# Writing a Mathematics Essay

While writing a mathematics paper requires 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. One addition constraint in mathematics writing is that mathematics follows rule of logic that are much more demanding compared to conventional writing, and your writing is required to show this logic. This is not to say that there is one specific way of presenting a mathematics argument. Rather, it means that additional considerations should be made for mathematics papers. Some of the additional conventions, which are discussed in this article are those related to defining new concepts and those related to organizing material through examples and theorems.

## How to Write a Strong Mathematics Thesis

Writing a mathematics paper is a skill that may take time to learn and mature. The tips provided in this article are meant to offer aspects to consider in one’s writing, the conventions to take note of, and the most common pitfalls that

ought to be avoided. While some of the tips may seem like common sense, it should be noted that even experienced writers can forget some of the guidelines. You should, therefore, reflect on the tips provided, and make the conscious decision to incorporate them in

your writing.

### Tips for Writing a Mathematics Research Paper

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

Relatedly, you need to use language correctly and precisely. More than any other discipline, mathematics requires the writer to be careful in his or her choice of words. Theorems, for instance, should be articulated unambiguously and carefully. Arguments made must also be clear and logical, and exposition ought to communicate what the writer intends. A mathematics research paper should, for example make sure to use the word “differentiable” correctly. You should also take care when using words that may possess unintended meanings. For example, using the word “simple” to refer to a ring when meaning that is easy to understand, could be mistaken as meaning that the ring lack ideals. Other words that can be easily misinterpreted include “natural”, “trivial”, and “complex”.

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

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

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