I have a question about the 10th exercise in Bartok's Mikrokosmos book 1 ("With alternate hands"): In the key signature the A's are indicated to be played flat. The left hand starts with it's fifth finger on D, which brings the thumb in the tenth measure on the A flat. Are you supposed to play the black key with the thumb? This seems weird, especially in a book for early beginners.
Yes, you are. For complete beginners, it is way easier to use the thumb on a black key than to deal with the massive complication of a change of position, and at the slow tempo and extremely easy texture of the piece, there isn't much risk of damage through hours of practicing in an unergonomic position.