TITLE: How does Schur determine Galois groups of truncated exponential series?
QUESTION [6 upvotes]: On Serge Lang (page.274 Example 8) and several algebra textbooks, it goes as 
$$f_n=\sum_{m=0}^n \frac{X^m}{m!}\qquad \operatorname{Gal}(f)=\begin{cases}
\mathfrak{S}_n& 4\nmid n\\ \mathfrak{A}_n& 4\mid n\end{cases}$$
It is claimed that the result is due to Schur, but the reference is in German and the full text is unavailable. Are there any textbook introducing it, or some review on it? And I know nothing about $f_n$, what can we say about it, such as its discriminant?

REPLY [2 votes]: There is a nice (and short) proof of this result using Newton polygons in "On the Galois groups of the exponential Taylor polynomials", by Robert F Coleman. 
A good exposition of the topic may be found here: https://mattbaker.blog/2014/05/02/newton-polygons-and-galois-groups/