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I have found that wikipedia is not a coherent, exhaustive, or detailed reference. I would like to find a similar resource that explains academic/scientific terms and methodologies clearly, briefly, and in a detailed manner. Ideally, this resource would be freely available on the Internet and provide descriptions that clarify these sorts of terms e.g: theory, theorem, hypothesis, assumption, conjecture, lemma, corollary, law, rule, principle, etc.

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    This may sound mean but it's not intended as such: have you tried a dictionary? – Marc Claesen Nov 28 '13 at 14:34
  • @MarcClaesen No problem. I would like something that describes these terms in more depth and more precisely than a dictionary or an encyclopedia. E.g. providing some examples and explaining why they are one thing or another. The dictionary says that a conjecture is a theory, which is "a body of principles, theorems, or the like". A principle is a law, and laws are only good for lawyers there... – Trylks Nov 28 '13 at 16:06
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    imho, wikipedia is remarkably good for many of the examples you laid out. For instance: en.wikipedia.org/wiki/Hypothesis is very good. I don't know how much more detail you require. The other alternative is to read books on research methodology. They will have most of these laid out in great detail. – Shion Nov 28 '13 at 16:48
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    I'm a little confused as to what you would like. You write that you'd like a reference source that is - amongst other things - brief and rigorous. It is occasionally possible to have both qualities. You find Wikipedia entries not exhaustive and therefore deficient. I suggest that it is quite unlikely to find a reference that is rigorous and exhaustive and, at the same time, brief. – Nicholas Nov 28 '13 at 20:56
  • Each definition should be brief and rigorous, the number of definitions should be exhaustive. I was assuming that exhaustiveness is referred to elements (like definitions) in a set, sorry for that. – Trylks Nov 29 '13 at 9:30
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Here is a short list of resources, for different fields, which I frequently use for reference:

  1. Springer, Encyclopedia of mathematics
  2. IEC, Electropedia: The World's Online Electrotechnical Vocabulary
  3. IUPAC, Compendium of Chemical Terminology - The Gold book
  4. IUPAC, Quantities, Units and Symbols in Physical Chemistry (pdf)
  5. JCGM, International Vocabulary of Metrology
  6. IEEE, The Authoritative Dictionary of IEEE Standards Terms (requires subscription)
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If you find wikipedia not clear and brief enough, try wiktionary instead. Instead of a full scale encyclopedia type site, wiktionary only provides definition and examples.

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Here is the result for entering "theorem" into Wolfram alpha:

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof.

Although not absolutely standard, the Greeks distinguished between "problems" (roughly, the construction of various figures) and "theorems" (establishing the properties of said figures; Heath 1956, pp. 252, 262, and 264).

According to the Nobel Prize-winning physicist Richard Feynman, any theorem, no matter how difficult to prove in the first place, is viewed as "trivial" by mathematicians once it has been proven. Therefore, there are exactly two types of mathematical objects: trivial ones, and those which have not yet been proven.

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