Undergraduate Programme and Module Handbook 2006-2007 (archived)
Module MATH4161: ALGEBRAIC TOPOLOGY IV
Department: MATHEMATICAL SCIENCES
MATH4161: ALGEBRAIC TOPOLOGY IV
| Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2006/07 | Module Cap | None. | Location | Durham |
|---|
Prerequisites
- Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Topology III (MATH3281).
Corequisites
- None.
Excluded Combination of Modules
- None.
Aims
- Provide a deeper knowledge in the field of topology (a balanced introduction having been provided in Topology III (MATH3281)).
Content
- Homotopy theory of cell complexes.
- Fundamental group.
- Covering spaces.
- Elements of homological algebra.
- Homology theory of topological spaces.
- Homotopy groups.
Learning Outcomes
Subject-specific Knowledge:
- Have a knowledge and understanding of topology demonstrated through the following topic areas:
- the fundamental group;
- the homology groups and their ranks;
- homotopy theory;
- homological algebra.
Subject-specific Skills:
- Have developed advanced technical and scholastic skills in the areas of Topology and Algebra.
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 | |
| Seminars | 18 | Weekly | 1 hour | 18 | |
| Other: Homework | 4 | ||||
| Preparation and Reading | 140 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 100% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| end of year written examination | 3 hours | 100% | |
Formative Assessment:
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