missing space after LaTeX macro added
typos: double 'by by'
extra space before the ending full stop removed
typos: double 'a a'
typo: 'ia a' -> 'is a' (seems better than 'via a'?)
typos: double 'are are'
typos: double 'do do'
typos: double 'to to'
typos: double 'be be'