I have a month to month rental and my landlady gave me a handwritten 15 day notice to terminate the agreement. I have already paid her through the end of November. What should I do?

What did your initial lease say? Most cover going month to month. It should have something saying the term of the notice. Most are at least 30 days.
If she has accepted rent through the end of November - then I would say she can't have you leave until the first of December unless she wants to give you all of your rent back.

Hopefully you have kept documentation of all rent paid and kept a copy of the original lease.

And why are they ending the lease. Is there some violation of the rental that is the problem are do they just want you out for some other reason.

And is it really a month-to-month if you have paid through the end of November? The point of a month-to-month is that either you or the landlord can change your mind with a 30-day notice. That seems to be defeated if you have paid months in advance.

I hope she gave you a receipt for what you paid through November.

Your lease should have something referencing the termination policy. If it doesn't, then your state has laws regarding the amount of time she needs to give you prior to terminating your lease.

I could be wrong, but I don't believe advance payment allows you to stay on the property; she simply has to provide you the notice and return your money.