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RE: The math behind cross-exchange arbitrage trading
I wrote my own software using existing API libraries. Only tested on a limited amount of exchanges and coin pairs, and could not find any profitability when fees are taken into account. Although arbitrage probably does exist, it not not a regular occurrence and in my limited experience not something that can be traded hundreds of times every day.
It can be profitable if you work with exchanges across continents. For example, I buy litecoin on coinexchange and sell it on altcointrader.co.za which is a South African crypto exchange. The margins are greater as you're selling in local currency which far weaker than the US dollar.