulty with the page numbering appearing as would like, please do not hesitate to con tact us for help.

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Organizing and Formatting Your Thesis and Dissertation

Learn about overall organization of your thesis or dissertation. Then, find details for formatting your preliminaries, text, and supplementaries.

Overall Organization

A typical thesis consists of three main parts – preliminaries, text, and supplementaries. Each part is to be organized as explained below and in the order indicated below:

1. Preliminaries:

• Title page (required)
• Copyright page (required)
• Abstract (required) only one abstract allowed
• Acknowledgments (optional) located in the Preliminary Section only
• Preface (optional)
• Autobiography (optional)
• Dedication (optional)
• Table of Contents (required)
• List of Tables (optional)
• List of Figures (optional)
• List of Plates (optional)
• List of Symbols (optional)
• List of Keywords (optional)
• Other Preliminaries (optional) such as Definition of Terms

3. Supplementaries:

• References or bibliography (optional)
• Appendices (optional)
• Glossary (optional)
• List of Abbreviations (optional)

Preliminaries

These are the general requirements for all preliminary pages.

• Preliminary pages are numbered with lower case Roman numerals.
• Page numbers are ½” from the bottom of the page and centered.
• The copyright page is included in the manuscript immediately after the title page and is not assigned a page number nor counted.
• The abstract page is numbered with the Roman numeral “ii”.
• The remaining preliminary pages are arranged as listed under “Organizing and Formatting the Thesis/Dissertation” and numbered consecutively.
• Headings for all preliminary pages must be centered in all capital letters 1” from the top of the page.
• Do not bold the headings of the preliminary pages.

A sample Thesis title page pdf is available here ,  and a sample of a Dissertation title page pdf is available here.

Refer to the sample page as you read through the format requirements for the title page.

• Do not use bold.
• Center all text except the advisor and committee information.

The heading “ Thesis ” or “ Dissertation ” is in all capital letters, centered one inch from the top of the page.

• Your title must be in all capital letters, double spaced and centered.
• Your title on the title page must match the title on your GS30 – Thesis/Dissertation Submission Form

Submitted by block

Divide this section exactly as shown on the sample page. One blank line must separate each line of text.

• Submitted by
• School of Advanced Materials Discovery 
• School of Biomedical Engineering
• Graduate Degree Program in Cell and Molecular Biology
• Graduate Degree Program in Ecology

If your department name begins with “School of”, list as:

• School of Education
• School of Music, Theatre and Dance
• School of Social Work

If you have questions about the correct name of your department or degree, consult your department. Areas of Study or specializations within a program are not listed on the Title Page.

Degree and Graduating Term block

• In partial fulfillment of the requirements
• For the Degree of
• Colorado State University
• Fort Collins, Colorado (do not abbreviate Colorado)

Committee block

• Master’s students will use the heading Master’s Committee:
• Doctoral students will use the heading Doctoral Committee:
• The Master’s Committee and Doctoral Committee headings begin at the left margin.
• One blank line separates the committee heading and the advisor section.
• One blank line separates the advisor and committee section.
• Advisor and committee member names are indented approximately half an inch from the left margin.
• Titles before or after the names of your advisor and your members are not permitted (Examples – Dr., Professor, Ph.D.).

Copyright Page

• A sample copyright page pdf is available here.
• A copyright page is required.
• A copyright page is included in the manuscript immediately after the title page.
• This page is not assigned a number nor counted.
• Center text vertically and horizontally.
• A sample abstract page pdf is available here – refer to the sample page as you read through the format requirements for the abstract.
• Only one abstract is permitted.
• The heading “ Abstract ” is in all capital letters, centered one inch from the top of the page.
• Three blank lines (single-spaced) must be between the “ Abstract ” heading and your title.
• Your title must be in all capital letters and centered.
• The title must match the title on your Title Page and the GS30 – Thesis/Dissertation Submission Form
• Three blank lines (single-spaced) must be between the title and your text.
• The text of your abstract must be double-spaced.
• The first page of the abstract is numbered with a small Roman numeral ii.

Table of Contents

• A sample Table of Contents page pdf is available.
• The heading “ Table of Contents ” is in all capital letters centered one inch from the top of the page.
• Three blank lines (single-spaced) follow the heading.
• List all parts of the document (except the title page) and the page numbers on which each part begins.
• The titles of all parts are worded exactly as they appear in the document.
• Titles and headings and the page numbers on which they begin are separated by a row of dot leaders.
• Major headings are aligned flush with the left margin.
• Page numbers are aligned flush with the right margin.

The text of a thesis features an introduction and several chapters, sections and subsections. Text may also include parenthetical references, footnotes, or references to the bibliography or endnotes.

Any references to journal publications, authors, contributions, etc. on your chapter pages or major heading pages should be listed as a footnote .

• The entire document is 8.5” x 11” (letter) size.
• Pages may be in landscape position for figures and tables that do not fit in “portrait” position.
• Choose one type style (font) and font size and use it throughout the text of your thesis. Examples: Times New Roman and Arial.
• Font sizes should be between 10 point and 12 point.
• Font color must be black. 
• Hyperlinked text must be in blue. If you hyperlink more than one line of text, such as the entire table of contents, leave the text black. 
• Margins are one inch on all sides (top, bottom, left, and right).
• Always continue the text to the bottom margin except at the end of a chapter.

• Please see preliminary page requirements .
• Body and references are numbered with Arabic numerals beginning with the first page of text (numbered 1).
• Page numbers must be centered ½” from the bottom of the page.

Major Headings

• A sample page pdf for major headings and subheadings is available here.
• Use consistent style for major headings.
• Three blank lines (single-spaced) need to be between the major heading and your text.
• Each chapter is started on a new page.
• The References or Bibliography heading is a major heading and the formatting needs to match chapter headings.

Subheadings

• A sample page pdf for major headings and subheadings is available here .
• Style for subheadings is optional but the style should be consistent throughout.
• Subheadings within a chapter (or section) do not begin on a new page unless the preceding page is filled. Continue the text to the bottom of the page unless at the end of a chapter.
• Subheadings at the bottom of a page require two lines of text following the heading and at least two lines of text on the next page.

Running Head

Do not insert a running head.

When dividing paragraphs, at least two lines of text should appear at the bottom of the page and at least two lines of text on the next page.

Hyphenation

The last word on a page may not be divided. No more than three lines in succession may end with hyphens. Divide words as indicated in a standard dictionary.

• The text of the thesis is double-spaced.
• Bibliography or list of reference entries and data within large tables may be single-spaced. Footnotes should be single spaced.
• Footnotes and bibliography or list of reference entries are separated by double-spacing.
• Quoted material of more than three lines is indented and single-spaced. Quoted material that is three lines or fewer may be single-spaced for emphasis.

Poems should be double-spaced with triple-spacing between stanzas. Stanzas may be centered if lines are short.

