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MATH4161: ALGEBRAIC TOPOLOGY IV

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Type Open
Level 4
Credits 20
Availability Available in 2023/24
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

More information

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