I think all of us could use a course in analytic continuation. Some of the things we're talking about in this thread rely heavily on theorems and terminology in analytic continuation theory. Some other related subjects include cohomology theory, fiber bundles, sheaf theory, and Riemann surfaces.
I think if we at least use the right terms, then we could all understand a little more. For example, different parts of the analytic continuation of a power series to its corresponding Riemann surface are not called "the logarithmic landscape" but could instead be called germs or sections.
There might even be nice formulas for analytic continuation, easily found if only we knew to search for "X theorem", since search terms can be a desicive factor in how successful a search is. I'm not sure if I can suggest anything in particular, but it certainly seems as if a little bit of rigor would do us some good.
Andrew Robbins
PS. A circle is a parametric plot of two sinusoidal functions. For concepts similar to a function, but impossible to describe with a function, see bipartite graph (and for self-maps, disjoint unions allow \( f : S \rightarrow S \)).
I think if we at least use the right terms, then we could all understand a little more. For example, different parts of the analytic continuation of a power series to its corresponding Riemann surface are not called "the logarithmic landscape" but could instead be called germs or sections.
There might even be nice formulas for analytic continuation, easily found if only we knew to search for "X theorem", since search terms can be a desicive factor in how successful a search is. I'm not sure if I can suggest anything in particular, but it certainly seems as if a little bit of rigor would do us some good.
Andrew Robbins
PS. A circle is a parametric plot of two sinusoidal functions. For concepts similar to a function, but impossible to describe with a function, see bipartite graph (and for self-maps, disjoint unions allow \( f : S \rightarrow S \)).