• Consult a style manual approved by your department for samples of footnotes.
• Footnotes are numbered consecutively throughout the entire thesis.
• Footnotes appear at the bottom of the page on which the reference is made.
• Footnotes are single-spaced.
• Consult a style manual approved by your department for samples of endnotes.
• Endnotes are numbered consecutively throughout the entire thesis.
• Endnotes may be placed at the end of each chapter or following the last page of text.
• The form for an endnote is the same as a footnote. Type the heading “endnote”.

Tables and Figures

• Tables and figures should follow immediately after first mentioned in the text or on the next page.
• If they are placed on the next page, continue the text to the bottom of the preceding page.
• Do not wrap text around tables or figures. Text can go above and/or below.
• If more clarity is provided by placing tables and figures at the end of chapters or at the end of the text, this format is also acceptable.
• Tables and Figures are placed before references.
• Any diagram, drawing, graph, chart, map, photograph, or other type of illustration is presented in the thesis as a figure.
• All tables and figures must conform to margin requirements.
• Images can be resized to fit within margins
• Table captions go above tables.
• Figure captions go below figures.
• Captions must be single spaced.

Landscape Tables and Figures

• Large tables or figures can be placed on the page landscape or broadside orientation.
• Landscape tables and figures should face the right margin (unbound side).
• The top margin must be the same as on a regular page.
• Page numbers for landscape or broadside tables or figures are placed on the 11” side.

Supplementaries

These are the general requirements for all supplementary pages.

• Supplementary pages are arranged as listed under “Organizing and Formatting the Thesis/Dissertation” and numbered consecutively.
• Headings for all supplementary pages are major headings and the formatting style needs to match chapter headings.

References or Bibliography

• The References or Bibliography heading is always a major heading and the formatting style needs to match chapter headings.
• References or Bibliography are ordered after each chapter, or at the end of the text.
• References or Bibliography must start on a new page from the chapter text.
• References are aligned flush with the left margin.
• The style for references should follow the format appropriate for the field of study.
• The style used must be consistent throughout the thesis.
• Appendices are optional and used for supplementary material.
• The Appendices heading is a major heading and the formatting style needs to match chapter headings.
• As an option the appendix may be introduced with a cover page bearing only the title centered vertically and horizontally on the page. The content of the appendix then begins on the second page with the standard one inch top margin.
• Quality and format should be consistent with requirements for other parts of the thesis including margins.
• Page numbers used in the appendix must continue from the main text.

A Foreign Language Thesis

Occasionally, theses are written in languages other than English. In such cases, an English translation of the title and abstract must be included in the document.

• Submit one title page in the non-English language (no page number printed).
• Submit one title page in English (no page number printed).
• Submit one abstract in the non-English language (page number is ii).
• Submit one abstract in English (page number is numbered consecutively from previous page – example: if the last page of the abstract in the foreign language is page ii the first page of the abstract in English is numbered page iii).

Multipart Thesis

In some departments, a student may do research on two or more generally related areas which would be difficult to combine into a single well-organized thesis. The solution is the multi-part thesis.

• Each part is considered a separate unit, with its own chapters, bibliography or list of references, and appendix (optional); or it may have a combined bibliography or list of references and appendix.
• A single abstract is required.
• The pages of a multi-part thesis are numbered consecutively throughout the entire thesis, not through each part (therefore, the first page of Part II is not page 1).
• The chapter numbering begins with Chapter 1 for each part, or the chapters may be numbered consecutively.
• Pagination is consecutive throughout all parts, including numbered separation sheets between parts.
• Each part may be preceded by a separation sheet listing the appropriate number and title.

Guidelines for Chapter Numbering in a Thesis: How to Structure and Order Your Research

Writing a thesis requires meticulous planning and organization. one crucial aspect of presenting your research in a coherent manner is chapter numbering. properly structuring and ordering your thesis chapters will not only enhance the readability of your work but also demonstrate your research skills. in this blog post, we will provide you with a comprehensive guide on how to effectively number your thesis chapters..

Why is Chapter Numbering Important in a Thesis?

Chapter numbering serves several purposes in a thesis:

• It facilitates easy navigation for readers and reviewers.
• It creates a logical flow and structure for your research.
• It allows readers to locate specific information or sections within your thesis quickly.
• It showcases your organizational skills and attention to detail.

General Guidelines for Numbering Thesis Chapters

Follow these guidelines to ensure clarity and consistency:

• Start with numbering from Chapter 1: Begin your chapter numbering with Chapter 1 instead of Chapter 0. This signifies the start of your thesis.
• Use Arabic numerals: Number your chapters using Arabic numerals (1, 2, 3, etc.) and avoid using Roman numerals (I, II, III) or alphabetical numbering.
• Avoid duplicate numbering: Ensure that each chapter has a unique number. Do not assign the same number to multiple chapters.
• Number your chapters in consecutive order: Follow a sequential order for chapter numbering. This helps readers understand the logical progression of your research.
• Consider using decimal numbering: If your research requires a more nuanced breakdown, you can use decimal numbering (e.g., Chapter 2.1, Chapter 2.2). However, use this approach sparingly and only when necessary to avoid excessive complexity.

Special Cases: Preliminary and Appendices Chapters

While most thesis chapters follow a conventional numbering structure, there are a few exceptions to consider:

• Preliminary chapters: The preliminary sections, such as the abstract, acknowledgments, and table of contents, should not be numbered. However, you can assign them lowercase Roman numerals (i, ii, iii, etc.) or use a separate style (e.g., Roman number format).
• Appendices: Appendices are additional sections that provide supplementary information but are not an integral part of the main thesis. You can choose to number appendices as A, B, C or use alphanumeric combinations (e.g., Appendix A, Appendix B.1).

Final Thoughts

Proper chapter numbering in your thesis is essential for maintaining clarity and ensuring a smooth reading experience for your audience. By following the guidelines provided in this blog post, you can structure and order your research effectively, leaving a positive impression on your readers and evaluators.

Remember, maintaining consistency and logical progression in your chapter numbering reinforces the professionalism and academic integrity of your thesis. So, take the time to plan and organize your chapters meticulously, and you will have a well-structured, cohesive thesis that effectively communicates your research findings.

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Required sections, guidelines, and suggestions.

Beyond those noted on the Formatting Requirements page , the Graduate School has no additional formatting requirements. The following suggestions are based on best practices and historic requirements for dissertations and theses but are not requirements for submission of the thesis or dissertation. The Graduate School recommends that each dissertation or thesis conform to the standards of leading academic journals in your field.

For both master’s and doctoral students, the same basic rules apply; however, differences exist in some limited areas, particularly in producing the abstract and filing the dissertation or thesis.

• Information in this guide that pertains specifically to doctoral candidates and dissertations is clearly marked with the term “ dissertation ” or “ doctoral candidates .”
• Information pertaining specifically to master’s candidates and theses is clearly marked with the term “ thesis ” or “ master’s candidates .”
• All other information pertains to both.

Examples of formatting suggestions for both the dissertation and thesis are available as downloadable templates .

Required? Yes.

Suggested numbering: Page included in overall document, but number not typed on page.

The following format for your title page is suggested, but not required.

