How did the United States refashion its relationship to the outside world in the early nineteenth century?

During the early 19th century (I'm looking at the time up
to the 1820s here) the US acted to try to have more of a presence on the international
stage.  They did not really try to compete with the superpowers of the day for world
influence, but they did try to become much more important than they had been.  I will
look at three ways in which this happened:

1. The
   Louisiana Purchase made the US a large nation in terms of territory.  This was important
   because it asserted that the US was going to be dominant on the continent of North
   America.


2. The War of 1812 declared that the US would
   protect what it saw as its rights.  It would be willing to go to war even with a
   superpower in order to enforce its territorial integrity and its trade
   rights.


3. The Monroe Doctrine asserted a sphere of
   influence for the US in the Americas.  It declared that the US would not tolerate new
   incursions by European countries in an area that it saw as its own back
   yard.