do you know good websites/books/PDFs in which many examples to topics are discussed? What I mean by that is, I am looking for sources where to each topic there are plenty of detailed discussed examples. So if I want to study Group Theory I can look it up and find good examples of different groups where also we have sets and mapping and it is proven that the given set with the mapping is indeed a group. Or manifolds/PDEs/ODEs/Integration/... I found one website which kinda helps but it is not perfect. Ncatlab.org
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mathsdummie1234
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For groups, there’s GroupNames (https://people.maths.bris.ac.uk/~matyd/GroupNames/). For modular forms/elliptic curves/number fields/some other stuff, LMFDB is pretty good. – Aphelli Feb 09 '23 at 12:24
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Perhaps you'll find An Infinitely Large Napkin by Evan Chen interesting. – Jesus Feb 09 '23 at 12:25
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An Infinitely Large Napkin is great, thanks a lot!!! – mathsdummie1234 Feb 09 '23 at 12:30
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This might sound like almost the opposite of what you're talking about, but there's an informal series of books called "Counterexamples in..." that consist primarily of a large collection of pathological constructions of objects which highlight how certain concepts are distinct from each other. To my knowledge, the first of these books was Counterexamples in Topology, which hosts a list of over 100 different topological spaces with different collections of properties.
Here's another post that includes a list of several of the "Counterexamples in" texts. It is an incomplete list, as at least two other texts in this vein have been published in the last few years, namely Counterexamples in operator theory (M. Mortad) and Counterexamples in measure and integration (R. Schilling, F. K"uhn).
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