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Make sure both you and your advisor agree on you being ready to graduate, and when you can graduate.
You chose a committee for your Preliminary Exam, but some of those members may have left Duke, or may be too busy to serve on your committee. You'll need four committee members besides your advisor. If you are an experimentalist, one of those members will need to be a theorist; if you are a theorist, one will need to be an experimentalist.
Duke won't let you graduate if you don't tell them you intend to by filling out an Intention to Receive Degree Form. You can fill out a form as far in advance of your graduation as you like -- if you're optimistic, you can fill it out during your first year. There is no penalty for filling the form out and then not graduating when you said you would, but there is a deadline for filling it out, based on when you want to graduate (May, September, or December of your chosen year).
The form will ask you for your thesis title and your committee. If you have to make later changes to either, it can be done, but will require more work on your part.
Duke maintains a thesis style guide which can be downloaded from their Academic Regulations Downloadable Forms page. The guide mentions the Intention to Receive Degree Form, the format which your thesis must follow, and the many steps you have to take to submit your thesis.
How to write a good thesis is far beyond the scope of this document. We're dealing with the technical issues here. If we lived in a just world, the graduate school would offer help on writing your thesis. I recommend you use LaTeX to compose your thesis, instead of a word processor such as MS Word. The rest of this section assumes you're using LaTeX.
If you don't know LaTeX but would like to learn, two books I recommend are LaTeX: A Document Preparation System, by Leslie Lamport, and The LaTeX Companion, by Michel Goossens, Frank Mittelbach, and Alexander Samarin. The former provides a general introduction to LaTeX. The latter explains LaTeX's features in more depth and discusses a number of useful packages, or add-ons, for LaTeX.
LaTeX is installed on all of the department-maintained Linux boxes. For Windows, you should download MiKTeX. For Macs running OS X, you can install LaTeX as part of the Fink project. For other Macs, OzTeX is a reasonable solution, though it's shareware. (In fact, all of the Mac LaTeX distributions I know of other than the base one installed by Fink are shareware.)
Any LaTeX distribution will most likely have the AMS-LaTeX libraries installed. They're worth using, as they're from the American Mathematical Society and have a lot of nifty additions. The LaTeX Companion describes the AMS packages in some detail. For full information about AMS-LaTeX, download the User's Guide from the AMS-LaTeX page.
LaTeX code is best written in a text editor rather than a full-blown word processor. People tend to be passionate about what text editor to use, especially under Linux. For Windows, I recommend WinEdt. It's shareware, but the department has a site license for it. To request a registration code from the department, email firstname.lastname@example.org. For Macs, try Alpha or BBEdit.
For your convenience, there's a style file for Duke dissertations. Note that this is not an official graduate school style file. Rather, it's a style file which follows all of the formatting guidelines laid out in the thesis guide. Instructions on its use are included in the file.
The style file makes use of a number of LaTeX packages: amsmath, setspace, saferef, cite, graphicx, chngpage. If any of these aren't installed in your system, search for them on CTAN, the Comprehensive TeX Archive Network.
You will need to schedule a day on which to defend your thesis. Talk to Donna Ruger to reserve either the Faculty Lounge or the conference room behind the Department Chair's office.
You're required to give a talk, usually 45 minutes to an hour. You can use printed slides or computer-projected ones. I recommend you project your slides, as it lets you modify your slides easily. This is especially important in the event that one of your committee members has concerns the day before your defense which require you to make changes. The department has a data projector which you can borrow. To schedule your usage of the projector, speak with Bill McNairy.
If you use MS PowerPoint to create your slides, consider using TeXPoint. TeXPoint is a plugin for PowerPoint which, if you have MiKTeX installed on your computer, can create bitmapped images of LaTeX-typeset equations. Best of all, the definition of the equation stays with the bitmap, so that you can easily edit and update the equations later.
If you'd prefer to use LaTeX to create your slides, yet want to use computer projection rather than printing out your slides, you can create a presentation using LaTeX and PDF. One tool to help you make your presentation is PPower4, a Java-based postprocessor for generating dynamic PDFs.
At least one week before your defense, you must have your thesis vetted by the Graduate School. They'll check that you have all required pages, and that your margins are all correct. Of course, if you're using the Duke Dissertation style file for LaTeX, you should be fine. The procedure for this check is explained in the thesis guide.
You should give copies of your thesis to your committee at least a week before your defense, to give them time to read it. Donna Ruger has a set of three-ring binders which you can use for distributing your thesis.
Remind your committee about your defense the day before. When you go to the defense, take with you the exam card the Graduate School gave you when you had your thesis checked, and two copies of both your thesis signature page and abstract signature page. At least one of those copies must be on the white, watermarked, acid-free, 25% cotton bond paper the thesis guide specifies. (You can get such paper from the Duke University Bookstore, though any office supply store also carries such paper.) Have your committee sign all five things (four signature pages and your exam card) once your defense is over. Then go party!
After your defense, you have thirty days in which to correct your thesis and submit it. If you need more than thirty days, you have to get permission from the Graduate School. The thesis guide will explain the procedure for doing so.
You'll have to pay the Bursar's office for your binding, microfilm, and copyright fees. You'll take several copies of your thesis to 013 Perkins, and return your exam card. All of this is explained in the thesis guide.
And once you've done that, you're finished! Congratulations.