Well, I have never really worked with assertions in my limited experience with Java and was wondering why I have read on a lot of sites and a lot of books that deal with assertions, the same warning that assert statements should not be used for argument checking in public methods?
I was wondering whether this had something to do with the order of execution of the assert statement relative to the other statements in Java.
The intent of assertions is to check your program logic -- an assertion failure is a "Stop everything -- there's a bug!" indication. In particular, an assertion failure indicates "there's a bug here", but "here" is somewhere internal to your code, and the cause of the failure can only really be determined by examining your code (which the user of your API cannot and should not be expected to do).
When you get bad data across an API, you want to indicate "Hey! You gave me bad data!" IllegalArgumentException and its kin are the way to indicate that.
(But note that there's nothing wrong with using assertion checks on parameters within your code -- where you're not supporting a truly "public" API that will be used by people outside your team.)
But this does bring up another point: To the extent reasonable/possible, you should "catch" internal exceptions of the IllegalArgumentException ilk that may occur due to your own bugs and convert them into FatalError exceptions or some such, so the user of your API isn't led to go looking for a bad parameter on his part when there's a bug in your code.
(Also note the distinction here between public -- the Java keyword -- and "public interface" -- meaning some interface that is made available as a "formal" API to be used by individuals outside your programming team. It's the latter case we're worried about here.)