• The title should be written using all capital letters, centered within the left and right margins, and spaced about 1.5 inches from the top of the page. (For an example, please see the template .)
• Carefully select words for the title of the dissertation or thesis to represent the subject content as accurately as possible. Words in the title are important access points to researchers who may use keyword searches to identify works in various subject areas.
• Use word substitutes for formulas, symbols, superscripts, Greek letters, etc.
• Below the title, at the vertical and horizontal center of the margins, place the following five lines (all centered):

Line 1: A Dissertation [or Thesis]

Line 2: Presented to the Faculty of the Graduate School

Line 3: of Cornell University

Line 4: in Partial Fulfillment of the Requirements for the Degree of

Line 5: Doctor of Philosophy [or other appropriate degree]

• Center the following three lines within the margins:

Line 2: Primary or Preferred Name [as registered with the University Registrar’s Office and displayed in Student Center]

Line 3: month and year of degree conferral [May, August, December; no comma between month and year]

Copyright Page

Suggested numbering: Page included in overall document, but number not typed on page

The following format for your copyright page is suggested, but not required.

• A notice of copyright should appear as the sole item on the page centered vertically and horizontally within the margins: © 20__ [Primary or Preferred Name [as registered with the University Registrar’s Office]. Please note that there is not usually a page heading on the copyright page.
• The copyright symbol is a lowercase “c,” which must be circled. (On Macs, the symbol is typed by pressing the “option” and “g” keys simultaneously. If the font does not have the © symbol, type the “c” and circle it by hand. On PCs, in the insert menu, choose “symbol,” and select the © symbol.)
• The date, which follows the copyright symbol, is the year of conferral of your degree.
• Your name follows the date.

Required?  Yes.

Suggested numbering: Page(s) not counted, not numbered

Abstract formats for the doctoral dissertation and master’s thesis differ greatly. The Graduate School recommends that you conform to the standards of leading academic journals in your field.

Doctoral candidates:

• TITLE OF DISSERTATION
• Student’s Primary or Preferred Name, Ph.D. [as registered with the University Registrar’s Office]
• Cornell University 20__ [year of conferral]
• Following the heading lines, begin the text of the abstract on the same page.
• The abstract states the problem, describes the methods and procedures used, and gives the main results or conclusions of the research.
• The abstract usually does not exceed 350 words in length (about one-and-one-half correctly spaced pages—but not more than two pages).

Master’s candidate:

• In a thesis, the page heading is simply the word “ABSTRACT” in all capital letters and centered within the margins at the top of the page. (The thesis abstract does not display the thesis title, author’s name, degree, university, or date of degree conferral.)
• The abstract should state the problem, describe the methods and procedures used, and give the main results or conclusions.
• The abstract usually does not exceed 600 words in length, which is approximately two-and-one-half to three pages of correctly spaced typing.
• In M.F.A. theses, an abstract is not required.

Biographical Sketch

Suggested numbering: iii (may be more than one page)

• Type number(s) on page(s).

The following content and format are suggested:

• The biographical sketch is written in third-person voice and contains your educational background. Sometimes additional biographical facts are included.
• As a page heading, use “BIOGRAPHICAL SKETCH” in all capital letters, centered on the page.
• Number this page as iii.

Required? Optional.

Suggested numbering: iv (may be more than one page)

The dedication page is not required and can contain whatever text that you would like to include. Text on this page does not need to be in English.

Acknowledgements

Suggested numbering: v (may be more than one page)

The following content and format are suggested, not required.

• The acknowledgements may be written in first-person voice. If your research has been funded by outside grants, you should check with the principal investigator of the grant regarding proper acknowledgement of the funding source. Most outside funding sources require some statement of acknowledgement of the support; some also require a disclaimer from responsibility for the results.
• As a page heading, use “ACKNOWLEDGEMENTS” in all capital letters, centered on the page.

Table of Contents

Suggested numbering: vi (may be more than one page)

The following are suggestions.

• As a page heading, use “TABLE OF CONTENTS” in all capital letters and centered on the page.
• List the sections/chapters of the body of the dissertation or thesis. Also, list preliminary sections starting with the biographical sketch. (Title page, copyright page, and abstract are not listed.)
• For theses and dissertations, the conventional format for page numbers is in a column to the right of each section/chapter title. The first page of each chapter/section is stated with a single number. Table of contents usually do not include a range of page numbers, such as 7-22.
• The table of contents is often single-spaced.

Two-Volume Theses or Dissertations

If the dissertation or thesis consists of two volumes, it is recommended, but not required, that you list “Volume II” as a section in the table of contents.

List of Figures, Illustrations, and Tables

Suggested numbering: vii (may be more than one page)

• If included, type number(s) on page(s).

As described in the formatting requirements above, figures and tables should be consecutively numbered. The Graduate School recommends that you conform to the styles set by the leading academic journals in your field. The items below are formatting suggestions based on best practices or historic precedents.

Table of contents format:

• As a page heading, use “LIST OF FIGURES,” “LIST OF ILLUSTRATIONS,” or “LIST OF TABLES” in all capital letters, centered on the page.
• There should be separate pages for “LIST OF FIGURES,” “LIST OF ILLUSTRATIONS,” or “LIST OF TABLES” even if there is only one example of each.
• The list should contain enough of the titles or descriptions so readers can locate items using the list. (It may not be necessary to include entire figure/illustration/table captions.)
• The list should contain the page number on which each figure, illustration, or table is found, as in a table of contents.
• The list of figures/illustrations/tables may be single-spaced.

Page format:

• Figures/illustrations/tables should be placed as close as possible to their first mention in the text. They may be placed on a page with no text above or below, or placed directly into the text. If a figure/illustration/table is placed directly into the text, text may appear above or below the figure/illustration/table; no text may wrap around the figure/illustration/table.
• If a figure/illustration/table appears on a page without other text, it should be centered vertically within the page margins. Figures/illustrations/tables should not be placed at the end of the chapter or at the end of the dissertation or thesis.
• Figure/illustration/table numbering should be either continuous throughout the dissertation or thesis, or by chapter (e.g. 1.1, 1.2; 2.1, 2.2, etc.). The word “Figure,” “Illustration,” or “Table” must be spelled out (not abbreviated), and the first letter must be capitalized.
• A caption for a figure/illustration should be placed at the bottom of the figure/illustration. However, a caption for a table must be placed above the table.
• If the figure/illustration/table, not including the caption, takes up the entire page, the figure/illustration/table caption should be placed alone on the preceding page and centered vertically and horizontally within the margins. (When the caption is on a separate page, the List of Figures or List of Illustrations or List of Tables can list the page number containing the caption.)
• If the figure/illustration/table, not including the caption, takes up more than two pages, it should be preceded by a page consisting of the caption only. The first page of the figure/illustration/table must include the figure/illustration/table (no caption), and the second and subsequent pages must also include, at the top of the figure/illustration/table, words that indicate its continuance—for example, “Figure 5 (Continued)”—and on these pages the caption is omitted.
• If figures/illustrations/tables are too large, they may be reduced slightly so as to render a satisfactory product or they must either be split into several pages or be redone. If a figure/illustration/table is reduced, all lettering must be clear, readable, and large enough to be legible. All lettering, including subscripts, must still be readable when reduced 25% beyond the final version. All page margin requirements must be maintained. Page numbers and headings must not be reduced.
• While there are no specific rules for the typographic format of figure/illustration/table captions, a consistent format should be used throughout the dissertation or thesis.
• The caption of a figure/illustration/table should be single-spaced, but then captions for all figures/illustrations/tables must be single-spaced.
• Horizontal figures/illustrations/tables should be positioned correctly—i.e., the top of the figure/illustration/table will be at the left margin of the vertical page of the dissertation or thesis (remember: pages are bound on the left margin). Figure/illustration/table headings/captions are placed with the same orientation as the figure/illustration/table when they are on the same page as the figure/illustration/table. When they are on a separate page, headings and captions are always placed in vertical orientation, regardless of the orientation of the figure/illustration/table. Page numbers are always placed as if the figure/illustration/table was vertical on the page.

