Undergraduate Programme and Module Handbook 2017-2018 (archived)
Module MATH3281: TOPOLOGY III
Department: Mathematical Sciences
MATH3281:
TOPOLOGY III
Type |
Open |
Level |
3 |
Credits |
20 |
Availability |
Available in 2017/18 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- Complex Analysis II (MATH2011) AND Analysis in Many
Variables II (MATH2031) AND Algebra II (MATH 2581).
Corequisites
Excluded Combination of Modules
Aims
- To provide a balanced introduction to Point Set, Geometric and
Algebraic Topology, with particular emphasis on surfaces and
knots.
Content
- Topological Spaces and Continuous Functions: Topology on a
set, open sets, closed sets, limit points and closure, examples of
topologies.
- Compactness and Connectedness.
- Topological groups and group actions.
- The Orthogonal groups. The Fundamental Group: calculation
for circle, homotopy type, homotopy equivalence.
- Generators and relations of groups, Tietze theorem, Van
Kampen's theorem.
- Compact surfaces, classical knots, basic knot
invariants.
Learning Outcomes
- By the end of the module students will: be able to solve
novel and/or complex problems in Topology.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Topology.
- have acquired a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
Topological spaces.
- Topological Groups and group actions.
- Fundamental group, homotopy type.
- Group presentations and Van Kampen's Theorem.
- Surfaces and Knots.
- In addition students will have specialised mathematical
skills in the following areas which can be used with minimal guidance:
Spatial awareness.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
understanding.
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for
the students and the lecturer on students' progress.
- 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 |
40 |
2 per week for 19 weeks and 2 in term 3 |
1 hour |
40 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
1 Hour |
8 |
|
Preparation and Reading |
|
|
|
152 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
three-hour end of year examination |
|
100% |
|
At least two written assignments in each of the
first two terms. No collections.
■ 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