This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2006-2007 (archived)
Module MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II
Department: Mathematical Sciences
MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 2 | 20 | Available in 2006/2007 | None. | Durham |
Pre-requisites
- 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 Combinations
- 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).
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 Differenciation; 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 | Attendance Monitored |
|---|---|---|---|---|---|
| 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 | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | three-hour written examination | 3 hours | 100% |
Formative Assessment
Weekly written assignments; no collection.
Students who do not attend monitored activities shown under Teaching Methods
and Learning Hours, or who fail to complete the summative or formative
assessment(s) specified above, may be subject to the Academic Progress
procedures defined in the University's General Regulation V, and may be
required to leave the University.