Photographs should be treated as illustrations. To be considered archival, photographs must be black-and-white. (If actual color photographs are necessary, they should be accompanied by black-and-white photographs of the same subject.) Color photos obtained digitally do not need to be accompanied by a black-and-white photograph. Make a high-resolution digital version of each photograph and insert it into your electronic document, following the guideline suggestions for positioning and margins.

Optional Elements

List of abbreviations.

As a page heading, use “LIST OF ABBREVIATIONS” in all capital letters, centered on the page.

List of Symbols

As a page heading, use “LIST OF SYMBOLS” in all capital letters, centered on the page.

Suggested numbering: xi (may be more than one page)

As a page heading, use “PREFACE” in all capital letters, centered on the page.

Body of the Dissertation or Thesis: Text

Suggested numbering: Begin page number at 1

• Text (required)
• Appendix/Appendices (optional)
• Bibliography, References, or Works Cited (required)

Please note that smaller font size may be appropriate for footnotes or other material outside of the main text. The following suggestions are based on best practice or historic precedent, but are not required.

• Chapter headings may be included that conform to the standard of your academic field.
• Textual notes that provide supplementary information, opinions, explanations, or suggestions that are not part of the text must appear at the bottom of the page as footnotes. Lengthy footnotes may be continued on the next page. Placement of footnotes at the bottom of the page ensures they will appear as close as possible to the referenced passage.

Appendix (or Appendices)

An appendix (-ces) is not required for your thesis or dissertation. If you choose to include one, the following suggestions are based on best practice or historic precedent.

• As a page heading, use “APPENDIX” in all capital letters, centered on the page.
• Place in an appendix any material that is peripheral, but relevant, to the main text of the dissertation or thesis. Examples could include survey instruments, additional data, computer printouts, details of a procedure or analysis, a relevant paper that you wrote, etc.
• The appendix may include text that does not meet the general font and spacing requirements of the other sections of the dissertation or thesis.

Bibliography (or References or Works Cited)

A bibliography, references, or works cited is required for your thesis or dissertation. Please conform to the standards of leading academic journals in your field.

• As a page heading, use “BIBLIOGRAPHY” (or “REFERENCES” or “WORKS CITED”) in all capital letters, centered on the page. The bibliography should always begin on a new page.
• Bibliographies may be single-spaced within each entry but should include 24 points of space between entries.

Suggested numbering: Continue page numbering from body

If you choose to include a glossary, best practices and historic precedent suggest using a page heading, use “GLOSSARY” in all capital letters, centered on the page.

Suggested numbering: Continue page numbering from glossary

If you choose to include one, best practices and historic precedent suggest using a page heading, use “INDEX” in all capital letters, centered on the page.

Font Samples

Sample macintosh fonts.

• Palatino 12
• Garamond 14
• New Century School Book
• Helvetica 12 or Helvetica 14
• Times New Roman 12
• Times 14 (Times 12 is not acceptable)
• Symbol 12 is acceptable for symbols

Sample TeX and LaTeX Fonts

• CMR 12 font
• Any font that meets the above specifications

Sample PC Fonts

• Helvetica 12

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Words or Numerals – Using and Formatting Numbers

Posted by Rene Tetzner | Nov 9, 2021 | PhD Success | 0 |

6.4 Using and Formatting Numbers Appropriately

Every academic or scientific author who must include many numbers while reporting his or her research is faced with the challenge of using and formatting those numbers in an accurate, consistent and appropriate manner. Your department and/or discipline may very well have specific conventions and guidelines regarding the use of numbers that must be observed, and these may be quite specific, or you may have been provided with no guidelines at all for using numbers in a scholarly manner. Unfortunately, there is considerable inconsistency in the advice style guides offer regarding numbers, and even the way in which numbers are referred to while talking about their formatting can be contentious, with some guidance insisting that numbers as numerals rather than words should be called ‘figures,’ while others use ‘numerals’ instead (in this book I use ‘numerals’ to avoid confusion with ‘figures,’ which I use when referring to graphs, illustrations and the like). Style guides tend to assign a number of the variant practices associated with numbers to the conventions of either British or American English, and in some cases the link to one style or the other is clear, but there seems little consensus on some of these matters, and different style guides based in one country can vary in their advice as much as guides claiming to present the two different forms of English. Fortunately, there are also several patterns of usage that are maintained across guidelines, and a healthy share of common sense in using these as you aim for accuracy, consistency and clear communication across all parts of your thesis that include numbers will produce an effective result.

6.4.1 Words or Numerals?

One of the main concerns when using numbers in scholarly writing is whether they should be expressed as words or numerals. In most cases, a threshold value is set: below this value, words are used to express numbers, whereas above it, numerals are used. Unfortunately, there is no single threshold value that applies to every discipline and every thesis, and for very practical reasons. In the humanities and other nontechnical contexts, for instance, the value is often set at 100, whereas in more technical or scientific contexts where numbers tend to be used more extensively, the value is usually 10; for books on music, the value is often 12, and for online writing, numerals are used much more frequently than words, so all numbers may appear as numerals. In addition, such threshold values are only general rules and there are exceptions that apply regardless of the precise value used, as the following points make clear:

• Large round numbers are usually expressed as words (‘four hundred’ and ‘three million’) or as a combination of words (or abbreviations) and numerals (‘3 million’ or ‘3m.’) even if they are over the threshold value, although this is rarer in the sciences.
• Approximations as opposed to exact numbers are generally written as words even if they are over the threshold value: ‘I saw about fifty of them.’
• For a series of quantities, numerals are usually used regardless of whether the numbers are above or below the set value: ‘4, 6, 8, 28, 42, 53, 79, 98, 109 and 127.’
• When a sentence or, in some cases, a paragraph contains one or more numbers that are over the threshold value as well as numbers that are under it, it is best for both consistency and legibility to use numerals for all the numbers: ‘from 83 to 137’ instead of ‘from eighty-three to 137,’ and ‘between 6 and 13’ instead of ‘between six and 13.’
• If two sets or categories of numbers are used together in a sentence, clarity and legibility are often improved by using words for one set or category and numerals for the other: ‘the Oxford manuscript consists of forty-four folios with 31 lines on each page, the Worcester manuscript of forty-one folios with 34 lines to a page and the York manuscript of only thirty-nine folios with 36 lines on each page.’
• All numbers that appear at the beginning of a sentence should be written out as words: ‘Fourteen is the age of consent,’ not ‘14 is the age of consent.’ Alternatively, the sentence can be rephrased or rearranged to avoid placing the number at the beginning (The age of consent is 14), and if the number opening a sentence would be particularly cumbersome when spelled out (e.g., ‘412,724’), this should definitely be done.

