Welcome to Probability II (MATH2647) webpages. One of the main aims of this module is to extend your knowledge of the subject and, most importantly, to further develop your probabilistic intuition thus adding a new dimension to your problem solving skills.

The main topics that we will cover are:

Sequences of events and their limits;
Elements of convergence and integration;
Generating functions;
Discrete time Markov chains and their applications;
Random walks [if time permits].

There are plenty of books on the subject; you might find some of the following texts interesting and/or useful:

Elementary Probability by D.Stirzaker [2nd ed., CUP, Cambridge, 2003; ISBN: 0-521-53428-3] is a nice introductory text discussing, in particular, generating functions and basics of Markov chains;
Markov Chains by J.R.Norris [CUP, Cambridge, 1997; ISBN:0-521-48181-3] provides a more advanced treatment of discrete and continuous time Markov chains; it also contains various applications and will be useful if you decide to follow Stochastic Processes III/IV in the future;
Intermediate probability: a computational approach by M.S.Paolella [Wiley, 2007; ISBN: 978-0-470-02637-3] discusses various topics which are important for applications, including generating functions and convergence;
Probability and random processes by G.R.Grimmett and D.Stirzaker [3rd ed., OUP, New York, 2001; ISBN:0-19-857223-9] is a more advanced text covering many different topics of contemporary probability; it can be useful if you decide to take Probability III/IV and/or Stochastic Processes III/IV in the coming years;