Bill Hennessy wrote:

I have several books on math & astronomy like Jean Meeus books. But what
I'm really looking for is a algorithm for the upper and lower culminations
of Polaris. Any one out thir know it?

Since Polaris's right ascension is about 2h32m, it will cross the
meridian whenever your local sidereal time is 02:32. The lower
culmination will occur just under twelve hours before and after,
whenever the LST is 14:32.

I'm pretty sure that any book of the sort you mention will include a
method of calculating LST -- and conversely, for determining the
clock time corresponding to a given ST -- but if you need additional
help feel free to ask.

--
Odysseus