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Expository papers in mathematics

Introduction

It's very helpful to have an introduction (and depending on how long your paper is a summary) to contextualize your paper. Introductions should not bomb the reader with severe mathematics. Keep it lightly. It is often interesting to judge the paper in an interesting question that can only be answered by understanding the material in your paper. Or if your topic is not something, you can integrate into a real problem, use your introduction to convince the reader of the relevance of the topic. Why is it interesting? Which subfields of mathematics is it relevant? Historical background, if you decide to use arbitrarily, will find a great home in the introduction.

Audience

As with any paper, it is important to know your audience. If your professor does not specify, ask. Can you assume that the reader has accepted your course? Or should your paper be accessible to the general public? With mathematics, it is essentially its own language, it is important to know how much hand holds and defines that your paper should do this. However, regardless of your audience, you must give concrete examples of the often abstract ideas.

Examples

Use examples in case of doubt! Examples are the best way to make your reader to the ground and make sure you understand your complex material. In particular, choose if your definitions or theorems are generally choosing a basic but illustrative example with which it costs. It is often helpful to give an example before specifying the general definition or theorem. In this way, the example relieves its reader into the general form, in contrast, that it serves as damage control after he had her with the abstraction.

Style

Let your voice come through! Just because it is a math paper, that does not mean that it has to maintain the stigma of the field, to be dry and clinical. Your reader should read your paper. So do not shy away from a punny, a sound, or vary your syntax. And have fun - just as you would write it in any piece. What a mathematical paper is unique is that actual definitions, theorems, assumptions, evidence, etc. must keep their formalities.

Thus, it is helpful to visually keep your informal prose from the more accurate and technical components of the paper. Paragraphs and punctuation are still crucial in mathepapers (and the same rules of grammar), but the prose can certainly and should be spliced ??by definitions, examples, theorems, evidence, etc. It would be helpful for the spirit and light eye to use fat printed and inexpensive language, optionally for distinguishing and consistency. In addition, papers are often divided into sections and subsections to enable the structural sense of the material.

Latex

latex is a sentence language that makes much of this formatting for them and is especially helpful to spend equations. It is the most commonly used language for writing technical math securities. Some professors can even require you to use latex. If so, Claremont Center is a helpful resource to learn for Mathematical Sciences (CCMS) software laboratory. They offer tutorials in the library.

Notation

Make sure you understand the conventions of the subfield that you discuss. Subfields of mathematics have specific ways to express things, and the same symbol can mean something completely different in two different subfields. In this vein, they clarify what their symbols mean. Now the mathematical shortships in the class lectures is prevalent, but in their paper no appearance must be made. Just as academic papers do not use on contractions and abbreviations, the prose of their math paper should use words.

Conclusion

You do not necessarily need a conclusion, but it's a beautiful way to pack.Many mathematical papers abruptly abrupt, so you really should not feel obliged to write a conclusion. If you choose to write, you can book it with some of the information forwarded in your introduction. It can be more mathematics in itself than the introduction, but it should not leave your reader with the sensations of overwhelmets. It may also contain the restrictions or expanding the applications of the topic / results, and it can highlight open problems and suggest areas for future research.

Bibliography

Of course you are suitable for your sources! It is a convention to use endnotes to quote information throughout the newspaper so that the set of the sentence is not interrupted. If you use latex, it compiles a bibliography for you while you write and quote. Make sure your sources are reliable and valid. Peer reviewed sources are ideal.

Further information on mathematical writing (including tips for writing Proofs, Poster and Research Papers) Reference Manual of writing for the mathematical sciences of Nicholas J. Higham (1998).

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