Undergraduate Programme and Module Handbook 2024-2025

Module MATH4161: ALGEBRAIC TOPOLOGY IV

Department: Mathematical Sciences

MATH4161: ALGEBRAIC TOPOLOGY IV

Type	Open	Level	4	Credits	20	Availability	Available in 2024/2025	Module Cap		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

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

Formative Assessment:

Eight assignments to be submitted.

■ 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