Is there a simulation of arduino under Linux ?

Is there a simulation of arduino under Linux ?

Why ? (I mean why you need it for Linux ?) (Which is another way of asking why you prefer to simulate rather that real world ?)
I know your a Math professor and that was my worst subject so I should have some grudge against math teachers but after
30 yrs in electronics I’ve learned that math is my friend and always ready to help me do things. Are you just not a hands-on
person or do you need the simulation to integrate it into your lectures ?

Take a look at the simavr project. Maybe it will do what you want. https://github.com/buserror-uk/simavr https://gitorious.org/simavr

There are various simulations.

The point however, is that the Arduino is largely used with attached hardware, and apart from a LED or two, that hardware is not readily amenable to simulation.