• Numbers used for certain purposes tend to be expressed as numerals regardless of whether they are over the threshold value or not, including page numbers, section and chapter numbers, volume numbers of books and journals, issue numbers of journals, numbers of items in a list, Bible chapter and verse numbers (Genesis 2:4), appendix, table and figure numbers, numbers within tables and figures, numbers in an abstract (though this is not always the case by any means), act and scene numbers, line and column numbers, reference and cross-reference numbers, legal document numbers, numbers that are exact measures, numbers that appear before abbreviations (17 cm), numbers indicating percentages (‘50%,’ but if not exact they occasionally appear as words with ‘per cent’ or ‘percent,’ never with %), numbers recording the scores of tests and games, the numbers of points in scales (a 5-point scale), house, hotel, apartment and building numbers, road and highway numbers, numbers indicating years (‘1960,’ ‘2014’ etc., although they can be written out if necessary – at the beginning of a sentence, for instance) and days of the month, and union and lodge numbers.
• When a number is part of an already hyphenated compound, a numeral should be used to avoid excessive hyphenation: ‘a 35-year-old man,’ not ‘a thirty-five-year-old man.’
• While fractions, like whole numbers, can be written as either words or numerals, when whole numbers and fractions are combined, it is better to use numerals: ‘she walked 5¾ miles,’ not ‘she walked five and three-quarters miles.’

Ordinal numbers generally follow the same pattern as cardinal numbers, appearing as words when they are below the threshold value (‘second,’ ‘fifth,’ ‘eighth’ etc.) and as numerals with the appropriate suffix when they are above it (‘74th,’ ‘82nd’ and ‘143rd’). However, some styles will recommend that ordinal numbers be written out in situations where cardinal numbers would not be, or that they be written out on all occasions except in notes, references and quotations (in the last, the format used in the source should be observed). When compound numbers are written as words, they are hyphenated (‘thirty-two,’ ‘eighty-seventh’ etc.) and the same is true of fractions (‘one-quarter’ and ‘two-thirds’), although fractions are often left open and sometimes this is done to indicate a focus on the number or individual parts of a quantity (he gave one third of his inheritance to his sister and another third to his brother) rather than on the proportion or single quantity (he gave two-thirds of his inheritance away). When written out as words, numbers are pluralised in the same way as other words (‘eights and nines,’ ‘seventies’ etc.), although ‘dozen,’ ‘hundred,’ ‘thousand,’ ‘million,’ ‘billion’ and ‘trillion’ tend to remain singular (‘two thousand,’ ‘seven million’ etc.) unless they express indefinite quantities (‘dozens of rabbits’ and ‘thousands of black flies’). Numbers above one can take plural or singular verbs depending on the precise meaning: ‘there were only fourteen participants,’ but ‘fourteen participants is a small sample,’ though the latter could also be worded to reflect both the plural and the singular nature of the concept (fourteen participants result in a small sample).

6.4.2 Arabic Numerals

When numbers are expressed as Arabic numerals, the plurals are formed simply by adding an ‘s’ – no apostrophe is needed (‘1970s’ and ‘low temperatures in the 20s,’ not ‘1970’s’ and ‘low temperatures in the 20’s’); only if the numbers are discussed as entities in themselves might apostrophes be appropriate for clarity (we chose 8’s and 10’s). When numerals appear with abbreviated measures (‘94 mm,’ ‘7 kg’ and ‘30 °C’) there should usually be a space between the numeral and the abbreviation, and the abbreviation should not be pluralised (see Sections 6.3.5 and 6.3.6). When numerals appear with other letters, however, there is generally no space between the numerals and the letters: ‘pp.47ff’ and ‘Item 7a.’ In nontechnical writing, numerals of four (5,698) or five (89,703) digits generally contain a comma after the third digit counting from the right, but in some instances the comma is not used in four-digit numerals (5698); if this is the case, the comma should nonetheless be used in four-digit numerals that appear in any figures or tables (and especially in any columns of tables) that also contain numerals with five or more digits so that alignment is preserved. Often in technical and scientific writing, the commas are not used, but spaces are used instead (‘5 698’ and ‘89 703’), though the four-digit numeral can appear without the space; if so and four-digit numerals appear in figures or tables (again, especially in the columns of tables) along with numerals of five digits or more, the space will need to be added to preserve alignment (for more information on tables and figures, see Section 4.4.1).

The same principle applies to digits after the decimal point: after three digits counted from the left, a space is often used (‘1.479 6’ and ‘7.798 99’), but not always if there are only four digits after the decimal point (1.4796), and alignment should be preserved in tables and figures by adding the space to such four-digit numerals if numerals of five or more digits also appear. In some styles and/or disciplines, the number of digits that appear after the decimal point should be consistent across all numerals used in a particular context or table: if four digits is the maximum number of post-decimal digits in any numeral, all numerals should bear four digits after the decimal, and zeroes can be added to achieve this when necessary. This is by no means a uniform practice, however, so you may only want to apply it in your thesis if it is required by the guidelines you are following or conventional in your discipline. Finally, the decimal point, not the European decimal comma, is used in Arabic numerals in scholarly English prose (‘4.75’ for ‘four point seven five,’ not ‘4,75’). Generally speaking, decimal fractions should feature a zero before the decimal (0.683), especially if they are discussed in relation to quantities of 1.00 and more; if, however, the quantity never reaches 1.00 (as in probabilities and correlation coefficients), the initial zero can be omitted, and the same is the case in ballistics (a .22-calibre rifle).

Technical writing in a number of the sciences can present other formatting challenges and issues which I do not have time or space to cover here, but detailed advice can be found in a number of places. Chapter 13 of Butcher’s Copy-Editing (Butcher et al., 2006) deals with ‘Science and Mathematics Books,’ for instance, and features several sections focussing on numbers (Section 13.1.4 on equations, Section 13.2.5 on miscellaneous items and Section 13.3 on units), as well as separate discussions of astronomy, biology, chemistry, computing, geology and medicine; the chapter also includes an excellent list of references (pp.347–349) for further help while working in these disciplines. Chapter 14 of New Hart’s Rules (Ritter, 2005) focuses on ‘Science, Mathematics, and Computing’ with Section 14.1.3, for example, covering numerals and Section 14.1.4 dealing with units, while other sections provide advice on degrees, temperatures and so on; here, too, there are separate discussions of certain disciplines, including biology, medicine, chemistry, computing, mathematics and astronomy with helpful discussions of the complex formats and punctuation of numerals in these disciplines. Punctuation in the form of commas or spaces is not required at all, however, for numerals used for certain purposes, such as page, column and line numbers, house and hotel room numbers, and reference and library call or shelf numbers. The numerals used for years and eras generally do not feature punctuation either, except BP (Before Present) and long BC dates (for more information on the formats of dates, see Section 6.4.4).

