Undergraduate Programme and Module Handbook 2013-2014 (archived)
Module MATH4171: RIEMANNIAN GEOMETRY IV
Department: Mathematical Sciences
MATH4171:
RIEMANNIAN GEOMETRY IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Available in 2013/14 |
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 Differential
Geometry III (MATH3021).
Corequisites
Excluded Combination of Modules
Aims
- Provide a knowledge of the intrinsic geometry of Riemannian
manifolds. This is a significant generalisation of the metric geometry
of surfaces in 3-space.
Content
- The metric geometry of Riemannian
manifolds.
- Geodesics.
- Various notions of curvature, and their effect on the
geometry of a Riemannian manifold.
- Second variation formula, global comparison theorems with
applications.
Learning Outcomes
- Have a knowledge and understanding of Riemannian geometry
demonstrated through the following topic areas:
- Riemannian manifolds;
- geodesics;
- Levi-Civita connection;
- curvature;
- global comparison results.
- Have developed advanced technical and scholastic skills in
the area of the geometry of surfaces in 3-space.
- Have developed an appreciation of high-level mathematical
reasoning.
- Have developed the ability to present well-reasoned arguments
and operate in complex and specialised contexts.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Teaching is by lectures 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 for 19 weeks and 2 in term 3. |
1 hour |
38 |
|
Other: Homework |
|
|
|
20 |
|
Preparation and Reading |
|
|
|
142 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
end of year written examination |
3 hours |
100% |
|
Four written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ 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