Best way to combine filtering and selecting items in a list

I'm building a web page to display a list of items. The list has three purposes:

  1. Display some very basic details about each item
  2. Provide a way of getting to more details, to view or edit them
  3. Provide a way of selecting multiple items to enable bulk operations

The list has several filters to limit the items displayed in the list. Multiple filters can be combined, and multiple values can be selected for each filter.

The list items can be selected, so that operations can be performed on multiple items. This works in a very similar way to gmail's functionality to select multiple emails to move or delete: there's a checkbox on each item, and another at the top to select/unselect all.

So far, the page looks like this:

Instructors List

In my head, there are two alternative ways the filtering/selecting could work:

  1. In the simpler version, if the user selects a few items, then changes the filters so that 2 of the selected items are no-longer visible, those 2 items are no-longer selected. Only items shown in the filtered list can be selected.

  2. The "power-user" version maintains the selection regardless of the filters, so the user can filter items, select a few, change the filters, and select more, building up the list of selected items, even if they're no-longer visible in the list.

Which of these would be a better design? Or is there another way? I suspect the simpler version is probably the behaviour users would expect, but is the power-user version a bad idea?