Why PhD Success?

To Graduate Successfully

This article is part of a book called "PhD Success" which focuses on the writing process of a phd thesis, with its aim being to provide sound practices and principles for reporting and formatting in text the methods, results and discussion of even the most innovative and unique research in ways that are clear, correct, professional and persuasive.

The assumption of the book is that the doctoral candidate reading it is both eager to write and more than capable of doing so, but nonetheless requires information and guidance on exactly what he or she should be writing and how best to approach the task. The basic components of a doctoral thesis are outlined and described, as are the elements of complete and accurate scholarly references, and detailed descriptions of writing practices are clarified through the use of numerous examples.

The basic components of a doctoral thesis are outlined and described, as are the elements of complete and accurate scholarly references, and detailed descriptions of writing practices are clarified through the use of numerous examples. PhD Success provides guidance for students familiar with English and the procedures of English universities, but it also acknowledges that many theses in the English language are now written by candidates whose first language is not English, so it carefully explains the scholarly styles, conventions and standards expected of a successful doctoral thesis in the English language.

Individual chapters of this book address reflective and critical writing early in the thesis process; working successfully with thesis supervisors and benefiting from commentary and criticism; drafting and revising effective thesis chapters and developing an academic or scientific argument; writing and formatting a thesis in clear and correct scholarly English; citing, quoting and documenting sources thoroughly and accurately; and preparing for and excelling in thesis meetings and examinations. 

Completing a doctoral thesis successfully requires long and penetrating thought, intellectual rigour and creativity, original research and sound methods (whether established or innovative), precision in recording detail and a wide-ranging thoroughness, as much perseverance and mental toughness as insight and brilliance, and, no matter how many helpful writing guides are consulted, a great deal of hard work over a significant period of time. Writing a thesis can be an enjoyable as well as a challenging experience, however, and even if it is not always so, the personal and professional rewards of achieving such an enormous goal are considerable, as all doctoral candidates no doubt realise, and will last a great deal longer than any problems that may be encountered during the process.

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Rene Tetzner

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• Academic writing
• Writing numbers: words and numerals

APA Style Guidelines for Numbers | Words or Numerals?

Published on August 7, 2015 by Sarah Vinz . Revised on July 23, 2023.

Numbers can be written either as words (e.g., one hundred) or numerals (e.g., 100). In this article we follow the guidelines of APA Style , one of the most common style guides used in academic writing .

In general, words should be used for numbers from zero through nine, and numerals should be used from 10 onwards. This is true for both cardinal numbers (e.g., two, 11) and ordinal numbers (e.g., second, 11 th ). However, there are some important exceptions to this rule.

Note that other style guides, such as Chicago Style,  address numbers differently (for example, in Chicago, you use words for numbers up to 100). Regardless of what style guide you follow, the most important thing is to be consistent in how you treat numbers throughout your document.

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Table of contents

Writing percentages, reporting statistical results that include numbers, writing numbers that are accompanied by measurements, writing long numbers, consistency may not be obvious, other interesting articles.

Use numerals for numbers from zero to nine that are followed by a precise unit of measurement.

The samples measured 7 cm in diameter. (“cm” is a unit of measurement)

But: These three samples were subjected to further testing.

Use words for any number that is used to start a sentence, with the exception of years.

Seventy-two thousand ink cartridges are sold every day.

Nineteenth-century novels often feature complicated plot lines.

But: 2008 saw record olive crops throughout the Mediterranean.

Use words for common fractions and set expressions.

According to the survey, two thirds of the employees are dissatisfied.

Understanding the Five Pillars of Islam is a critical first step.

The Fourth of July is traditionally marked by a firework display.

Prevent plagiarism. Run a free check.

With percentages, the standard is to use numerals and “%” (not “percent”).

According to the report, 45% of the workforce is employed in the service sector. Only 6% currently work in agriculture.

The main exception is if you are using a percentage to begin a sentence. In this case, use words to express the entire percentage.

Thirteen percent of the patients reported that their symptoms improved after taking the experimental drug.

If your paper includes quantitative research, you probably have data to report. Statistics, mathematical functions, ratios, and percentages are all written using numerals. This is true regardless of whether they are included within a table or as part of the actual text. Keep the following guidelines in mind:

• Report most statistics to two decimal places (such as M = 5.44).
• Report statistics that could never exceed 1.0 to three decimal places (such as p < .001).
• If a value has the potential to exceed 1.0, use the leading zero. If a value can never exceed 1.0, do not use the leading zero.
• Italicize values that are not Greek letters (such as M , SD , p , and F ).
• Include spaces before and after =, >, and <.

The average IQ of the participants was relatively high ( M = 137.33, SD = 4.54).

The results of the second test were statistically significant, t (12) = 4.11, p < .05.

There are further detailed guidelines about reporting statistics in APA .

If a number comes immediately before a unit of measurement, use numerals.

Each patient received  5 mg  of the experimental drug.

The tallest participant was 2.03 m .

Also use numerals for precise ages, times, dates, scores, points on a scale, and amounts of money.

The final score of Ghana 2, Brazil 1 did not represent a decisive victory.

Children under 8 years receive a $50 discount.

But: Most girls start reading when they are about five years old. (“about” makes the number imprecise)

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Longer numbers follow specific rules:

• Use a period to indicate a decimal point.
• Starting with 1,000, use commas to separate every three digits.

The region has an average of 43.75 doctors for every 10,000 people.

Some predict that the number of users will reach 2 billion by 2020.

One of the main reasons why writing numbers is complicated is that consistently applying the rules may lead to a text that actually seems very in consistent. Consider the following paragraphs:

At about the age of seven , the girl’s height was 1.47 m. This placed her in the fifth percentile, although her weight placed her in the top 7% of her class. By the time she was 9 years old, she was taller than half of the boys in her year. Five years later, she was still ranked 15 th .

Thirteen thousand viewers watched the performance of Shakespeare’s Twelfth Night from the park, while another 2,000 watched from the surrounding buildings and 1.2 million watched it on television. As one  out of every 11 residents saw at least part of the play, this one event can definitely be considered a success.

These texts may look awkward because so many different number formats have been used, but don’t be deceived – the above guidelines have all been followed.

If you are not required to strictly follow a particular style (such as APA format ), you may have some flexibility to modify the guidelines presented in this article. Just be sure to apply any modifications you make throughout your entire document.

If you want to know more about AI for academic writing, AI tools, or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!

