What U.S. War (s) began in 1801

My son said he had never heard of them about 10 yrs or so ago

 

Very interesting and informative.
You might be interested in this:
Bombardment of Algiers (1816) - Wikipedia

I don't know if anyone in America reads the 'Captain Hornblower' books by C.S. Forester or has watched the Television series, but Capt. Hornblower's superior officer in the books is Admiral Pellew, and it was he who commanded the attack upon Algiers.

 

I thoroughly enjoyed the Hornblower TV series.

 

It was mentioned in little more than passing for me

think maybe 1.5 pages or so?

not much

 

Marines should know of this, should they not?

The action is memorialized in a line of the Marines' Hymn—"the shores of Tripoli". The capturing of the city gave American negotiators leverage in securing the return of hostages and the end of the war.​

 

What stands out most is this aspect (highlighting added):

In March 1786, Thomas Jefferson and John Adams went to London to negotiate with Tripoli's envoy, ambassador Sidi Haji Abdrahaman (or Sidi Haji Abdul Rahman Adja). When they enquired "concerning the ground of the pretensions to make war upon nations who had done them no injury", the ambassador replied:

It was written in their Koran, that all nations which had not acknowledged the Prophet were sinners, whom it was the right and duty of the faithful to plunder and enslave; and that every mussulman who was slain in this warfare was sure to go to paradise. He said, also, that the man who was the first to board a vessel had one slave over and above his share, and that when they sprang to the deck of an enemy's ship, every sailor held a dagger in each hand and a third in his mouth; which usually struck such terror into the foe that they cried out for quarter at once.​

 

I was going to guess the wars with the Barbary States.

My recollection from my history classes in college were that Jefferson was forced to sign a treaty with the Barbary States that stated the U.S was not a Christian nation. A bad move in my opinion, but the U.S did not have any force projection into Europe or North Africa at all in the early 1800s.