A Compilation of Various Examples

At some point, I decided to try learning one example from mathematics, per day. Hilbert or Feynman or some other famous person said it is good to always have (counter)examples on hand. That way, one can use them as testing grounds when learning a new result or when looking for evidence in support of a particular claim.

The examples I seek can be constructions, lemmas, theorems, etc. I was mildly successful at first but lost steam, eventually (around the middle of 2019). Still, here are some examples of varying depth. Some examples, I think every mathematician should know while others are more for specialists. Some really shouldn't be called examples as much as Fields medal worthy theorems. I'm sure there are mistakes in these notes. Email me if you spot them. Needless to say, these are not exhaustive. Also, I occasionally mention some colleagues by name in these notes.

I have also made many notes. I've included some of the ones made on TeX or GoodNotes but not the ones from the markdown editor Zettlr. Email me if you're interested in the Zettlr notes.

Notes on Geometry

Notes on Physics

Other Random Notes