I recently purchased Project Standard 2003 and intend to use it on my MAC with and OS X operating system. Can I do that?

Microsoft Project does not natively work on Mac/OSX.

Here's one possible way to do it (requires you to purchase install and configure Windows on your Mac, and this example show how it can be integrated)

http://blogs.technet.com/b/projectsupport/archive/2013/05/21/project-online-how-do-i-use-my-apple-mac.aspx