# Are manifolds typically taught to undergraduates outside mathematics (and possibly theoretical physics) tracks? [closed]

I'm writing my dissertation on symplectic structure-preserving algorithms for Hamiltonian systems simulation, and I'm trying to figure out how much exposition is necessary for it to be readable by scientists, engineers and related professionals.

I'm actually in love with the chapter-opening sentence "Manifolds are possibly the most interesting and powerful mathematical structure to be bypassed in a typical undergraduate course in the sciences". But I'm not sure that is literally true.

• I would definitely not assume familiarity with manifolds if you want non-(math PhD) readers to understand it. – usul Jan 14 '17 at 1:23
• how much exposition is necessary for it to be readable by scientists, engineers and related professionals: Basically, all of it. But do you really want to write a textbook on manifolds into your dissertation? If it were me, I would probably just start with "Let $M$ be a manifold. (For an introduction to manifolds, see the textbooks [3], [7], [34].)" – Nate Eldredge Jan 14 '17 at 4:57

• @GerhardPaseman I can't say one way or the other for sure (hence the caveat at the end), but is that something undergraduates are really learning, and are they really learning about manifolds? Presumably they are mostly learning about submanifolds of $\mathbb{R}^n$, which isn't really the same. – Ben Webster Jan 14 '17 at 18:36