QUES: Their eardrums are often burst to prevent them from barking

correct the punctuation.

CORRECTED: Their eardrums are often burst to prevent them from barking.

QUES: Check qualified agencies and organisations for au pair placements see below

correct the punctuation.

CORRECTED: Check qualified agencies and organisations for au pair placements (see below).

QUES: His mathematical work was extremely broad and his 67 papers range across many topics such as linear algebra invariant theory integral calculus potential theory functional analysis and geometry

correct the punctuation.

CORRECTED:
His mathematical work was extremely broad and his 67 papers range across many topics such as linear algebra, invariant theory, integral calculus, potential theory, functional analysis, and geometry.