Undergraduate Programme and Module Handbook 2023-2024 (archived)

# Module MATH4327: Topics in Probability IV

## Department: Mathematical Sciences

### MATH4327: Topics in Probability IV

Type | Open | Level | 4 | Credits | 10 | Availability | Available in 2023/24 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) Complex Analysis II (MATH2011) and either: [Probability II (MATH2647)] OR [Stochastic Processes III (MATH3251)] OR [Markov Chains II (MATH2707) AND Analysis III (MATH3011)].

#### Corequisites

- None

#### Excluded Combination of Modules

- None

#### Aims

- To introduce one or two contemporary topics in probability theory and to develop and apply them.

#### Content

- One or two of the following topics will run each year:
- Random graphs and probabilistic combinatorics
- Random walks in space
- Geometric probability
- Random matrix theory
- Probability and phase transition
- Conformally invariant probability
- Interacting particle systems

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve seen and unseen problems on the given topics.
- Have a knowledge and understanding of this subject demonstrated through an ability to analyse the behaviour of the probabilistic systems explored in the course.
- Reproduce theoretical mathematics concerning probabilistic systems at a level appropriate to Level 4, including key definitions and theorems.

Subject-specific Skills:

- In addition students will have enhanced mathematical skills in the following areas: probabilistic intuition.

Key Skills:

- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lecturing demonstrates the development of mathematical ideas into a coherent body of material, and how the theory is applied to practical examples.
- Four homework assignments provide formative assessment and feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 21 | 2 per week in Epiphany term; 1 in Easter term | 1 hour | 21 | |

Problem classes | 4 | Fortnightly in Epiphany term | 1 hour | 4 | |

Preparation and reading | 75 | ||||

Total | 100 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 2 hours | 100% |

#### Formative Assessment:

Four assignments

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University