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MATH4161: ALGEBRAIC TOPOLOGY IV

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 4
Credits 20
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Mathematics modules to the value of 100 credits in Years 2and 3, with at least 40 credits at Level 3 and including Topology III(MATH3281).

Corequisites

  • None.

Excluded Combinations of Modules

  • None.

Aims

  • Provide a deeper knowledge in the field of topology (a balancedintroduction 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 inthe areas of Topology and Algebra.

Key Skills:

  • Have highly specialised skills in the following area: Spatialawareness 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 theapplication of the theory to practical examples.
  • Subject material assigned for independent study develops theability to acquire knowledge and understanding without dependence onlectures.
  • Assignments for self-study develop problem-solving skills andenable students to test and develop their knowledge andunderstanding.
  • Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquiredand 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 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 hours100 

Formative Assessment

Eight assignments to be submitted.

More information

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