Alexander Bruce, Earl of Carrick

Alexander de Bruce, 1st and last Earl of Carrick  [of the 3rd? creation] was born illegitimately before 1317.2 He was the son of Edward  de Bruce, 1st Earl and last of Carrick and Isabella  of Strathbogie.1  He married Eleanor Douglas, daughter of Sir  Archibald Douglas and Beatrice  Lindsay. He died on 19 July 1333, killed in action, without male issue.

Alexander de Bruce, 1st and last Earl of Carrick was created 1st Earl of Carrick [Scotland] circa 1330. He fought in the Battle of Halidon Hill on 19 July 1333.
http://thepeerage.com/p10246.htm#i102460

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Numbering the Earls of Carrick is rather pointless, since by this time the title belonged to the Scottish royal family and was generally conferred within said family - usually, but not always, to the ruler's eldest son.

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http://en.wikipedia.org/wiki/Alexander_de_Brus,_Earl_of_Carrick

Alexander Bruce, Earl of Carrick (died 1333) was the Natural son of Edward Bruce and his mistress, Isabel, daughter of John de Strathbogie, 9th Earl of Atholl.

He played an ambivalent role during Edward Balliol's first invasion of Scotland. For a time he fell in with Balliol, but then he rejoined the Bruce loyalist side.

He was killed fighting on the Scottish side at the Battle of Halidon Hill. http://en.wikipedia.org/wiki/Battle_of_Halidon_Hill

Alexander was the first husband of Eleanor Douglas, daughter of Sir Archibald Douglas, Guardian of Scotland, they had issue:

Eleanor de Brus, who reputedly married Sir William de Cunynghame of Kilmaurs.