This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.

Postgraduate Handbook 2022-2023 (archived)

Module MATH41120: Algebraic Topology

Department: Mathematical Sciences

MATH41120: Algebraic Topology

Type	Level	Credits	Availability	Module Cap	Location
Tied	4	20	Available in 2022/2023	None.	Durham

Tied To

G1K509: Mathematical Sciences

Pre-requisites

Prior knowledge of Topology at undergraduate level.

Corequisites

None

Excluded Combinations

Topology

Aims

Provide a deeper knowledge in the field of topology.

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 toplogy demonstrated through the following topics:
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

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
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 complex and specialised problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total Hours
Lectures	42	2 per week for 20 weeks and 2 in term 3	1 Hour	42
Problems Classes	8	four in each of terms 1 and 2	1 Hour	8
Preparation and Reading				150
Total				200

Summative Assessment

Component	Component Weighting	Element	Length/Duration	Element Weighting	Resit Opportunity
Examination	100%	Written examination	3 hours	100%

Formative Assessment

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students..

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.