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MATH41120: Algebraic Topology

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Type Tied
Level 4
Credits 20
Availability Available in 2024/2025
Module Cap None.
Location Durham
Department Mathematical Sciences

Prerequisites

  • Prior knowledge of Topology at undergraduate level.

Corequisites

  • None

Excluded Combinations of Modules

  • 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

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

More information

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