Most students find that doing the research for the thesis is the most challenging part of graduate school. They often budget their time to allow a very short period for the actual writing of the thesis.
This plan invariably leads to an unpleasant surprise: writing results in a form that other people can understand is a very slow process! Here are some of the often unanticipated reasons:
Even after you are on track, you will probably find that a ``good'' day of writing produces about 5 pages, leading to an overall average of perhaps a quarter page per day.
Some habits begun early in your research will help:
A student who has developed skill at writing non-technical term papers as an undergraduate will have an easier time of learning to be a good technical writer, but there is one additional skill that must be added: you must also be a good teacher!
When you write a term project, you are explaining the work of others. You have a good idea of what is immediately obvious and what is more difficult to grasp, since you recently went through the exercise of grasping the material yourself.
It is easy to be fooled into thinking that since something is now obvious to you after several years of study, it is also obvious to your reader. The most difficult part of thesis writing is organizing and presenting your material in an understandable way.
An important early step is to develop a tentative outline. The outline will probably change several times, but it is important always to have a current one foremost in your mind so that you can make the pieces fit together smoothly.
A typical outline will be of the form:
Chapter 1: IntroductionWhat is the problem?
Why is it important?
What have other people done?
What are the central ideas and contributions of your approach?
How is the rest of the thesis organized?
Chapter 2: The problemDefine the problem.
Introduce the jargon.
Discuss the basic properties.
Chapter 3: Big idea 1
...
Chapter: Big idea
Chapter: Conclusion
Recapitulate what you have accomplished and why it is important.
Discuss ideas for future work.
Don't think that the thesis must be written starting at page 1 and continuing until the end. Most often, the presentation of the ``big ideas'' shapes the presentation of ``the problem.'' The introduction is often written (or at least rewritten) last. The important thing is to jump in and begin writing something, and make notes along the way of how other sections need to be adapted so that they all work together.
One way to organize each chapter is to present the material to a group of fellow students. (If you cannot find an audience, then present to an imaginary one.) If you can organize your ideas into a coherent hour lecture, on a level understandable by your fellow students, you are probably ready to write a chapter.
Remember that the style of thesis writing is expository: you are trying to communicate your ideas, their significance, and their limitations. It is not the compressed style of a page-limited conference paper or journal article. Don't make your reader work too hard! At the same time, don't talk down to the reader, wasting time with repetition or adding unnecessary filler. Committee members and later readers will resent such tactics.
See 15.6 for suggestions on writing manuals.
A major decision to make is the choice of document processing system in which to write your text. Knowledge of a good text processing system is almost as basic a tool to a professional in the mathematical and computational sciences as calculus or a good programming language. Although technical typists used to be common, they are an increasingly rare breed, and professionals are expected to be able to produce their own manuscripts.
Currently, the most popular typesetting and formatting systems are Tex, AMS-Tex, and Latex. Less elaborate systems (e.g., Microsoft Word) might get you through your thesis, but eventually you may be forced to use one of these systems in order to communicate with colleagues and to transmit manuscripts to journals. The Tex-based systems can be used on workstations, personal computers, etc., and most journals can accept files in these formats, thus saving you the enormous job of proof-reading a manuscript that has been typeset after conversion.
Each university has a set of style requirements for the thesis. These requirements often give rules for the use of different fonts, the format for bibliographies, the width of the margins, etc. Check around and see if your department or university has a style file compatible with with your typesetting system, so that you can satisfy these rules easily. If not, be prepared to iterate a few times to make the style-checkers happy.
Ideally, you have chosen your committee members because of their interest in your research area and in you. Ideally, the members have followed your research over the course of a year or more, and understand your problem and your approach. Ideally, they all get along well, and egos are not a factor. And ideally, they are willing to take the time to read your thesis in detail and give you valuable feedback.
But the world is not always ideal. You might be very lucky to find one professor other than your advisor who is willing to listen and read and comment meaningfully. Other committee members may prefer a less active role, at one extreme, simply showing up for your oral exam and questioning you. Rules or reality may have dictated that some committee members have little interest in your research area, or little time to devote to mentoring.
Whatever the situation, draw your committee members as much into the process as they wish to be. If the committee is established early, then stop by or send a brief update to them two or three times a year so that they can follow your progress. If it is established after the thesis is written, give them plenty of time to read the thesis, and then contact each one, asking whether it would be helpful if you stopped by to answer questions or discuss your work. You don't want to be surprised at the oral exam by a very unhappy committee member.
After the oral exam, it is courteous to give a bound or electronic copy of the final version of the thesis to each committee member, and to express gratitude for the time they spent on your committee. Their participation should be noted in your thesis acknowledgements.