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First Principles and Machine Learning-Based Analyses of Stability and Reactivity Trends for High-Entropy Alloy Catalysts

Since its inception, the field of heterogeneous catalysis has evolved to address the needs of the ever-growing human population. Necessity, after all, fosters innovation. Today, the world faces numerous challenges related to anthropogenic climate change, and that has necessitated, among other things, a search for new catalysts that can enable renewable energy conversion and storage, sustainable food and chemicals production, and a reduction in carbon emissions. This search has led to the emergence of many promising classes of materials, each having a unique set of catalytic properties. Among such candidate materials, high-entropy alloys (HEAs) have very recently shown the potential to be a new catalyst design paradigm. HEAs are multimetallic, disordered alloys containing more than four elements and, as a result, possess a higher configurational entropy, which gives them considerable stability. They have many conceivable benefits over conventional bimetallic alloy catalysts—greater site heterogeneity, larger design space, and higher stability, among others­. Consequently, there is a need to explore their application in a wide range of thermal and electrocatalytic reaction systems so that their potential can be realized.

In the past few decades, first principles-based approaches involving Density Functional Theory (DFT) calculations have proven to be effective in probing catalytic mechanisms at the atomic scale. Fundamental insights from first principles studies have also led to a detailed understanding of reactivity and stability trends for bimetallic alloy catalysts. However, the express application of first principles approaches to study HEA catalysts remains a challenge, due to the large computational cost incurred in performing DFT calculations for disordered alloys, which can be represented by millions of different configurations. A combination of first principles approaches and computationally efficient machine learning (ML) approaches can, however, potentially overcome this limitation.

In this thesis, combined workflows involving first principles and machine learning-based approaches are developed. To map catalyst structure to properties graph convolutional network (GCN) models are developed and trained on DFT-predicted target properties such as formation energies, surface energies, and adsorption energies. Further, the Monte Carlo dropout method is integrated into GCN models to provide uncertainty quantification, and these models are in turn used in active learning workflows that involve iterative model retraining to both improve model predictions and optimize the target property value. Dimensionality reduction methods, such as principal components analysis (PCA) and Diffusion Maps (DMaps), are used to glean physicochemical insights from the parameterization of the GCN.

These workflows are applied to the analysis of binary, ternary, and quaternary alloy catalysts, and a series of fundamental insights regarding their stability are elucidated. In particular, the origin and stability of “Pt skins” that form on Pt-based bimetallic alloys such as Pt 3 Ni in the context of the oxygen reduction reaction (ORR) are investigated using a rigorous surface thermodynamic framework. The active learning workflow enables the study of Pt skin formation on stepped facets of Pt 3 Ni (with a complex, low-symmetry geometry), and this analysis reveals a hitherto undiscovered relationship between surface coordination and surface segregation. In another study, an active learning workflow is used to identify the most stable bulk composition in the Pd-Pt-Sn ternary alloy system using a combination of exhaustively sampled binary alloy data and prudently sampled ternary alloy data. Lastly, a new GCN model architecture, called SlabGCN, is introduced to predict the sulfur poisoning characteristics of quaternary alloy catalysts, and to find an optimal sulfur tolerant composition.

On another front, the electrocatalytic activity of quinary HEAs towards the ORR is investigated by performing DFT calculations on HEA structures generated using the High-Entropy Alloy Toolbox (HEAT), an in-house code developed for the high-throughput generation and analysis of disordered alloy structures with stability constraints (such as Pt skin formation). DFT-predicted adsorption energies of key ORR intermediates are further deconvoluted into ligand, strain, and surface relaxation effects, and the influence of the number of Pt skins on these effects is expounded. A Sabatier volcano analysis is performed to calculate the ORR activities of selected HEA compositions, and correspondence between theoretical predictions and experimental results is established, to pave the way for rational design of HEA catalysts for oxygen reduction.

In summary, this thesis examines stability and reactivity trends of a multitude of alloy catalysts, from conventional bimetallic alloys to high-entropy alloys, using a combination of first principles approaches (involving Density Functional Theory calculations) and machine learning approaches comprising graph convolutional network models.

Data Science-Driven Discovery of Multimetallic Oxygen-cycle Electrocatalysts for Enhanced Energy Conversion

Office of Basic Energy Sciences

Degree Type

• Doctor of Philosophy
• Chemical Engineering

Campus location

• West Lafayette

Advisor/Supervisor/Committee Chair

Additional committee member 2, additional committee member 3, additional committee member 4, usage metrics.

• Chemical engineering not elsewhere classified
• Catalysis and mechanisms of reactions

NWP Visiting Professor News

Nwp welcomes visiting assistant professor nina lohman this fall.

Essayist and editor Nina Lohman joins the Nonfiction Writing Program this year as a Visiting Assistant Professor. Author of the new book  The Body Alone , the founder and editor of  Brink  magazine, and the powerhouse organizer behind Iowa City’s annual Mission Creek Literary Festival, Nina is teaching this Fall’s Thesis Workshop and the seminar Angle of Repose: Mapping Narrative Terrains in Hybrid Texts. In the Spring, she’ll teach a number of equally cool undergrad nonfiction courses. Welcome, Nina!

Dodie Bellamy Named 2024-25 Bedell Distinguished Visiting Professor

This coming Spring, multi-talented writer Dodie Bellamy will join the NWP as the 2024-25 Bedell Distinguished Visiting Professor. Bellamy is an essayist, novelist, and poet. A collaborator with many artists, Bellamy is the author of numerous books, including Bee Reaved , When the Sick Rule the World , Cunt-Ups , and Pink Steam . We look forward to the perspectives she’ll bring to the NWP this Spring.

NOTICE: The University of Iowa Center for Advancement is an operational name for the State University of Iowa Foundation, an independent, Iowa nonprofit corporation organized as a 501(c)(3) tax-exempt, publicly supported charitable entity working to advance the University of Iowa. Please review its full disclosure statement.

Procept BioRobotics: Risk Capital Unlock With FDA Hydros Approval

• The FDA's approval of Procept's Hrydos system is a meaningful catalyst to the investment debate.
• Investors have added ~$5/share in market value since the announcement.
• PRCT's Q2 '24 numbers were equally as strong and exhibited an extensive runway of growth ahead in my view.

Pgiam/iStock via Getty Images

Investment update

Following my last publication on PROCEPT BioRobotics Corporation ( NASDAQ: PRCT ) around 12 months ago, the stock is +146% and now trades above $78/share. The most recent catalyst was the FDA's 510(k) approval of the company's HYDROS Robotic System ("Hydros"), extending PRCT's offerings in benign prostatic hypertrophy ("BPH") even further.

Investors have bought PRCT on the news + the stock gapped above a key ~$70/share technical level in the days following (Figure 1). This is meaningful as it nudged this level 3x and was rejected on each attempt, now investors price the stock >$75/share as mentioned. Arguably, the approval has added ~$5/share in immediate market value, therefore, given the change in valuation multiple. This is now a $4Bn company by market value, >2x gain since I originally rated this name a buyback in '22.

