The subject of Probability Theory came up for the first time in the beginning of the 17th century, when it was tried to analyse games of chance. In this connection, one usually used combinatorial methods (ratio of the numbers of "advantageous" to the numbers of all possible cases). In the 20th century, the Russian mathematician Kolmogorov finally thought up the axiomatic fundations of probability theory (based on measure theory) which are still used today.
Nowadays, the theory of stochastic processes (which is part of probability theory) is of immense importance. This theory is brought to bear for instance in the queuing theory (telephon systems, traffic, etc.) or in financial mathematics.
Mathematical Statistics deals with the problem of developing methods in order to analyse statistical data: Based on observations, on would like to draw conclusion concerning certain parameters of the underlying distribution. Quite often, one also would like to test some hypothesis based on these observations.
Nowadays, statistics is used in a lot of different branches in natural sciences, economics and social sciences.
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