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You might be looking for: Groupprops versus Wikipedia
This article describes how Groupprops users can effectively make use of Wikipedia for seeking information and ideas in group theory and related subjects.
Since both Groupprops and Wikipedia are rapidly growing and changing, the article focusses on aspects that are more likely to remain stable than on specific current content.
Some things to keep in mind about Wikipedia
Wikipedia has a lot of dynamically growing content coming from a number of different perspectives. However, Wikipedia's content within specific areas of group theory is not currently in the best shape. It is possible, and likely, that the content will improve over time, but there are some fundamental aspects of Wikipedia's policy that should be kept in mind:
- Wikipedia is an encyclopaedia. It has policies like notability, neutral point of view, no original research. These policies are suitable for an encyclopaedia, which need to provide a fair representation of a wide range of content, rather than provide isolated in-depth knowledge of a particular piece of content. I suspect that in many respects, Wikipedia beats encyclopaedias of the past in breadth; however, as an encyclopaedia, it is by its very policy limited to covering things that are important, notable, stand the test of time, and are agreeable to all.
- Wikipedia is meant to be read by all. So, the kind of organizational experiments that we run on Groupprops aren't possible on Wikipedia. At any rate, they haven't been done till now, since it would be very hard to decide on these kind of organizational policies and have everybody find them acceptable.
- Wikipedia is meant to be edited by all, or at least by a large number of people. This means that a lot of the code on Wikipedia pages is administrative code that gives information on what defects are currently there in the article. Such information is largely missing from the front-up of Groupprops pages.
- Wikipedia has a very huge flow of content, often written by different people. It's like a sea of activity with lot of people creating splashes and then other people cleaning things up and making something more durable.
Finding group theory on Wikipedia
The central point for group theory on Wikipedia is:
Most resources can be obtained from here. These include:
- A list of group theory topics
- A glossary of group theory
- The Wikimedia Commons category on group theory: This provides images, soundclips and other media resources for group theory.
Subcategory structure within this category
The category group theory has a subcategory structure, which is not yet stable, and is likely to be improved over the course of time. The way Wikipedia works with and uses categories is very different from the way they're used in Groupprops. Firstly, a category in Wikipedia is more of a loose related to thing than a precise is a thing, as is the case in Groupprops. So a category in Wikipedia titled Lie groups doesn't just give those things that are Lie groups, it gives any article that is related in a strong way to Lie groups. In Groupprops, a category titled particular groups actually lists only things that are specific groups.
What falls under group theory?
One powerful thing about Wikipedia is that it has content, not just on group theory and very closely related material, but also on more far-out material, and it also has articles that may read better from the perspective of somebody who wants to get a general picture of a broad area. In fact, many of the articles listed under the group theory category in Wikipedia are on subjects that do not precisely fall under group theory, and this leads to a natural mixing around and jumping into other subjects. This is one of the advantages of using Wikipedia (though not a disadvantage for Groupprops: we serve a somewhat different purpose).
Article quality of Wikipedia articles varies greatly. In general, the more people there are who have edited the article, the more likely it is to be correct; this does not give a guarantee about how good the presentation is or how useful the information is to a group theory student.
On Groupprops, we measure our articles against a number of parameters, most of which keep in mind the concerns of group theory students and teachers. Wikipedia does not use similar metrics; it's concern is to create a good encyclopaedic article. So to make the best of content on Wikipedia, keep in mind that their concerns, and their metrics, are different from ours.
When checking an article on Wikipedia, try the following:
- Check for references, and check the references. Wikipedia is best used as a starting point towards further resources
- Check the talk page to see if the article has had any contentious issues in the past
- See the history page to know how many people have been editing the article
There don't appear to be any videos, as of now, on using Wikipedia for mathematics-related knowledge gathering. Videos on using Wikipedia can be easily obtained by a Google Video Search.