Tips for Writing Your Mathematics Paper
The most important thing to remember about a dissertation or research paper in the field of mathematics is that the basic rules that apply to all such documentation apply to papers in math as well: your paper must be written in English (which is to say it cannot be a series of mathematical formulas), should begin with a clear and concise introduction that states the primary hypothesis, and offers a structure of development that puts the primary hypothesis in context. This last aspect of your manuscript is probably the most important to keep in mind, especially as a means of not becoming intimidated at the prospect of preparing formal research in this discipline.
The primary purpose of your paper is to present the results of your research, but that is not all that it will do. It will also put the results of this research in context. Your paper is not just an opportunity for you to provide the answer to one specific question. In this field in particular, your paper is also an opportunity for you to show your familiarity with the general field of study and to demonstrate that you know more than just your own results and the proofs of these that you are providing in the paper. As is the case with virtually all academic documentation in all academic disciplines, the best way to begin is to begin with a formal and comprehensive outline of your paper.
Once you have completed your outline, you can begin with the writing of your thesis. Your paper will begin with an introduction which explains what your research has revealed, summarizing the problems that you have worked on and how these problems influenced your overall results. Your introduction will usually be followed by a section that gives some background with respect to the problem that you are describing. Don’t forget that while it is true that your reader will probably be a formal mathematician, your reader has not been involved in your specific research over the past several months, so keep in mind that your reader may benefit from definitions and clarifications in the most complex elements of your work. You will also want to refer to other work in the field that is relevant to your thesis, and this material can appear in a separate section devoted to background material or in your conclusion. Again, keep in mind that your dissertation must be written in English and that it cannot be in the form of notes or sequences of unexplained formulas. It is important not to start sentences with symbols and it is especially important never to use the same symbol for two different things. All of these aspects of your research paper in mathematics are aspects that can benefit from the assistance of a professional editor.