Removing memorized addresses from Apple Mail

To remove entries one at a time

First begin typing the address. Select the outdated @math.ukans.edu address.

Next, click on the blue oval around the address.  A menu will pop up.  You can then click "Remove from Previous Recipients List" and the address will be removed and not be used for autocompletion in the future.  You can then backspace over this address and begin addressing the message to the proper address.

To remove multiple entries at once

With Mail.app open, select Window->Previous Recipients.

This window will pop up, you will then be able to select the addresses and click "Remove From List".