I want to know that is there any authentic book which has all the definitions atleast upto under graduate level of concepts such as point of inflection, monotonicity, tangency, concavity etc. as I found different definitions in different sources and some were missing certain conditions while some were imposing extra ones.
2026-03-28 14:05:35.1774706735
Mathematics Equivalent of IUPAC Gold Book
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Maybe a mathematical dictionary will help.
For example, the Concise Oxford Dictionary of Mathematics. The link has entries for monotonicity and tangency and the rest that I checked, although they are hidden behind a paywall.
Otherwise, I would recommend the Hazewinkel-edited Encyclopedia of Mathematics and Eric Weinstein-edited Mathworld. For your interest, there are the corresponding articles for monotonic functions (Encyclopedia and Mathworld). Both of these websites show references (for example, in this case, Rudin and Royden) and these can be easily corroborated.