Instructor: Nick Barton, Laszlo ErdÃ¶s

Teaching Assistant: Harald Ringbauer

The concept of probability is fundamental to many scientific disciplines; understanding probability is important for modelling and data analysis, as well as for its intrinsic mathematical interest. This course teaches the basic principles by using a variety of examples, from computer science through to biology:

I. Basic Probability: history, definitions, applications

II. Discrete and Continuous Probability: random variables, distributions, statistics.

III. Stochastic Processes: random walks, Brownian motion, diffusion.

IV. Threshold Phenomena: branching, random graphs.

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Date | Topic | |
---|---|---|

Nov 23 | History | NB |

Nov 25 | Counting | LE |

Nov 30 | Induction | LE |

Dec 2 | Counting & Probability | LE |

Dec 7 | Conditional probability | LE |

Dec 9 | Random Variables I | NB |

Dec 14 | Random Variables II | NB |

Dec 16 | ** Statistics Symposium | |

Jan 11 | Random walk | NB |

Jan 13 | Branching processes | NB |

Jan 18 | Diffusion | LE |

Jan 20 | Brownian motion | LE |

Jan 25 | Statistical physics | LE |

Jan 27 | Exam |

Problem Sheet 1 (due on December 14th)

Problem Sheet 2 (due on January 13th)

Problem Sheet 3 (due on January 25th)

The course roughly follows the schedule of last year. Accompanying material including expanded lecture notes can be found here. Most of the topics from this year are covered in these notes.

Course 1:

- Schar et al, 2004 (pdf)
- Stott et al, 2004 (pdf)
- Schar Jendritsky, 2004 (pdf)
- History of Probability (pdf)
- History of Probability (nb)

Branching Processes (13.1.; updated to 2014 version!)