It's surprising to me - 300+ level courses were part of my undergrad required coursework - of course I wasn't studying at Stanford. Are course numbers standardized across academia or unique to an institution?
Course numbers are not standardized, although there are common numbering schemes. There are some uncommon ones such as MIT's, which uses a number and a dot instead of a subject name. And I've never known what institution the typical "CS 101" numbering scheme applies to.
Afaik they're unique—and not monotonously increasing in difficulty either. Here's Stanford's numbering system for reference: https://cs.stanford.edu/academics/courses