Undergraduate Programme and Module Handbook 2010-2011 (archived)

# Module MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II

## Department: Mathematical Sciences

### MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2010/11 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Core A Mathematics (MATH1012) and Core B1 (MATH1051)

#### Corequisites

- None

#### Excluded Combination of Modules

- Probability and Actuarial Mathematics II (MATH2161), Contours and Probability II (MATH2561), Codes and Probability II (MATH2571) and Codes and Geometric Topology II (MATH21411).

#### Aims

- To provide basic notions of two separate topics in mathematics with a view to study them in more depth in subsequent years.

#### Content

- Topic 1: Probability: Markov chains, random walks, real and complex generating functions, convergence in function space.
- Topic 2: Geometric topology: knots, surfaces, knot invariants.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in the given topics.
- Have an awareness of the abstract concepts of theoretical mathematics in the field of the given topics.
- Have a knowledge and understanding of the major theories of these subjects demonstrated through one or more of the following topic areas: Probability: Markov Chains, random walks, real and complex generating functions, convergence in function space; Geometric topology: knots, surfaces, knot invariants.

Subject-specific Skills:

- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling.

Key Skills:

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

- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- 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 | 38 | 2 per week | 1 Hour | 38 | |

Tutorials | 10 | Fortnightly for 20 weeks | 1 Hour | 10 | ■ |

Problems Classes | 10 | Fortnightly for 20 weeks | 1 Hour | 10 | |

Preparation and Reading | 142 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 50% | ||
---|---|---|---|

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

end of year written examination | 1 hour 45 minutes | 100% | yes |

Component: Examination | Component Weighting: 50% | ||

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

end of year written examination | 1 hour 45 minutes | 100% | yes |

#### Formative Assessment:

Weekly written 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