Chess Heroz (Android) As far as chess training applications go the Chess Heroz application is excellent.

My question though is can anyone explain the mathematics behind the ratings system?

I am new to chess ratings and believe that there are a number of systems used?
I am new to chess ratings and believe that there are a number of
  systems used?


Every chess federation (doesn't quite equal every country because some countries, like the UK, have several federations) has its own rating system. In addition FIDE, the international chess federation, has its rating system.


  Can anyone explain the mathematics behind the ratings system?


The basic mathematical principle behind rating systems is that every time you play a game, or group of games, against already graded opposition, your results and their respective ratings are used to adjust your rating or give you a rating for the first time.

Because players' ratings can change with different speed depending on their strength and age there is usually not a single constant factor which is used for all rating adjustments. Instead the factor will give bigger corrections / adjustments for young players, who are likely to be improving rapidly, and smaller corrections / adjustments for players who have been playing for a long time or who already have a high rating because these players are less likely to change in strength very much. Rather for these players the variability they show in playing strength likely just reflects the fact that they are human beings who have good days and bad days.

For details of how FIDE ratings are calculated you can read FIDE's Rating Regulations.

Section 8 - The working of the FIDE Rating System - gives the mathematical rules and tables used in calculating FIDE ratings.