A mahout is an elephant-driver, from Hindi महावत mahāvat, from Sanskrit महामात्र mahāmātra "great in measure", applied to a high officer. Sanskrit mahā- "great" is from the Proto-Indo-European form *meǵ- "great".
A ptarmigan is a kind of grouse, and the word is from Scots Gaelic tàrmachan. The p was added apparently because it was thought the word was of Greek origin, like pterodactyl or ptarmica.
tàrmachan is possibly from tàrmaich "to gather, settle", from *tórmaich, a prefixed form of Old Irish mogaid "to increase", which is from PIE *meǵ-. The connection of "gather, settle" with the bird is "perhaps with reference to the birds settling to breed" (says the OED).