sreahw/schuller-geometric

Source code for lecture notes

schuller-geometric's Issues

Publish a PDF that can be printed on lulu.com

Hi Simon! Thank you so much for these invaluable notes. I attempted printing them out on lulu.com and got this error-

Would it be possible for you to update the PDF to satisfy these constraints or provide some pointers on how I could do the same?

Definition in lecture 14

The definition of an algebra being "semisimple if it contains no non-trivial abelian ideals" on line 41 should be changed to "semi-simple if it contains no non-zero abelian ideals", or, mirroring the first phrase, "semi-simple if it is non-abelian and it contains no non-trivial ideals". Otherwise, remark 14.2 wouldn't make sense; as it stands, the one-dimensional Lie algebra si semisimple because it has no non-trivial ideals (in particular, no-nontrivial abelian ideals).

Reserve \colon for ("type") signatures

The notes currently use, at several places, the \mapsto notation (which is used to define a "value" of the type "function") right after the \colon which is normally followed by a function's signature and can be read, more or less, as \in (assuming that the subsequent \to expression constructs a "type", or a set of appropriate functions).

An example of the offending sentence:

schuller-geometric/ga/12grassmann.tex

Line 49 in d324cd4

&f &\mapsto &\Phi^*(f) := f\circ \phi.

A cleaner alternative:

Or simply:

P.S. This "issue" is not a call to action, but more of a remark. I'm leaving it because I think Frederic Schuller's lectures are a great example of the fine balance between what constitutes a "clear exposition" of a subject, and a "coarse-to-fine" one. The former means that the exposition is rigorous and accurate enough not be confusing, which includes notation. The latter means that (at most times) it's not overwhelming, and gives relevant pieces in a sensible order. These notes can serve an example and it would be only fair if we were to slightly adjust the style

Possible error on page 59

On page 59, we see the proof that the space of (1,1)-tensors is isomorphic to the endomorphisms on the dual space. The construction in the forwards direction takes a (1,1)-tensor T and maps it to the endomorphism mapping a covector \omega to the covector T(-, \omega). I believe it should be T(\omega, -), since T is a bilinear map V* x V -> K, and the covector \omega lives in V*.