How effective is Wikipedia for first line of attack?

Question

I am learning some pretty disconnected concepts of mathematics for a project I am working on. I was reading about matrices and suddenly had to know about Markov Chains and that lead me to read about Multivariate Expectations and so on.

I was initially spending time in the library with the main book and everytime I encountered a problem, I'd go looking for a book which I thought would explain it, read it and return to the main one. Just as an experiment, I tried using Wikipedia to understand the concepts and then did google searches with 'site:.edu' references to look for coursenotes and then browsed through some of those till I felt comfortable and went back to main book.

For mathematics, is Wikipedia a good first line of attack?

Answer 1

I use it sometimes as a first choice. Other times I start with Google and the first hit will be a Wikipedia page. My experience is mainly with statistics and probability but I sometimes also use it for other topics. My children were taught in school to never use wikipedia as a direct reference in their reports. The issue to keep in mind is that there is free access to publish in Wikipedia and so many items may not be thoroughly check for validity. But my experience as a professional statistician is that most articles are statistical topics were posted or edited by trained professionals and the article are very accurate to the point and informative. They also avoid specialized jargon that the public is unaware of. Most article site reputable reference sources. After you read the Wikipedia article you should check out some of these references and make sure that the authors of the Wikipedia article have said things that are consistent with reputable sources.

Sometimes when answering questions on this site and CV I go to Wikipedia to refresh my memory on a topic or to provide a formula I forgot how to produce exactly.

Answer 2

Wikipedia has to be taken with some grain of salt. Most of the mathematics is correct, but even then you might get concepts in a form that are either too general or not general enough. Wikipedia is a useful starting point for looking something up, provided you already have a solid foundation and the means to look something up in an actual library.

But in order to get the foundations, I would suggest that you use actual books or lecture notes that are at your level. You might look something up from time to time to fill small gaps, but there is a logical structure to mathematics that needs to be followed. You use results to prove further results and to actually understand them all, you have to start at the beginning.

I think that if you read about matrices and need to know about Markov chains first, your book on matrices is likely to be too advanced for you.