User:MarSch/math article structure

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These are my views on what the structure of a mathematics article should be.

Motivation

The article should start with a motivational discussion of why the subject of the article is interesting. This should take the form of an abstract of the whole article as is found on many featured articles. It should explain why this subject exists and what good it is and what it's major results are. Also it should be put into perspective by explaining how it relates to other areas of mathematics. What does it generalize, what generalizes it?

Informal description

Then there should be an informal introduction/description. This should say in words with few or no formulas, and without lies, as much as possible about the subject.

Formal description

Up to here the mathematics article looks very much like any other article, but this part is a bit different. The reader should now know what this article is about and it is time to dive into the formal description. Full definitions should be given. In case of alternatives they should all be given and shown to be equivalent. Notation should be introduced and explained. Also don't forget to include examples, including a trivial example for each definition. Each example should however be different enough from the others to add information.

Applications

The reader should now be able to understand some calculations and thus it is time for some applications. This will show how the theory is put into practice, which is very important as you can only understand mathematics by doing mthematics.

Related subjects

Internal links to related subjects. Generalizations and what not.

External links

Links to this subject elsewhere, like for example on MathWorld or PlanetMath.

References

List of some good or standard works on the subject.

Some general remarks

• Each part should start easy and continue to the more challenging, not the other way around.
• Autoreference your formulas as much as possible by
  • using them in calculations, or
  • proving them.
• If certain parts of the article get too dominant then they should be moved to a separate page. The main page should include a short version and a link to the full version. The subpage should contain a backlink. Most importantly it should always be clear where to add a piece of information.

I'm not sure about where to stick history yet, but in the User:MarSch/example_math_article_structure it goes in right after motivation.