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MATH4161: Algebraic Topology IV

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Type Open
Level 4
Credits 20
Availability Available in 2025/2026
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Geometric Topology III (MATH3491).

Corequisites

  • None.

Excluded Combinations of Modules

  • None.

Aims

  • Provide a deeper knowledge in the field of topology (a balanced introduction having been provided in Geometric Topology III (MATH3491)).

Content

  • Homotopy theory of cell complexes.
  • Elements of homological algebra.
  • Homology theory of topological spaces.
  • Cohomology and manifolds.
  • Cup products and the cohomology ring.
  • Homotopy groups.

Learning Outcomes

Subject-specific Knowledge:

  • Have a knowledge and understanding of topology demonstrated through the following topic areas:
  • homological algebra;
  • cohomology ring;
  • the homology groups and their ranks;
  • homotopy theory.

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

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problem Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
On Campus Written Examination3 hours100

Formative Assessment

Eight assignments to be submitted.

More information

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