Here I'll run through PRCT's latest developments + provide some colour on the Hydros approval, reiterating my buy thesis in doing so.

This is a name I am tremendously familiar with having covered it extensively the last few years here on Seeking Alpha. Check out the coverage here:

• Procept BioRobotics: Aquablation System Meaningful Insulator
• BioRobotics: Positioning Into FY22 Earnings (Technical Analysis)
• Procept BioRobotics: Adding Value Through Robust Unit Economics, Reiterate Buy

TradingView

Investment thesis

The integration of artificial intelligence ("AI") and technology into invasive surgery has already produced exceptional advancements across the treatment spectrum. Founded in 2007 and headquartered in San Jose, California, PRCT is a BPH pure-play. In my view, its AquaBeam/Aquablation therapy 1) has the potential to create a medical breakthrough in BPH treatment, 2) is a potential long-term compounder, and 3) has interesting economics in the mix. Aquablation is differentiated to other forms of BPH treatment as a heat-free option using heat-free waterjet resection.

I continue to rate PRCT a buy due to 1) business momentum [FY'24 guidance reaffirmed], 2) long-term outlook [sales ramp + underlying market] + 3) the FDA's Hydros approval adding ~$5/share additional market value. Net-net, reiterate buy.

Compelling catalysts

(1). hydros (overview + differentiators).

The Hydros system is an advanced iteration of PRCT's Aquablation therapy. There are four main "components" of the system, which is shown in Figure 2, including the following:

AI-Enhanced treatment planning using "FirstAssist AI", an artificial intelligence tool developed from a comprehensive repository of previous Aquablation therapy procedures. Utilizing advanced image recognition algorithms, this tool aims to assist in identifying critical anatomical structures on ultrasound imaging (see: Figure 3).

Advanced imaging integration: that merges ultrasound with digital cystoscopy + dual high-definition touchscreens. The dual-modality imaging is said to provide a better view and distinction of anatomical structures, theoretically enabling more precise interventions. This is a major advantage of Aquablation in the first place (accuracy) thus any addition to its precision should be given high marks in my view.

Robotic-assisted resection that utilizes a heat-free waterjet for tissue resection, guided by AI - this is the same as the current AquaBeam etc. except it will be guided by a treatment plan developed through FirstAssist. There are a couple of upsides to this - (i) again to accuracy, but (ii) there's scope to offer more 'standardized' BPH procedures based on the anatomical variances seen within patients. This might be a bit into the future, but PRCT has been using this kind of language for the last 18 months or so.

Workflow optimization by streamlining the Aquablation therapy process. This is due to 1) design, 2) ergonomics and 3) interface - ultimately, the better the surgeon experience, the better the patient outcomes will be, and the more of these they will place.

PRCT Website

I wanted to see how Hydros stacks up against competing offerings (exc. AquaBeam) so I completed a comparative analysis with Teleflex ( TFX ) UroLift and Boston Scientific's ( BSX ) Rezum Water Vapor system [I am buy on TFX buy the way, check out my analysis here - was part of my play on BPH + prostate cancer alongside EDAP ( EDAP ) and Profound Medical ( PROF )]).

Critically, the major differences are 1) in the use of AI, and 2) training requirements in the use of robotics vs. non-robotic system. Each has its own benefits, but I must say, the use of AI in precision + imaging could be a long-term plus in my opinion.

Company filings, Author

(2 ). Fundamental momentum

PRCT's Q2 FY'24 earnings were strong in my view and exhibit the continued momentum it is embarking on. The installed base was +72% higher YoY to 400 systems in the field. Even though <60% of this base has been active >12mo, management reported monthly utilization was +15% YoY. So 1) the installed base is on the way to doubling, and 2) each site is more productive with utilizations up as a whole.

Revenues of ~$53mm were produced by 40 sales reps [$1.3m per rep] and this is great as it's added +10 reps since FY'23 getting us an additional $40mm in top-line revenues on a TTM basis. The average sales price on its AquaBeam system in Q2 was $378K, and it sold 47 of them.

CMS rules are exquisitely important here. CMS posted its '25 proposed rule back in July, and management's language on the Q2 call explains codes on its Aquablation system well:

The Level 6 APC code for Aquablation has a proposed payment that would provide the hospital $9,209 and the ASC setting $6,666 for each Aquablation procedure which is a 5% and 7% increase respectively over the 2024 rates.

As such, we're looking at +500-700bps or rate increase and this is a tailwind in my view - especially given recent FDA approvals, as further favourable increases aren't out of the question.

Both handpieces revenue + international sales were large contributors in Q2, up 101% and 79% YoY respectively. Handpiece ASPs came to ~$3,200 to drive this result, and it shipped ~8,000 units during the period. The handpiece is proving to be an attractive tail of sales for the company once systems are placed - i.e., the razor + razor blade model.

Meanwhile, gross profits earned on total assets employed on the balance sheet have stretched up to $0.26 on the dollar in Q2 (Figure 5). This has increased from <$0.10 on the dollar in FY'21, indicating 1) the higher units placed, 2) the tail of income built from handpieces, and 3) the increased utilization of the entire installed base.

Company filings

Valuation and conclusion

ORCT sells at ~19x forward sales and investors continue paying this on expected growth. It is expecting ~$216mm in FY'24 sales under these assumptions and valued in market at $4.12Bn. Consensus eyes $216mm this year as well, stretching 40% higher in FY'25E to $304mm. If the business does hit these estimates (my numbers imply ~$340mm see: Appendix 1) the same 19x multiple gets us to $5.7Bn or $111/share, otherwise 42% upside from today. In my view, this is high and the margin of safety is high at 19x as we can compress to 15x and still trade at $87/share under these assumptions (21% contraction still providing ~6% upside). In my view, PRCT is worth at least what we pay for it today in the downside scenario, and worth multiples of in the upside case.

As such, I reiterate PRCT as a buy, eyeing $111/share as the next price objective.

Key downside risks to the thesis include 1) management hitting <25% sales growth as this hurts the valuation, 2) pace of new installed base slowing to zero, 3) valuations compressing <10x sales (I give this ~10% probability), and 4) the broader set of macroeconomic risks that must be considered at this point in the cycle, namely the inflation/rates axis, and geopolitical risks that could spill over into broad equity markets. These factors cannot be ignored, as they may have an outsized effect on PRCT.

Investors must recognize these risks in full before proceeding further.

Appendix 1.

Author's estimates

This article was written by

Analyst’s Disclosure: I/we have a beneficial long position in the shares of PRCT either through stock ownership, options, or other derivatives. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Seeking Alpha's Disclosure: Past performance is no guarantee of future results. No recommendation or advice is being given as to whether any investment is suitable for a particular investor. Any views or opinions expressed above may not reflect those of Seeking Alpha as a whole. Seeking Alpha is not a licensed securities dealer, broker or US investment adviser or investment bank. Our analysts are third party authors that include both professional investors and individual investors who may not be licensed or certified by any institute or regulatory body.

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