Can the mats be connected in series rather than in parallel? 

No. Wiring the system in series would cause overheating and would lead to a system failure fairly quickly.

A parallel wiring system means that in the unlikely event of a fault, only the damaged/faulty mat will fail  – the rest of the mats will still operate perfectly.

A fault in a system wired in series means the whole system would fail leaving the property with no heating whatsoever.