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**Writing a Mathematics Essay**

While writing a mathematics paper needs the skills and care applied to other academic writings, a mathematics essay is somewhat different and even harder than conventional essays in terms of additional conventions and constraints. In mathematics writing, one additional constraint is that mathematics follows a logical rule that is much more demanding than conventional writing, and your writing demands to show this logic. This is not to say that there is one particular way of presenting an argument in mathematics. Rather it means that for mathematics papers, additional considerations should be made. Some of the additional conventions addressed in this article are those relating to the definition of new concepts and those relating to material organisation through examples and theorems.

### How to Write a Strong Mathematics Thesis

Writing a paper in mathematics is a skill that might take time to learn and mature. The tips given in this article are intended to offer considerations to take into account in one’s writing, the conventions to take note of, and the most common pitfalls that should be avoided. While some of the tips might seem like common sense, it should be noted that some of the guidelines can be forgotten even by experienced writers. Therefore you should reflect on the provided tips and make the conscious decision to incorporate them into your writing.

### Tips for Writing a Mathematics Research Paper

When writing a mathematics essay, one important consideration is to apply brevity to your writing. In other words, without the use of jargon and unnecessary words, you should undertake to write as directly and as simply as possible. This is not to say that to be good, the ultimate essay must be short, or that some details need to be omitted. Rather it implies that a good thesis in mathematics is one in which each sentence, phrase or word contributes to the communication of your message.

Relatedly, you need to precisely and accurately use language. Mathematics requires the writer to be careful in his or her choice of words, more than any other discipline. Theorems, for example, should be unambiguously and carefully articulated. Arguments made must also be clear and logical, and what the author intends should be communicated by exposition. A research paper on mathematics should for example, ensure that the word “differentiable” is correctly used. When using words which may have unintended meanings, you should also take care. For instance, when it means that it is easy to understand, using the word “simple” to refer to a ring could be mistaken as implying that the ring lacks ideals. “Natural”, “trivial”, and “complex” are other words that can be easily misinterpreted.

It is stronly recommended that you organise your mathematics dissertation in order to make your exposure clear. In many cases, when testing theorems, students tend to start collecting results before proving a theorem or creating a theory that condenses results as special cases. When writing the results, a student may choose to first prove a general theorem before obtaining a special case as a corollary. However, it may be more appropriate to start with a few specific examples that outline important concepts and inspire more general work to be done. However in either case, you should not be tempted first to prove a specific theorem, followed by a more general one, as this would mean undertaking an unnecessary repetition.

Another useful recommendation to write a strong mathematics term paper is to write a good introduction. Most of the readers of mathematics papers tend to read the introduction and skim through theorems. In addition, if your reviewer reads a grant or fellowship proposal, his or her opinion on your work is most likely to be significantly influenced by the introduction. As a result, we recommend that you put a lot of effort and time into a strong introduction in writing. You should introduce the topic you are working on, motivate a solution to the problem, summarise or clearly state your findings, and explain the significance of the findings. Try to connect your work to the work of others in the same field as much as possible. Always remember that the introduction is meant to ‘sell’ your work and convince others of its significance. As such, write your introduction after completing the body of the paper. More importantly, listen to the criticism and make a point of learning from it.

*In summary, to write a good mathematics paper, you need to:*

- Apply brevity
- Use language correctly and precisely
- Organize appropriately and
- Write a good introduction