Undergraduate Programme and Module Handbook 2008-2009 (archived)

# Module MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II

## Department: Mathematical Sciences

### MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2008/09 and alternate years thereafter | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Core Mathematics A (MATH1012) and Core Mathematics B1 (MATH1051) [the latter may be a co-requisite].

#### Corequisites

- Core Mathematics B1 (MATH1051) unless taken before.

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Foundation Mathematics (MATH1641), Complex Analysis II (MATH2011), Contours and Symmetries II (MATH2111), Contours and Actuarial Mathematics II (MATH2171) and Contours and Probability II (MATH2**1).

#### Aims

- To study two seperate topics in mathematics at least one of which will introduce geometrical thinking.

#### Content

- Complex differentiation.
- Power Series.
- Contour Integrals.
- Calculus of residues.
- Mobius transformations.
- Models of hyperbolic space.
- Geodesics, length, arclength.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve unseen problems in basic complex analysis and geometry.
- Reproduce theoretical mathematics in the fields of basic complex analysis and geometry to a level appropriate to Level 2.
- Have a knowledge and understanding of this subject demonstrated through one or more of the following topic areas: Complex Differentiation; Power Series; Contours integrals and calculus of residues; Mobius transformations; Models of hyperbolic space; Geodesics, Length, arclength.

Subject-specific Skills:

- In addition students will have enhanced mathematical skills in the following area: Spatial awareness

Key Skills:

- Have highly specialised skills in the following area: Spatial awareness and Abstract reasoning.

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

- Teaching is by lectures and seminars through which the main body of knowledge is made available.
- Students do regular formative work solving problems to gain insight into the details of the relevant theories and procedures.
- End of year examinations assess the learning.

#### 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 | ■ |

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

Preparation and Reading | 142 | ||||

Total | 200 |

#### Summative Assessment

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

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

three-hour written examination | 3 hours | 100% |

#### Formative Assessment:

Weekly written assignments; no collection.

■ 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